User talk:Jogaka

Maryam Alamer 14204223 Problem 1 Dynamic light scattering (DLS) or quasi-elastic light scattering" (QELS) or "photon correlation spectroscopy" (PCS) refers to observing scattered light so as to aid in determining defining properties of a particle dispersion or molecular solution like zeta potential, size of the particle, measuring the diffusion rate of the protein particles as well as particle’s molecular weight. This motion data is then processed to obtain size distribution of a given sample. The method of finding the size is given by obtaining "hydrodynamic radius" or "Stokes radius" of the particles. This radius depends on shape and mass. The basic principle behind the study is first by illuminating the sample by passing it in a polarizer using a laser beam. The scattered light is then passed in a second polarizer where it is picked up by the photomultiplier and the final image is casted on a screen creating a speckle pattern. The solution’s molecules are hit with the light and the majority of the particles diffract the light in all angles. This occurs when the particle’s diameter which is far much lesser than the wavelength of the illuminated light. Therefore, every molecule will diffract the incoming light in all courses, a phenomenon known as Rayleigh scattering. The diffracted light from the majority of the particles can either interfere productively (light sections) or destructively (dark sections). This procedure is repeated at brief time intervals and the subsequent speckle patterns are studied by an autocorrelation that compares light intensity at every spot after some time. Figure 2: Dynamic light scattering measures variation in scattered intensity with time at a fixed scattering angle (typically 90o) ,while static light scattering measures scattered intensity as a function of angle Small particles in solutions are subject to Brownian motion since most of the molecules are not constant but rather they are suspended in the solution. They move haphazardly because of the impact with solvent molecules, this kind of movement is called Brownian Motion. The rate of Brownian movement can be specifically measured from the scattered light pattern produced by the moving particles, a method known as photon correlation spectroscopy (PCS) or quasi-elastic light scattering (QELS) now usually referred to as DLS. The connection between the speed of Brownian movement of a molecule and that molecule's size is characterized by the Stokes-Einstein comparison: Where: D = speed of Diffusion of particles, k = Boltzmann’s constant, T = absolute temperature, η = viscosity, r = hydrodynamic radius. Small particles should diffuse faster than larger ones since (D) is inversely proportional to the radius of particles. This is the principle of the DLS analysis. In the sample, the separation between particles is continously changing because of a Doppler movement between the frequency of incoming and scattering light. This distance influences the phase overlap of diffracted light because the brightness of the spots on the intensity in speckle pattern will fluctuate with time. The rate of power fluctuating depends on how quick the particles are moving (quick for smaller particles, moderate for bigger particles). There are several steps undertaken to study the time scale of the fluctuations related to the particles motion that include: 1.        Measure fluctuations and change them into  an  Intensity Correlation Function. 2.        Describe the corresponding movement of the particles in relation to molecule size and Electric-Field Correlation Function. 3.        The Seigert Relationship has to be equated to the correlating functions. 4.        Analyze information utilizing cumulants or fitting schedules. To start with, the Intensity Correlation Function G2(Ԏ) is meant to describe the speed of scattering intensity. This is done by comparing the intensity at various tieme inervals, that is initial time t upto a certain final (t + Ԏ ) this providing a pqoductive quantitative measurement of the flickering light Mathematically,): The Electric Field Correlation Function, G1(Ԏ ) correlates the particles motion since it is difficult identify how every particles move.  The motion of the  particles relative to each other can be analyzed using this equation. E(t) and E(t+ Ԏ ) refers to the scattering electric fields at  the initial time t to a later time (t + Ԏ ). G1(t )  will decay exponentially with a decay constant ┌ for a monodisperse undergoing Brownian motion, The diffusivity in the Brownian Motion and the decay constant is related to each other by Where : ɵ= angle at which detector is located Q= magnitude of the scattering wave vector n = refraction index of solution, q2= the distance the particles travels . The speed of the particles can be determined by measuring how long it takes the function to go to zero. The Seigert Relationship can be used to equate the two functions Where B= baseline Ɓ= instrumental response, the both are constant In a conductor, the conduction band which is the highest occupied band is not completely full. Hence, electrons can move to and from the neighboring atoms freely in the process conducting electricity. •     EF lies inside an allowed band (1 electron/unit cell). In an insulator, the highest occupied band known as the valence band is usually full. The conduction band is the first unfilled band found above the valence band. The valence band and the conduction are separated by a wide gap which at room temperature, no energy is enough to move the elctrons from the valence band to the conduction band where they would be able to contribute to conduction, hence no electrical conduction in insultors. •         The Fermi level lies at the top of a band (full band). Large gap between bands In a semiconductor, the gap between the valence band and the conduction band is littler, and at room temperature there is adequate energy to move a few electrons from the valence band into the conduction band, permitting some conduction. An increase in temperature builds the conductivity of a semiconductor as more electrons have enough energy to make the bounce to the conduction band. There are two different types of semiconductors: Intrinsic semiconductors: it is semiconductors in pure state. For each electron that hops into the conduction band, the missing electron creates a gap that can move openly in the valence band. The number of gaps will equal to the quantity of electrons that have jumped. Extrinsic semiconductors: The gap in the band is controlled by doping which involves adding little impurities to the material so as to change the electrical conductivity of the lattice structure. For extrinsic semiconductors, the quantity of the holes does not match with the quantity of the electrons jumped. Extrinsic conductors are of two P type (positive charge doped) and n type (negative charge doped) Explain how the wave function of an electron placed in a one-dimensional periodic potential can be solved using the Bloch wave approach? A Bloch wave is a kind of wave function for a molecule in an intermittently repeating environment, most usually an electron in a crystal. Bloch waves are vital due to the Bloch's theory, which expresses that the energy eigenstates for an electron in a crystal can be expressed as Bloch waves. A wave function ψ is a Bloch wave in the event that it has the structure: Where: r i=position, ψ= Bloch wave, u= a periodic function with the same periodicity as the crystal, k= a vector of real numbers called the crystal wave vector, e= Euler's number, i= the imaginary unit. In other words, thus, after multiplying a plane wave by a periodic function, you get a Bloch wave. ·                     Describes lattice periodic parts, (depending on the value of the wave-vector k) ·                      describes wave function of a free particle. This factor retains the same form as for free particles. These Bloch wave energy eigenstates are written with subscripts as ψn k, where: n= discrete index, called the band index, that is usually present since there are many Bloch waves containing similar k (each with a different periodic component u). in a given band (i.e., for constant n), ψn k changes continuously with k, hence its energy too. For any reciprocal lattice vector K, ψn k = ψn (k+K). Hence, clear and distinct Bloch waves occur for k-values within the first Brillouin zone of the reciprocal lattice. in solid substances, the discussion revolves around crystals - periodic lattices. In this discussion, a 1D lattice of positive ions will be discussed. If the spacing between ions is a, then the potential lattice will supposedly look like illustrated: According to Bloch's theorem, the solution of the wave function using the Schrödinger equation when the potential is periodic, can be written as: Here, u(x) is a periodic function which satisfies u(x + a) = u(x) There are problems with the boundary condition encountered when approaching the edges of the lattice. Following the Born-von Karman boundary conditions, the ion lattice can be represented as a ring. Assuming L is the lattice length and  that L ≫ a, the amount of ions in the lattice will be so big, that if one is comparing one ion, the surrounding of the environment is almost linear, and the electron wave function will remain constant. So now, instead of two boundary conditions we get one circular boundary condition (b) Describe how the Bloch wave approach uses symmetry aspects of the periodic potential in order to simplify the solution.? The issue of electrons in the solids is a numerous electron issue. The full Hamiltonian of the solid contains not just the one-electron potential depicting the interactions of the electrons with atomic nuclei, however pairing potential additionally portrays the electron-electron interactions. The simplest methodology for use is a free electron model. The next step in building the complexiy is independent electron approximation assuming that each of the interactions are portrayed by a successful potential. A standout amongst the most imperative properites of this potential is it is periodic on a cross section. U(r)= U(r+T) where the T is the lattice vector. Explain the nature of Excitons in semiconductor? a.)Excitation is a bound condition of an electron and holes, the both are pulled towards each other by electrostatic Coulomb force. The separation between the electron and the hole is called Bohr radices of excitation as it is a couple of nanometers. Because of Coulomb interaction, the electrons and holes existing in a material are known structure excitons. In this manner, the optical nature of semiconductors can be comprehended by researching the properties of the excitons. An exciton is made out of an electron and a hole. In bulk semiconductors, the exciton can move anyhowly in all ways. At the point when the length of a semiconductor is shortened to the same as the exciton radius, i.e., to a couple of nanometers, quantum confinement impact happens and the exciton properties are adjusted. Depending with the measurement of the confinement, three sorts of confined structures are discussed: 1.                 In a QW, exciton can move freely in other two directions when the material size is reduced only in one direction. 2.        In a QWR, the material size is lessened in two direction and the exciton can move unreservedly in one way as only. 3.        In a QD, the material size is lessened in all directions and the exciton cannot move freely in any direction in these restricted structures. Accordingly, these structures are a great possibility for creating  optoelectronic gadgets, for example, semiconductor light-discharging diodes and laser diodes. Semiconductor materials have their electronic structures sorted out in groups: a valence band created by the overlap of the occupied energetic levels of the individual structural units and a conduction band produced by the overlapp of the vacant levels. Generally, the conduction and the valence band in many semiconductors are consistent if intraband energetic spacing littler than kBT (T is the temperature). Once the electron is advanced into the conduction band a hole is left in the valence band; the semiconductor gets to be conductive and the electron and gap move uninhibitedly using their kinetic energy. The move starting from the earliest stage to the energized state happens as an after effect of some external disturbance, e.g. a photon. The electron in the conduction band and the hole in the valence band can be held together by the electrostatic attraction, to shape exciton. The intercation in the middle of electron and opening can be portrayed by a hydrogen like Hamiltonian where the M is the total mass M= me*+mh* and μ is the reduced mass μ= me*mh*/ (me*+mh*); me* and mh* are the effective masses of the electron and hole, respectively Explain the concept of the effective Bohr radius in semiconductors? a)                 The Bohr radius (a0 or r Bohr) is a physical constant, almost equal to the distance between the proton and electron in a hydrogen atom in its groundstate. value is 5.2917721067(12)×10−11 m. Bohr exciton radius is defined as At the point when quantum dot size is lesser than the exciton Bohr radius, the electron hole pair energy levels in quantum dots can't be dealt with further based on the hydrogen model. The most reduced energy level of the exciton is presently delocalized over the whole quantum dot. The exciton levels are given by taking care of the traditional quantum mechanical issue of a particle in a box. For the situation where the electron and gap are kept in a little space, the coulomb fascination is irrelevantly little contrasted with a potential U(r) that depicts a spherically symmetric potential well of length r. the relating Hamiltonian is Boher diameter determines the type of confinement for example; ·                    3-10 times Bohr diameter is weak confinement ∆E≈ 1/M* (M* is effective mass of excitation) ·                    Lesser than 3 Bohr diameter is a strong confinement ∆E≈ 1/µ* (µ* is effective mass of holes and electron). What are QDS? Why is their optical response is tunable? b)                 b)         Quantum dots (QD) are nanoscale semiconductor gadgets that the material size is decreased in all directions and the exciton can't move in any directions in any course, that implies the electrons and gaps are bound in every one of the three spatial. The electronic properties of the quantum dots fall between those of mass semiconductors and those of discrete particles of practically identical size. Band gap can be tuned as an element of molecule size and shape for a given composition. For instance the photoluminescence of a QD can be controlled to particular wavelengths by controlling molecule width: •          larger QDs (range of 5-6 nm)emit longer wavelengths bringing about discharge colors, for example, orange or red. •          Smaller QDs (range of 2-3 nm) emit shorter wavelengths bringing about colors like blue and green. c)                 The capacity to control the emission from Q dots by chancing it is size is known as the size quantization impact. Their optical reaction is tunable on the grounds that evolving size, shape, and structure, quantum dots can change their absorptive and emissive properties significantly d)                 Explain how the bandgap is changing with their physical size and explain why smaller Quantum Dots are blue-shifted in their optical response? The band hole can get to be stronger in the solid confinement where the extent of the quantum dot is lesser than the Exciton Bohr range ab* as the energy levels split up. where ab is the Bohr radius=0.053 nm, m is the mass, μ is the decreased mass, and εr is the size-dependent dielectric constant value. Thus, increment in the aggregate emision energy which is the sum of the energy levels in the smaller band gaps in the solid confinement which is bigger than the energy levels in the band holes of the first levels in the weak confinement and the emissions at different wavelengths. For the most part, the littler the extent of the crystal → the bigger the band gap→ the more noteworthy the distinction in energy between the most astounding valence band and the least conduction band gets to be. The bigger size of the crystal→ the littler the band gab→ the littlest the distinction in energy between the most elevated valence band and the least conduction band. In this manner quantum specks with various sizes can radiate light of various colors, the reason is the quantum control impact. So 1-The bigger the spot, the redder (lower energy) its fluorescence range. 2-littler specks radiate bluer (higher energy) light. Figure: 1 splitting of energy levels in quantum dots due to the quantum confinement effect, semiconductor band gap increases with decrease in size of the nanocrystal. For (blue-shifted): When the quantum dots are lit up by UV light, a percentage of the electrons get enough energy to break free from the molecules. This capacity permits them to move around the nanoparticle, and make a conduction band in which electrons are allowed to travel through a material and become a conductor. At the point when these electrons drop once more into the external circle around the particle (the valence band), they radiate light. The shade of that light relies on upon the vitality contrast between the conduction band and the valence band. Figure 2:      Electrons in a quantum dot generating light.

Maryam Alamer 14204223

Problem 1 Dynamic light scattering (DLS) or quasi-elastic light scattering" (QELS) or "photon correlation spectroscopy" (PCS) refers to observing scattered light so as to aid in determining defining properties of a particle dispersion or molecular solution like zeta potential, size of the particle, measuring the diffusion rate of the protein particles as well as particle’s molecular weight. This motion data is then processed to obtain size distribution of a given sample. The method of finding the size is given by obtaining "hydrodynamic radius" or "Stokes radius" of the particles. This radius depends on shape and mass. The basic principle behind the study is first by illuminating the sample by passing it in a polarizer using a laser beam. The scattered light is then passed in a second polarizer where it is picked up by the photomultiplier and the final image is casted on a screen creating a speckle pattern. The solution’s molecules are hit with the light and the majority of the particles diffract the light in all angles. This occurs when the particle’s diameter which is far much lesser than the wavelength of the illuminated light. Therefore, every molecule will diffract the incoming light in all courses, a phenomenon known as Rayleigh scattering. The diffracted light from the majority of the particles can either interfere productively (light sections) or destructively (dark sections). This procedure is repeated at brief time intervals and the subsequent speckle patterns are studied by an autocorrelation that compares light intensity at every spot after some time. Figure 2: Dynamic light scattering measures variation in scattered intensity with time at a fixed scattering angle (typically 90o) ,while static light scattering measures scattered intensity as a function of angle

Small particles in solutions are subject to Brownian motion since most of the molecules are not constant but rather they are suspended in the solution. They move haphazardly because of the impact with solvent molecules, this kind of movement is called Brownian Motion. The rate of Brownian movement can be specifically measured from the scattered light pattern produced by the moving particles, a method known as photon correlation spectroscopy (PCS) or quasi-elastic light scattering (QELS) now usually referred to as DLS. The connection between the speed of Brownian movement of a molecule and that molecule's size is characterized by the Stokes-Einstein comparison: Where: D = speed of Diffusion of particles, k = Boltzmann’s constant, T = absolute temperature, η = viscosity, r = hydrodynamic radius. Small particles should diffuse faster than larger ones since (D) is inversely proportional to the radius of particles. This is the principle of the DLS analysis.

In the sample, the separation between particles is continously changing because of a Doppler movement between the frequency of incoming and scattering light. This distance influences the phase overlap of diffracted light because the brightness of the spots on the intensity in speckle pattern will fluctuate with time. The rate of power fluctuating depends on how quick the particles are moving (quick for smaller particles, moderate for bigger particles).

There are several steps undertaken to study the time scale of the fluctuations related to the particles motion that include:

1.	Measure fluctuations and change them into an  Intensity Correlation Function.

2.	Describe the corresponding movement of the particles in relation to molecule size and Electric-Field Correlation Function.

3.	The Seigert Relationship has to be equated to the correlating functions.

4.	Analyze information utilizing cumulants or fitting schedules.

To start with, the Intensity Correlation Function G2(Ԏ) is meant to describe the speed of scattering intensity. This is done by comparing the intensity at various tieme inervals, that is initial time t upto a certain final (t + Ԏ ) this providing a pqoductive quantitative measurement of the flickering light Mathematically,):

The Electric Field Correlation Function, G1(Ԏ ) correlates the particles motion since it is difficult identify how every particles move. The motion of the particles relative to each other can be analyzed using this equation.

E(t) and E(t+ Ԏ ) refers to the scattering electric fields at the initial time t to a later time (t + Ԏ ). G1(t ) will decay exponentially with a decay constant ┌ for a monodisperse undergoing Brownian motion, The diffusivity in the Brownian Motion and the decay constant is related to each other by Where : ɵ= angle at which detector is located Q= magnitude of the scattering wave vector n = refraction index of solution, q2= the distance the particles travels

. The speed of the particles can be determined by measuring how long it takes the function to go to zero.

The Seigert Relationship can be used to equate the two functions  Where B= baseline Ɓ= instrumental response, the both are constant

In a conductor, the conduction band which is the highest occupied band is not completely full. Hence, electrons can move to and from the neighboring atoms freely in the process conducting electricity. •	EF lies inside an allowed band (1 electron/unit cell). In an insulator, the highest occupied band known as the valence band is usually full. The conduction band is the first unfilled band found above the valence band. The valence band and the conduction are separated by a wide gap which at room temperature, no energy is enough to move the elctrons from the valence band to the conduction band where they would be able to contribute to conduction, hence no electrical conduction in insultors. •	The Fermi level lies at the top of a band (full band). Large gap between bands In a semiconductor, the gap between the valence band and the conduction band is littler, and at room temperature there is adequate energy to move a few electrons from the valence band into the conduction band, permitting some conduction. An increase in temperature builds the conductivity of a semiconductor as more electrons have enough energy to make the bounce to the conduction band. There are two different types of semiconductors: Intrinsic semiconductors: it is semiconductors in pure state. For each electron that hops into the conduction band, the missing electron creates a gap that can move openly in the valence band. The number of gaps will equal to the quantity of electrons that have jumped. Extrinsic semiconductors: The gap in the band is controlled by doping which involves adding little impurities to the material so as to change the electrical conductivity of the lattice structure. For extrinsic semiconductors, the quantity of the holes does not match with the quantity of the electrons jumped. Extrinsic conductors are of two P type (positive charge doped) and n type (negative charge doped)

Explain how the wave function of an electron placed in a one-dimensional periodic potential can be solved using the Bloch wave approach? A Bloch wave is a kind of wave function for a molecule in an intermittently repeating environment, most usually an electron in a crystal. Bloch waves are vital due to the Bloch's theory, which expresses that the energy eigenstates for an electron in a crystal can be expressed as Bloch waves. A wave function ψ is a Bloch wave in the event that it has the structure: Where: r i=position, ψ= Bloch wave, u= a periodic function with the same periodicity as the crystal, k= a vector of real numbers called the crystal wave vector, e= Euler's number, i= the imaginary unit. In other words, thus, after multiplying a plane wave by a periodic function, you get a Bloch wave. •	 Describes lattice periodic parts, (depending on the value of the wave-vector k) •	  describes wave function of a free particle. This factor retains the same form as for free particles.

These Bloch wave energy eigenstates are written with subscripts as ψn k, where: n= discrete index, called the band index, that is usually present since there are many Bloch waves containing similar k (each with a different periodic component u). in a given band (i.e., for constant n), ψn k changes continuously with k, hence its energy too. For any reciprocal lattice vector K, ψn k = ψn (k+K). Hence, clear and distinct Bloch waves occur for k-values within the first Brillouin zone of the reciprocal lattice. in solid substances, the discussion revolves around crystals - periodic lattices. In this discussion, a 1D lattice of positive ions will be discussed. If the spacing between ions is a, then the potential lattice will supposedly look like illustrated: According to Bloch's theorem, the solution of the wave function using the Schrödinger equation when the potential is periodic, can be written as: Here, u(x) is a periodic function which satisfies u(x + a) = u(x) There are problems with the boundary condition encountered when approaching the edges of the lattice. Following the Born-von Karman boundary conditions, the ion lattice can be represented as a ring. Assuming L is the lattice length and  that L ≫ a, the amount of ions in the lattice will be so big, that if one is comparing one ion, the surrounding of the environment is almost linear, and the electron wave function will remain constant. So now, instead of two boundary conditions we get one circular boundary condition

(b) Describe how the Bloch wave approach uses symmetry aspects of the periodic potential in order to simplify the solution.? The issue of electrons in the solids is a numerous electron issue. The full Hamiltonian of the solid contains not just the one-electron potential depicting the interactions of the electrons with atomic nuclei, however pairing potential additionally portrays the electron-electron interactions. The simplest methodology for use is a free electron model. The next step in building the complexiy is independent electron approximation assuming that each of the interactions are portrayed by a successful potential. A standout amongst the most imperative properites of this potential is it is periodic on a cross section. U(r)= U(r+T) where the T is the lattice vector.

Explain the nature of Excitons in semiconductor? a.)Excitation is a bound condition of an electron and holes, the both are pulled towards each other by electrostatic Coulomb force. The separation between the electron and the hole is called Bohr radices of excitation as it is a couple of nanometers. Because of Coulomb interaction, the electrons and holes existing in a material are known structure excitons. In this manner, the optical nature of semiconductors can be comprehended by researching the properties of the excitons. An exciton is made out of an electron and a hole. In bulk semiconductors, the exciton can move anyhowly in all ways.

At the point when the length of a semiconductor is shortened to the same as the exciton radius, i.e., to a couple of nanometers, quantum confinement impact happens and the exciton properties are adjusted. Depending with the measurement of the confinement, three sorts of confined structures are discussed: 1.	In a QW, exciton can move freely in other two directions when the material size is reduced only in one direction. 2.	In a QWR, the material size is lessened in two direction and the exciton can move unreservedly in one way as only.

3.	In a QD, the material size is lessened in all directions and the exciton cannot move freely in any direction in these restricted structures.

Accordingly, these structures are a great possibility for creating  optoelectronic gadgets, for example, semiconductor light-discharging diodes and laser diodes. Semiconductor materials have their electronic structures sorted out in groups: a valence band created by the overlap of the occupied energetic levels of the individual structural units and a conduction band produced by the overlapp of the vacant levels. Generally, the conduction and the valence band in many semiconductors are consistent if intraband energetic spacing littler than kBT (T is the temperature).

Once the electron is advanced into the conduction band a hole is left in the valence band; the semiconductor gets to be conductive and the electron and gap move uninhibitedly using their kinetic energy. The move starting from the earliest stage to the energized state happens as an after effect of some external disturbance, e.g. a photon. The electron in the conduction band and the hole in the valence band can be held together by the electrostatic attraction, to shape exciton. The intercation in the middle of electron and opening can be portrayed by a hydrogen like Hamiltonian where the M is the total mass M= me*+mh* and μ is the reduced mass μ= me*mh*/ (me*+mh*); me* and mh* are the effective masses of the electron and hole, respectively

Explain the concept of the effective Bohr radius in semiconductors? a)	The Bohr radius (a0 or r Bohr) is a physical constant, almost equal to the distance between the proton and electron in a hydrogen atom in its groundstate.

value is 5.2917721067(12)×10−11 m. Bohr exciton radius is defined as At the point when quantum dot size is lesser than the exciton Bohr radius, the electron hole pair energy levels in quantum dots can't be dealt with further based on the hydrogen model. The most reduced energy level of the exciton is presently delocalized over the whole quantum dot. The exciton levels are given by taking care of the traditional quantum mechanical issue of a particle in a box. For the situation where the electron and gap are kept in a little space, the coulomb fascination is irrelevantly little contrasted with a potential U(r) that depicts a spherically symmetric potential well of length r. the relating Hamiltonian is

Boher diameter determines the type of confinement for example; •	3-10 times Bohr diameter is weak confinement ∆E≈ 1/M* (M* is effective mass of excitation) •	Lesser than 3 Bohr diameter is a strong confinement ∆E≈ 1/µ* (µ* is effective mass of holes and electron).

What are QDS? Why is their optical response is tunable? b)	b)	Quantum dots (QD) are nanoscale semiconductor gadgets that the material size is decreased in all directions and the exciton can't move in any directions in any course, that implies the electrons and gaps are bound in every one of the three spatial. The electronic properties of the quantum dots fall between those of mass semiconductors and those of discrete particles of practically identical size. Band gap can be tuned as an element of molecule size and shape for a given composition. For instance the photoluminescence of a QD can be controlled to particular wavelengths by controlling molecule width: •	larger QDs (range of 5-6 nm)emit longer wavelengths bringing about discharge colors, for example, orange or red. •	Smaller QDs (range of 2-3 nm) emit shorter wavelengths bringing about colors like blue and green. c)	The capacity to control the emission from Q dots by chancing it is size is known as the size quantization impact. Their optical reaction is tunable on the grounds that evolving size, shape, and structure, quantum dots can change their absorptive and emissive properties significantly d)	Explain how the bandgap is changing with their physical size and explain why smaller Quantum Dots are blue-shifted in their optical response? The band hole can get to be stronger in the solid confinement where the extent of the quantum dot is lesser than the Exciton Bohr range ab* as the energy levels split up. where ab is the Bohr radius=0.053 nm, m is the mass, μ is the decreased mass, and εr is the size-dependent dielectric constant value. Thus, increment in the aggregate emision energy which is the sum of the energy levels in the smaller band gaps in the solid confinement which is bigger than the energy levels in the band holes of the first levels in the weak confinement and the emissions at different wavelengths. For the most part, the littler the extent of the crystal → the bigger the band gap→ the more noteworthy the distinction in energy between the most astounding valence band and the least conduction band gets to be. The bigger size of the crystal→ the littler the band gab→ the littlest the distinction in energy between the most elevated valence band and the least conduction band. In this manner quantum specks with various sizes can radiate light of various colors, the reason is the quantum control impact. So 1-The bigger the spot, the redder (lower energy) its fluorescence range. 2-littler specks radiate bluer (higher energy) light.

Figure: 1 splitting of energy levels in quantum dots due to the quantum confinement effect, semiconductor band gap increases with decrease in size of the nanocrystal.

For (blue-shifted): When the quantum dots are lit up by UV light, a percentage of the electrons get enough energy to break free from the molecules. This capacity permits them to move around the nanoparticle, and make a conduction band in which electrons are allowed to travel through a material and become a conductor.

At the point when these electrons drop once more into the external circle around the particle (the valence band), they radiate light. The shade of that light relies on upon the vitality contrast between the conduction band and the valence band. Figure 2:      Electrons in a quantum dot generating light.

Maryam Alamer 14204223

Problem 1 Dynamic light scattering (DLS) which is also known as "photon correlation spectroscopy" (PCS) or quasi-elastic light scattering" (QELS). The observation of scattered light assists to determine defining characteristics of a particle dispersion or molecular solution such as particle size, molecular weight, zeta potential and measure the rate of diffusion of the protein particles. This motion data is conventionally processed to derive a size distribution for the sample, where the size is given by the "Stokes radius" or "hydrodynamic radius" of the protein particle. This hydrodynamic size depends on both mass and shape (conformation). The basic principle is the sample is illuminated through a polarizer by a laser beam. The scattered light then goes through a second polarizer where it is collected by a photomultiplier and the resulting image is projected onto a screen this is known as a speckle pattern( the speckle pattern moves as the particle move and creates flickering. The molecules in the solution are hit with the light and all of the molecules diffract the light in all directions that happens when the sample of particles with diameter much smaller than the wavelength of light is irradiated, the each particle will diffract the incident light in all direction, this called Rayleigh scattering. The diffracted light from all of the molecules can either interfere constructively (light regions) or destructively (dark regions). This process is repeated at short time intervals and the resulting set of speckle patterns are analyzed by an autocorrelation that compares the intensity of light at each spot over time. Figure 2: Dynamic light scattering measures variation in scattered intensity with time at a fixed scattering angle (typically 90o) ,while static light scattering measures scattered intensity as a function of angle Small particles in solution are subject to Brownian motion as a result of the particle samples are not constant but they are suspended in the solution. They move randomly due to collision with solvent molecules, this type of motion is called Brownian Motion. The speed of Brownian motion can be directly measured from the scattered light pattern produced by the moving particles, a technique known as photon correlation spectroscopy (PCS) or quasi-elastic light scattering (QELS) but presently referred to as DLS.The relation between the speed of Brownian motion of a particle and that particle’s size is defined by the Stokes-Einstein equation:

Where D = Diffusion speed of particles, k = Boltzmann’s constant, T = absolute temperature, η = viscosity, and r = hydrodynamic radius. (D) is inversely proportional to the radius of particles thus small particles should diffuse faster than larger ones, this is a key concept in DLS analysis. In the sample, the distance between particles is constantly changing due to a Doppler shift between the frequency of incoming light and frequency of the scattering light. This distance affects the phase overlap of diffracted light since the brightness of the spots on the speckle pattern will fluctuate in intensity. The rate of intensity fluctuating relies on how fast the particles are moving (fast for small particles, slow for large particles). In order to study the time scale of the fluctuations related to the particle movement, there are several steps: 1.	Measure fluctuations an convert into an Intensity Correlation Function. 2.	Describe the correlated movement of the particles, as related to particle size into an Electric-Field Correlation Function. 3.	 Equate the correlation functions, with the Seigert Relationship. 4.	Analyze data using cumulants or fitting routines.

Fristly, the Intensity Correlation Function G2(Ԏ) is used to describe the rate of change in scattering intensity by comparing the intensity at time t to the intensity at a later time (t + Ԏ ) providing a quantitative measurement of the flickering of the light. Mathematically,):

Secondly, Electric Field Correlation Function, G1(Ԏ ) is used to correlate the motion of the particles since it is not possible to know how each particles moves from fluctuation. This

equation defines the motion of the particles relative to each other

Where E(t) and E(t+ Ԏ ) are the scartting electric fields at time t and (t + Ԏ ). For a monodisperse undergoing Brownian motion, G1(t )  will decay exponential with a decay constant ┌ The decay constant is related by Brownian Motion to the diffusivity by The q is the magnitude of the scattering wave vector and q2 reflects the distance the particles travel, n is the refraction index of solution, ɵ is angle at which detector is located. By measuring how long it takes the function to go to zero, we can tell how fast the particles are moving

Thirdly, the two correlation function can be equated using the Seigert Relationship Where B is the baseline and Ɓ is instrumental response, the both are constant

In a conductor, the highest occupied band, known as the conduction band, is not completely full. This allows the electrons to move in and out from neighboring atoms and therefore conduct easily. •	EF lies inside an allowed band (1 electron/unit cell). In an insulator, the highest occupied band is full, is called the valence band. The first unfilled band above the valence band is the conduction band. The gap between the valence band and the conduction band is large and at room temperature there is not enough energy available to move electrons from the valence band into the conduction band, where they would be able to contribute to conduction, and there is no electrical conduction in an insulator. •	The Fermi level lies at the top of a band (full band). Large gap between bands In a semiconductor, the gap between the valence band and the conduction band is smaller, and at room temperature there is sufficient energy available to move some electrons from the valence band into the conduction band, allowing some conduction. An increase in temperature increases the conductivity of a semiconductor as more electrons have enough energy to make the jump to the conduction band. There are two different types of semiconductors: Intrinsic semiconductors: it is semiconductors in pure state. For every electron that jumps into the conduction band, the missing electron generates a hole that can move freely in the valence band. The number of the holes will equal the number of electrons that have jumped. Extrinsic semiconductors: The band gap is controlled by adding small impurities to the materials. This process is called doping or adding impurities to the lattice that can change the electrical conductivity of the lattice. In the extrinsic semiconductors, the number of the holes does not equals the number of the electrons jumped. There are two different kinds of extrinsic semiconductors P type (positive charge doped) n type (negative charge doped)

Explain how the wave function of an electron placed in a one-dimensional periodic potential can be solved using the Bloch wave approach? A Bloch wave is a type of wave function for a particle in a periodically-repeating environment, most commonly an electron in a crystal. Bloch waves are important because of Bloch's theorem, which states that the energy eigenstates for an electron in a crystal can be written as Bloch waves.A wave function ψ is a Bloch wave if it has the form : where r is position, ψ is the Bloch wave, u is a periodic function with the same periodicity as the crystal, k is a vector of real numbers called the crystal wave vector, e is Euler's number, and i is the imaginary unit. In other words, if you multiply a plane wave by a periodic function, you get a Bloch wave. •	 Describes lattice periodic parts, (depending on the value of the wave-vector k) •	  describes wave function of a free particle. This factor retains the same form as for free particles.

These Bloch wave energy eigenstates are written with subscripts as ψn k, where n is a discrete index, called the band index, which is present because there are many different Bloch waves with the same k (each has a different periodic component u). Within a band (i.e., for fixed n), ψn k varies continuously with k, as does its energy. Also, for any reciprocal lattice vector K, ψn k = ψn (k+K). Therefore, all distinct Bloch waves occur for k-values within the first Brillouin zone of the reciprocal lattice. When talking about solid materials, the discussion is mainly around crystals - periodic lattices. Here we will discuss a 1D lattice of positive ions. Assuming the spacing between two ions is a, the potential in the lattice will look something like this: According to Bloch's theorem, the wave function solution of the Schrödinger equation when the potential is periodic, can be written as: Where u(x) is a periodic function which satisfies u(x + a) = u(x) When nearing the edges of the lattice, there are problems with the boundary condition. Therefore, we can represent the ion lattice as a ring following the Born-von Karman boundary conditions. If L is the length of the lattice so that L ≫ a, then the number of ions in the lattice is so big, that when considering one ion, its surrounding is almost linear, and the wave function of the electron is unchanged. So now, instead of two boundary conditions we get one circular boundary condition

(b) Describe how the Bloch wave approach uses symmetry aspects of the periodic potential in order to simplify the solution.? The problem of electrons in the solid is a many-electron problem. The full Hamiltonian of the solid contains not only the one-electron potential describing the interactions of the electrons with atomic nuclei, but pair potential also describes the electron-electron interaction. The simplest approach is a free electron model. The next step in building the complexity is independent electron approximation, assuming that all the interactions are described by an effective potential. One of the most important properites of this potential is it is periodic on a lattice. U(r)= U(r+T) where the T is the lattice vactor

Explain the nature of Excitons in semiconductor? a)	Excitation is a bound state of an electron and holes, the both are attracted to each other by electrostatic Coulomb force. The distance between the electron and the hole is called Bohr radices of excitation as it is few nanometers. This electrically netural quasiparticles finds in the insulators, semiconductors and some liquid. Due to Coulomb interaction, the electrons and holes existing in a material are known form excitons. Therefore, the optical nature of semiconductors can be understood by investigating the properties of the excitons. An exciton is composed of an electron and a hole. In bulk semiconductors, the exciton can move freely in all directions. When the length of a semiconductor is reduced to the same order as the exciton radius, i.e., to a few nanometers, quantum confinement effect occurs and the exciton properties are modified. Depending on the dimension of the confinement, three kinds of confined structures are defined: 1.	In a QW, the material size is reduced only in one direction and the exciton can move freely in other two directions. 2.	In a QWR, the material size is reduced in two directions and the exciton can move freely in one direction only. 3.	In a QD, the material size is reduced in all directions and the exciton can not move freely in any direction. In these confined structures. As a result, these structures are good candidates for developing high-high performance optoelectronic devices such as semiconductor light-emitting diodes and laser diodes. Semiconductor materials have their electronic structures organized in bands: a valence band generated by the overlap of the occupied energetic levels of the individual structural units and a conduction band generated by the overlap of the unoccupied levels. Generally the conduction and the valence band in bulk semiconductors are continuous if intraband energetic spacing is smaller than kBT (T is the temperature). Once the electron is promoted into the conduction band a hole is left behind in the valence band; the semiconductor becomes conductive and the electron and hole move freely on the expense of their kinetic energy. The transition from the ground state to the excited state occurs as a result of some external perturbation, e.g. a photon. The electron in the conduction band and the hole in the valence band can be held together by the electrostatic attraction, to form exciton. The interaction between electron and hole can be described by a hydrogen like Hamiltonian where the M is the total mass M= me*+mh* and μ is the reduced mass μ= me*mh*/ (me*+mh*); me* and mh* are the effective masses of the electron and hole, respectively

Explain the concept of the effective Bohr radius in semiconductors? b)	The Bohr radius (a0 or r Bohr) is a physical constant, approximately equal to the most probable distance between the proton and electron in a hydrogen atom in its groundstate.

value is 5.2917721067(12)×10−11 m. Bohr exciton radius is defined as When quantum dot size is smaller than the exciton Bohr radius, the electron hole pair energy levels in quantum dots cannot be treated further based on hydrogen model. The lowest energy level of the exciton is now delocalized over the entire quantum dot. The exciton levels are given by solving the classical quantum mechanical problem of a particle in a box. For the case where the electron and hole are confined in a small space, the coulomb attraction is negligibly small compared to a potential U(r) that describes a spherically symmetric potential well of length r. the corresponding Hamiltonian is

Boher diameter determines the type of confinement for example; •	3-10 times Bohr diameter is weak confinement ∆E≈ 1/M* (M* is effective mass of excitation) •	Smaller than 3 Bohr diameter is strong confinement ∆E≈ 1/µ* (µ* is effective mass of holes and electron).

What are QDS? Why is their optical response is tunable? c)	Quantum dots (QD) are nanoscale semiconductor devices that the material size is reduced in all directions and the exciton cannot move freely in any direction, that means the electrons and holes are confined in all three spatial. The electronic properties of the quantum dots fall between those of bulk semiconductors and those of discrete molecules of comparable size. Band gap can be tuned as a function of particle size and shape for a given composition. For example the photoluminescence of a QD can be manipulated to specific wavelengths by controlling particle diameter: •	larger QDs (radius of 5-6 nm)emit longer wavelengths resulting in emission colors such as orange or red. •	Smaller QDs (radius of 2-3 nm) emit shorter wavelengths resulting in colors like blue and green. The ability to control the emission from Q dot by chancing it is size is called the size quantization effect. Their optical response is tunable because changing size,shape, and composition, quantum dots can change their absorptive and emissive properties dramatically

d)	Explain how the bandgap is changing with their physical size and explain why smaller Quantum Dots are blue-shifted in their optical response? The band gap can become larger in the strong confinement regime where the size of the quantum dot is smaller than the Exciton Bohr radius ab* as the energy levels split up

where ab is the Bohr radius=0.053 nm, m is the mass, μ is the reduced mass, and εr is the size-dependent dielectric constant. As a result, increase in the total emission energy which is the sum of the energy levels in the smaller band gaps in the strong confinement regime is larger than the energy levels in the band gaps of the original levels in the weak confinement regime and the emission at various wavelengths. Generally, the smaller the size of the crystal → the larger the band gap→ the greater the difference in energy between the highest valence band and the lowest conduction band becomes. The larger size of the crystal→ the smaller the band gab→ the smallest the difference in energy between the highest valence band and the lowest conduction band. Therefore quantum dots with different sizes have the ability to emit light of different colors, the reason is the quantum confinement effect. So 1- The larger the dot, the redder (lower energy) its fluorescence spectrum. 2- smaller dots emit bluer (higher energy) light.

Figure: 1 splitting of energy levels in quantum dots due to the quantum confinement effect, semiconductor band gap increases with decrease in size of the nanocrystal.

For (blue-shifted): When the quantum dots are illuminated by UV light, some of the electrons receive enough energy to break free from the atoms. This ability allows them to move around the nanoparticle, and create a conduction band in which electrons are free to move through a material and conduct electricity. When these electrons drop back into the outer orbit around the atom (the valence band), they emit light. The color of that light depends on the energy difference between the conduction band and the valence band.

Figure 2:      Electrons in a quantum dot generating light.

Surname 1

Name Professor Institutional affiliation Date due Society and class Society is divided into classes according to various factors that make a class connected to one another. Society is mainly classified according to wealth where there are the wealthy, middle class and lastly the poor. In the novels "Pride and Prejudice" by Jane Austen and Cervantes' "Don Quixote", society and class has been thoroughly depicted through the various characters in the books in a bid to bring the theme of society and class forward. In this paper therefore I will discuss the theme of social class as depicted in both the books. To begin with, Pride and Prejudice is a story that was set in the early 19th century and is basically a love story but it has more than the love message in it. Marriage today and even early on in the society was and is an important aspect in one's life bearing in mind the main reason is due to love. Throughout her novel, Austen describes the society during the 19th century in England in a way to bring to awareness about the social issues that affected her society through marriage which had been for economic reasons and social background instead of true love so as to achieve a certain class (Austen). In order to illustrate the importance of getting married for love and not for other reason the author uses Elizabeth Bennet. Elizabeth through the whole story is the only woman who is seen to marry his man not for his wealth but for true love unlike her daughters and mother who were wedded by their husbands for wealth not true love. This shows how the society views class as an important aspect in their life and no one want to be associated with the low class hence the actions of Elizabeth are a great achievement during her generation. The Marriage between Lydia and Wickham's is other example of a bad marriage. The author used it to try and show how people were trying to get into marriage for beauty reasons hence get into the class of beauty. The marriage as illustrated by Jane was based on appearances, good looks but false love. However, the society did not want anyone to get married or marry someone of an ugly something which makes such wedding that were not based on true love fade with time. Later on, the wedding comes to an end showing that it was not for true love(Austen and Chapman). In another instance, both Jane and Bingley are strongly attracted to one another. Both of them have dignity and they strongly love one another. However, outside forces emanating from influence of social class came tumbling down their relationship from its heights. His sisters and Darcy believe and say that the family of Bennet family is far below their social ladder hence did not deserve love and attention from him who was high on the society ladder. This relationship is truly meant to show how the well up people in the society ladder despises those low in the society ladder. It shows how the Regency Period was a period that was filled with social immobility where the wealthy did not want to be associated with the poor and since they did not want to share their wealth with them(Austen). A comical and even devastating relationship of marriage is seen when Charlotte Lucas and Mr Collins wed. Taking into account that one week before he had loved Jane and Elizabeth, he could not possibly be in love. However, Charlotte, old and naïve as she is marries Mr. Collins so as acquire financial freedom and achieve a good class in society hence having social security. Her mother and the social class pressure her to have Mr. Collins as her husband. Charlotte says, "I can see what you are feeling, you must be amazed, surprised, as Mr. Collins wanted to marry you. However when you take your time and think it all over, I know and hope that you will be satisfied with your decision. I am no romantic, you know. I never was. I ask only a comfortable home; and, considering Mr. Collin's character, connections, and situation in life, I am convinced that my chance of happiness with him is as fair as most people can boast on entering the marriage state." However, she soon starts to realize that he is such an intolerable man and she even says that she is ashamed to be associated with him. However, Charlotte continue to put up with all the weakness in his man since the only alternative for her is to quit but when she quit she risks losing her financial security as well as society class security(Austen). The author clearly writes about the effects that class has on marriage, and marriage on class. Using irony and satire, Jane illustrates how people are influenced by wealth and social rank to make their marriage decisions. The author satirizes the convention of marriage in her novel placed on an acquisitive society, demonstrating that the mere personally liking, wealth, and class factors can produce only misery, shame, unhappiness and isolation. The contrast between Elizabeth and Darcy show that the society believes that one can only be married for other reasons other than love. As one reads the novel deeper and deeper, it is evident that power of money and social rank in the past were very important. Social class in Cervantes' novel "Don Quixote" appears as an obstruction to what characters desire to achieve. For instance, most of the lovers in the novel have to overcome a lot of difficulties of societal segregation so as to move on with their love and make it prosperous. It is clear that only through tricks, disguises as well as acts of imagination will characters bypass their social circumstances and act according to their real values.

Throughout Don Quixote, the differences between social classes are seen to operate on various different levels. For instance, the novel emphasizes about Sancho's peasant status, Don Quixote's own genteel upbringing, as well as the Duke and Duchess status of aristocracy. However, the novel is hesitant to mock any one class compared to the other. In the novel, Sancho's peasant common sense makes the noblemen appear foolish (Cervantes Saavedra and Grossman). However, his shortcomings such as lack of education and ignorance make him look very foolish as he is always seen. Furthermore, Don Quixote almost invariably sees far beyond any restrictions of social class to the inner worth of the people he meets. His nature of being a good person actually makes him imagine that people are of higher classes than they are actually worth. This makes people see from the perspective that country girls become princesses prostitutes become ladies and innkeepers become lords (Cervantes Saavedra and Smollett). However, Cervantes at some instances mocks the nobility and class system of the Spanish affluent using the title of the book "Don Quixote" by making the main character, Quixote, a hidalgo, the lowest of the nobility with neither great disadvantages nor advantages in the society. The author in his novel want to demonstrate how and why the aristocratic class system has an inadequacy and shows how the human potential is highly hindered by it. By using various tools such as storytelling and illustrating the relationship between Sancho and Quixote, the author hopes to show that friendships and relationship can overcome barriers possibly brought by social class division (Cervantes Saavedra and Grossman).

During this period when the book "Don Quixote" was written, new art and culture emerged from Spain which was a great deal and achievement that could probably bring prosperity among the various society class as well as unite them through the art. However, the great divide between social classes kept the nation stuck in abject poverty despite the promising emergence of art. This made the whole society poor and poor swinging it to a halted economic development state. The author also criticizes the class structure all through the narrative. Cervantes seek to illustrate that the noble duchess and duke are the antagonists in the second part of the novel and hence centers conflicts on many of the characters so as to show class mismatches (Cervantes Saavedra and Smollett).

In most parts of the novel, most of the love stories attempt to cross-class boundaries established between the man and the woman in the relationship because of their differences in society ladder. To mention a few of these stories, the love interests of various characters such as Luncinda and Cardenio who come from different ladders of the society since their families hail from different wealth classes also Quixote and the peasant Dulcinea he claims as his lady. Also, Zoraida and the Christian captive get to love one another and their love for each at last has devastating effects since it makes them lose their entire fortunes and have a great impact on their families (Cervantes Saavedra and Grossman). Through these stories, Cervantes hopes to show the audience how there was societal immobility during this time as well as illustrate how in order to achieve what you wanted in such a society you needed to go past the norms. Cervantes wants to show however that it is still possible to achieve societal mobility through showing these possibilities of lovers who marry across society ladders and religious boundaries through these love stories (Cervantes Saavedra and Smollett).

In the book, the most memorable story of a successful relationship that was of distinct societal class was between two characters Quixote and Sancho of. Cervantes uses character development so as to show the adventures of the two and how they help overcome the barriers. At the beginning of the novel, Quixote sees Sancho as his junior and a person whose opinions are not meangful to her at all. At one point, Quixote even goes to an extent to tell Sancho that he should not talk to her in the rest of their adventure. Sancho was a peasant and a servant while Quixote was a gentleman, hence from different classes but they eventually come to a love affair. At the end of the novel, Sancho and Quixote become closer and become good friends. They actually treat one another fairly, and Sancho stays with Quixote until he dies. This relationship actually show society barriers can be broken if individual actually want to. In conclusion, society is a vital organ in both the novels and the society has been shown as one which possesses class. In both the books, it is clear that none of the people want to be associated with the weak class; all want to be in the strong and wealthy class. However, the social immobility in all the above stories is one which can be overcome by individuals wanting to go past the boundaries.

References Austen, Jane and R. W Chapman. The Novels Of Jane Austen. Oxford [Oxfordshire]: Oxford University Press, 1933. Print. Austen, Jane. Pride And Prejudice. Champaign, Ill.: Project Gutenberg. Print. Cervantes Saavedra, Miguel de and Edith Grossman. Don Quixote. New York: Ecco, 2003. Print. Cervantes Saavedra, Miguel de and T Smollett. The Adventures Of Don Quixote De La Mancha. New York: Farrar, Straus, Giroux, 1986. Print.

Surname 1

Name Professor Institutional affiliation Date due Society and class Society is divided into classes according to various factors that make a class connected to one another. Society is mainly classified according to wealth where there are the wealthy, middle class and lastly the poor. In the novels "Pride and Prejudice" by Jane Austen and Cervantes' "Don Quixote", society and class has been thoroughly depicted through the various characters in the books in a bid to bring the theme of society and class forward. In this paper therefore I will discuss the theme of social class as depicted in both the books. To begin with, Pride and Prejudice is a story that was set in the early 19th century and is basically a love story but it has more than the love message in it. Marriage today and even early on in the society was and is an important aspect in one's life bearing in mind the main reason is due to love. Throughout her novel, Austen describes the society during the 19th century in England in a way to bring to awareness about the social issues that affected her society through marriage which had been for economic reasons and social background instead of true love so as to achieve a certain class (Austen). In order to illustrate the importance of getting married for love and not for other reason the author uses Elizabeth Bennet. Elizabeth through the whole story is the only woman who is seen to marry his man not for his wealth but for true love unlike her daughters and mother who were wedded by their husbands for wealth not true love. This shows how the society views class as an important aspect in their life and no one want to be associated with the low class hence the actions of Elizabeth are a great achievement during her generation. The Marriage between Lydia and Wickham's is other example of a bad marriage. The author used it to try and show how people were trying to get into marriage for beauty reasons hence get into the class of beauty. The marriage as illustrated by Jane was based on appearances, good looks but false love. However, the society did not want anyone to get married or marry someone of an ugly something which makes such wedding that were not based on true love fade with time. Later on, the wedding comes to an end showing that it was not for true love(Austen and Chapman). In another instance, both Jane and Bingley are strongly attracted to one another. Both of them have dignity and they strongly love one another. However, outside forces emanating from influence of social class came tumbling down their relationship from its heights. His sisters and Darcy believe and say that the family of Bennet family is far below their social ladder hence did not deserve love and attention from him who was high on the society ladder. This relationship is truly meant to show how the well up people in the society ladder despises those low in the society ladder. It shows how the Regency Period was a period that was filled with social immobility where the wealthy did not want to be associated with the poor and since they did not want to share their wealth with them(Austen). A comical and even devastating relationship of marriage is seen when Charlotte Lucas and Mr Collins wed. Taking into account that one week before he had loved Jane and Elizabeth, he could not possibly be in love. However, Charlotte, old and naïve as she is marries Mr. Collins so as acquire financial freedom and achieve a good class in society hence having social security. Her mother and the social class pressure her to have Mr. Collins as her husband. Charlotte says, "I can see what you are feeling, you must be amazed, surprised, as Mr. Collins wanted to marry you. However when you take your time and think it all over, I know and hope that you will be satisfied with your decision. I am no romantic, you know. I never was. I ask only a comfortable home; and, considering Mr. Collin's character, connections, and situation in life, I am convinced that my chance of happiness with him is as fair as most people can boast on entering the marriage state." However, she soon starts to realize that he is such an intolerable man and she even says that she is ashamed to be associated with him. However, Charlotte continue to put up with all the weakness in his man since the only alternative for her is to quit but when she quit she risks losing her financial security as well as society class security(Austen). The author clearly writes about the effects that class has on marriage, and marriage on class. Using irony and satire, Jane illustrates how people are influenced by wealth and social rank to make their marriage decisions. The author satirizes the convention of marriage in her novel placed on an acquisitive society, demonstrating that the mere personally liking, wealth, and class factors can produce only misery, shame, unhappiness and isolation. The contrast between Elizabeth and Darcy show that the society believes that one can only be married for other reasons other than love. As one reads the novel deeper and deeper, it is evident that power of money and social rank in the past were very important. Social class in Cervantes' novel "Don Quixote" appears as an obstruction to what characters desire to achieve. For instance, most of the lovers in the novel have to overcome a lot of difficulties of societal segregation so as to move on with their love and make it prosperous. It is clear that only through tricks, disguises as well as acts of imagination will characters bypass their social circumstances and act according to their real values.

Throughout Don Quixote, the differences between social classes are seen to operate on various different levels. For instance, the novel emphasizes about Sancho's peasant status, Don Quixote's own genteel upbringing, as well as the Duke and Duchess status of aristocracy. However, the novel is hesitant to mock any one class compared to the other. In the novel, Sancho's peasant common sense makes the noblemen appear foolish (Cervantes Saavedra and Grossman). However, his shortcomings such as lack of education and ignorance make him look very foolish as he is always seen. Furthermore, Don Quixote almost invariably sees far beyond any restrictions of social class to the inner worth of the people he meets. His nature of being a good person actually makes him imagine that people are of higher classes than they are actually worth. This makes people see from the perspective that country girls become princesses prostitutes become ladies and innkeepers become lords (Cervantes Saavedra and Smollett). However, Cervantes at some instances mocks the nobility and class system of the Spanish affluent using the title of the book "Don Quixote" by making the main character, Quixote, a hidalgo, the lowest of the nobility with neither great disadvantages nor advantages in the society. The author in his novel want to demonstrate how and why the aristocratic class system has an inadequacy and shows how the human potential is highly hindered by it. By using various tools such as storytelling and illustrating the relationship between Sancho and Quixote, the author hopes to show that friendships and relationship can overcome barriers possibly brought by social class division (Cervantes Saavedra and Grossman).

During this period when the book "Don Quixote" was written, new art and culture emerged from Spain which was a great deal and achievement that could probably bring prosperity among the various society class as well as unite them through the art. However, the great divide between social classes kept the nation stuck in abject poverty despite the promising emergence of art. This made the whole society poor and poor swinging it to a halted economic development state. The author also criticizes the class structure all through the narrative. Cervantes seek to illustrate that the noble duchess and duke are the antagonists in the second part of the novel and hence centers conflicts on many of the characters so as to show class mismatches (Cervantes Saavedra and Smollett).

In most parts of the novel, most of the love stories attempt to cross-class boundaries established between the man and the woman in the relationship because of their differences in society ladder. To mention a few of these stories, the love interests of various characters such as Luncinda and Cardenio who come from different ladders of the society since their families hail from different wealth classes also Quixote and the peasant Dulcinea he claims as his lady. Also, Zoraida and the Christian captive get to love one another and their love for each at last has devastating effects since it makes them lose their entire fortunes and have a great impact on their families (Cervantes Saavedra and Grossman). Through these stories, Cervantes hopes to show the audience how there was societal immobility during this time as well as illustrate how in order to achieve what you wanted in such a society you needed to go past the norms. Cervantes wants to show however that it is still possible to achieve societal mobility through showing these possibilities of lovers who marry across society ladders and religious boundaries through these love stories (Cervantes Saavedra and Smollett).

In the book, the most memorable story of a successful relationship that was of distinct societal class was between two characters Quixote and Sancho of. Cervantes uses character development so as to show the adventures of the two and how they help overcome the barriers. At the beginning of the novel, Quixote sees Sancho as his junior and a person whose opinions are not meangful to her at all. At one point, Quixote even goes to an extent to tell Sancho that he should not talk to her in the rest of their adventure. Sancho was a peasant and a servant while Quixote was a gentleman, hence from different classes but they eventually come to a love affair. At the end of the novel, Sancho and Quixote become closer and become good friends. They actually treat one another fairly, and Sancho stays with Quixote until he dies. This relationship actually show society barriers can be broken if individual actually want to. In conclusion, society is a vital organ in both the novels and the society has been shown as one which possesses class. In both the books, it is clear that none of the people want to be associated with the weak class; all want to be in the strong and wealthy class. However, the social immobility in all the above stories is one which can be overcome by individuals wanting to go past the boundaries.

References Austen, Jane and R. W Chapman. The Novels Of Jane Austen. Oxford [Oxfordshire]: Oxford University Press, 1933. Print. Austen, Jane. Pride And Prejudice. Champaign, Ill.: Project Gutenberg. Print. Cervantes Saavedra, Miguel de and Edith Grossman. Don Quixote. New York: Ecco, 2003. Print. Cervantes Saavedra, Miguel de and T Smollett. The Adventures Of Don Quixote De La Mancha. New York: Farrar, Straus, Giroux, 1986. Print.

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Surname 1

Name Professor Institutional affiliation Date due Society and class Society is divided into classes according to various factors that make a class connected to one another. Society is mainly classified according to wealth where there are the wealthy, middle class and lastly the poor. In the novels "Pride and Prejudice" by Jane Austen and Cervantes' "Don Quixote", society and class has been thoroughly depicted through the various characters in the books in a bid to bring the theme of society and class forward. In this paper therefore I will discuss the theme of social class as depicted in both the books. To begin with, Pride and Prejudice is a story that was set in the early 19th century and is basically a love story but it has more than the love message in it. Marriage today and even early on in the society was and is an important aspect in one's life bearing in mind the main reason is due to love. Throughout her novel, Austen describes the society during the 19th century in England in a way to bring to awareness about the social issues that affected her society through marriage which had been for economic reasons and social background instead of true love so as to achieve a certain class (Austen). In order to illustrate the importance of getting married for love and not for other reason the author uses Elizabeth Bennet. Elizabeth through the whole story is the only woman who is seen to marry his man not for his wealth but for true love unlike her daughters and mother who were wedded by their husbands for wealth not true love. This shows how the society views class as an important aspect in their life and no one want to be associated with the low class hence the actions of Elizabeth are a great achievement during her generation. The Marriage between Lydia and Wickham's is other example of a bad marriage. The author used it to try and show how people were trying to get into marriage for beauty reasons hence get into the class of beauty. The marriage as illustrated by Jane was based on appearances, good looks but false love. However, the society did not want anyone to get married or marry someone of an ugly something which makes such wedding that were not based on true love fade with time. Later on, the wedding comes to an end showing that it was not for true love(Austen and Chapman). In another instance, both Jane and Bingley are strongly attracted to one another. Both of them have dignity and they strongly love one another. However, outside forces emanating from influence of social class came tumbling down their relationship from its heights. His sisters and Darcy believe and say that the family of Bennet family is far below their social ladder hence did not deserve love and attention from him who was high on the society ladder. This relationship is truly meant to show how the well up people in the society ladder despises those low in the society ladder. It shows how the Regency Period was a period that was filled with social immobility where the wealthy did not want to be associated with the poor and since they did not want to share their wealth with them(Austen). A comical and even devastating relationship of marriage is seen when Charlotte Lucas and Mr Collins wed. Taking into account that one week before he had loved Jane and Elizabeth, he could not possibly be in love. However, Charlotte, old and naïve as she is marries Mr. Collins so as acquire financial freedom and achieve a good class in society hence having social security. Her mother and the social class pressure her to have Mr. Collins as her husband. Charlotte says, "I can see what you are feeling, you must be amazed, surprised, as Mr. Collins wanted to marry you. However when you take your time and think it all over, I know and hope that you will be satisfied with your decision. I am no romantic, you know. I never was. I ask only a comfortable home; and, considering Mr. Collin's character, connections, and situation in life, I am convinced that my chance of happiness with him is as fair as most people can boast on entering the marriage state." However, she soon starts to realize that he is such an intolerable man and she even says that she is ashamed to be associated with him. However, Charlotte continue to put up with all the weakness in his man since the only alternative for her is to quit but when she quit she risks losing her financial security as well as society class security(Austen). The author clearly writes about the effects that class has on marriage, and marriage on class. Using irony and satire, Jane illustrates how people are influenced by wealth and social rank to make their marriage decisions. The author satirizes the convention of marriage in her novel placed on an acquisitive society, demonstrating that the mere personally liking, wealth, and class factors can produce only misery, shame, unhappiness and isolation. The contrast between Elizabeth and Darcy show that the society believes that one can only be married for other reasons other than love. As one reads the novel deeper and deeper, it is evident that power of money and social rank in the past were very important. Social class in Cervantes' novel "Don Quixote" appears as an obstruction to what characters desire to achieve. For instance, most of the lovers in the novel have to overcome a lot of difficulties of societal segregation so as to move on with their love and make it prosperous. It is clear that only through tricks, disguises as well as acts of imagination will characters bypass their social circumstances and act according to their real values.

Throughout Don Quixote, the differences between social classes are seen to operate on various different levels. For instance, the novel emphasizes about Sancho's peasant status, Don Quixote's own genteel upbringing, as well as the Duke and Duchess status of aristocracy. However, the novel is hesitant to mock any one class compared to the other. In the novel, Sancho's peasant common sense makes the noblemen appear foolish (Cervantes Saavedra and Grossman). However, his shortcomings such as lack of education and ignorance make him look very foolish as he is always seen. Furthermore, Don Quixote almost invariably sees far beyond any restrictions of social class to the inner worth of the people he meets. His nature of being a good person actually makes him imagine that people are of higher classes than they are actually worth. This makes people see from the perspective that country girls become princesses prostitutes become ladies and innkeepers become lords (Cervantes Saavedra and Smollett). However, Cervantes at some instances mocks the nobility and class system of the Spanish affluent using the title of the book "Don Quixote" by making the main character, Quixote, a hidalgo, the lowest of the nobility with neither great disadvantages nor advantages in the society. The author in his novel want to demonstrate how and why the aristocratic class system has an inadequacy and shows how the human potential is highly hindered by it. By using various tools such as storytelling and illustrating the relationship between Sancho and Quixote, the author hopes to show that friendships and relationship can overcome barriers possibly brought by social class division (Cervantes Saavedra and Grossman).

During this period when the book "Don Quixote" was written, new art and culture emerged from Spain which was a great deal and achievement that could probably bring prosperity among the various society class as well as unite them through the art. However, the great divide between social classes kept the nation stuck in abject poverty despite the promising emergence of art. This made the whole society poor and poor swinging it to a halted economic development state. The author also criticizes the class structure all through the narrative. Cervantes seek to illustrate that the noble duchess and duke are the antagonists in the second part of the novel and hence centers conflicts on many of the characters so as to show class mismatches (Cervantes Saavedra and Smollett).

In most parts of the novel, most of the love stories attempt to cross-class boundaries established between the man and the woman in the relationship because of their differences in society ladder. To mention a few of these stories, the love interests of various characters such as Luncinda and Cardenio who come from different ladders of the society since their families hail from different wealth classes also Quixote and the peasant Dulcinea he claims as his lady. Also, Zoraida and the Christian captive get to love one another and their love for each at last has devastating effects since it makes them lose their entire fortunes and have a great impact on their families (Cervantes Saavedra and Grossman). Through these stories, Cervantes hopes to show the audience how there was societal immobility during this time as well as illustrate how in order to achieve what you wanted in such a society you needed to go past the norms. Cervantes wants to show however that it is still possible to achieve societal mobility through showing these possibilities of lovers who marry across society ladders and religious boundaries through these love stories (Cervantes Saavedra and Smollett).

In the book, the most memorable story of a successful relationship that was of distinct societal class was between two characters Quixote and Sancho of. Cervantes uses character development so as to show the adventures of the two and how they help overcome the barriers. At the beginning of the novel, Quixote sees Sancho as his junior and a person whose opinions are not meangful to her at all. At one point, Quixote even goes to an extent to tell Sancho that he should not talk to her in the rest of their adventure. Sancho was a peasant and a servant while Quixote was a gentleman, hence from different classes but they eventually come to a love affair. At the end of the novel, Sancho and Quixote become closer and become good friends. They actually treat one another fairly, and Sancho stays with Quixote until he dies. This relationship actually show society barriers can be broken if individual actually want to. In conclusion, society is a vital organ in both the novels and the society has been shown as one which possesses class. In both the books, it is clear that none of the people want to be associated with the weak class; all want to be in the strong and wealthy class. However, the social immobility in all the above stories is one which can be overcome by individuals wanting to go past the boundaries.

References Austen, Jane and R. W Chapman. The Novels Of Jane Austen. Oxford [Oxfordshire]: Oxford University Press, 1933. Print. Austen, Jane. Pride And Prejudice. Champaign, Ill.: Project Gutenberg. Print. Cervantes Saavedra, Miguel de and Edith Grossman. Don Quixote. New York: Ecco, 2003. Print. Cervantes Saavedra, Miguel de and T Smollett. The Adventures Of Don Quixote De La Mancha. New York: Farrar, Straus, Giroux, 1986. Print.