Wikipedia:Reference desk/Archives/Science/2019 June 15

= June 15 =

Principle quantum number for lanthanum
What is its value? Sandbh (talk) 19:33, 15 June 2019 (UTC)
 * Principal quantum number is a property of an electron. From the electron configuration [Xe] 5d1 6s2 you can see the maximum value is 6 for the ground state atom. For an excited atom it could be higher. Graeme Bartlett (talk) 22:47, 15 June 2019 (UTC)

Is it 5 for the 5d differentiating electron? And is it 4 according to the Madelung approximation, which erroneously predicts lanthanum should have a 4f differentiating electron? Sandbh (talk) 20:07, 16 June 2019 (UTC)
 * For the "5d differentiating electron" the principle quantum number of the electron would be 5 as you can see by the "5". But as for the principle quantum number of the element, it would still be counted as 6, (it is in Period 6 in the periodic table. Similarly the 4f electron is of principle quantum number 4, but the element is still principle quantum number 6 thanks to the 6s electrons. Rearranging the electrons between D and F subshells may excite the atom a bit but it does not change its principal quantum number until you can get enough energy to get a 7s electron. Note that an La3+ ion would go down to principle quantum number 5. Graeme Bartlett (talk) 00:31, 17 June 2019 (UTC)

Thank you. I understand what you mean by principle quantum number (PQN) = period number, in the case of the conventional periodic table. Does this “rule” fail in the case of palladium, with its 4d10 outer configuration? It is in period 5 but it’s PQN is 4. More broadly, there appears to be some terminological sloppiness in the literature. For example, the PQN is sometimes associated with the period number (per your answer) whereas in the case of the Madelung “rule” diagram the PQN is the idealised differentiating electron. Have I interpreted this correctly? In the case of La then, the PQN can be 6, 5, or 4 depending on the electron being referred to i.e. the 6s of the highest occupied orbital; the 5d as the actual differentiating electron; and the erroneous 4f as the differentiating electron according to the Madelung rule diagram. No wonder there is so much confusion around this topic. I intend to improve some of our own articles, once I have a clear understanding. Sandbh (talk) 12:22, 17 June 2019 (UTC)
 * Each electron has a PQN. An atom has (usually) many electrons, each with its own PQN. Atoms (elements) don't have PQN in the same way because electrons can come and go without changing the elemental identity. Elements have a fixed period (chemistry) based on the sequence of protons, but the jump back to a lower PQN, for example in lanthanum the "next electron added after 6s2 is 5d", is still a linear increase in nuclear proton count, not a backward change. Lanthanum is still in Period 6. In keeping with your questions and preceding explanations, lanthanum does have its "last" electron added in n=5 but its highest populated electron shell is still n=6. DMacks (talk) 14:58, 17 June 2019 (UTC)

Thank you. Yes, the PQN applies to the electron in question, not the atom per se. I don’t understand what you mean by “elements having a fixed period based on the sequence of protons”. In a conventional table, Sc is in period 4; in a left-step table, Sc is in period 5. Even in a conventional table this would not appear to work given Pd in period 5 has a PQN, based on its outer configuration of 4d10, of 4. There seems to be much confusion surrounding this concept, including on my part. For example this source gives the quantum number of La as 4 (presumably based on the aufbau approximation or Madelung rule diagram). Sandbh (talk) 10:01, 18 June 2019 (UTC)