Wikipedia:Reference desk/Archives/Science/2022 July 28

= July 28 =

Ion speed augmented when capturing electron ?
In vacuum, when Ion at speed V1 is capturing an electron at speed V2 superior to V1, is V1 augmented ? Malypaet (talk) 21:23, 28 July 2022 (UTC)


 * V1 and V2 in same direction, of course. Malypaet (talk) 21:30, 28 July 2022 (UTC)


 * In the terminology of physics, velocity is a a physical vector quantity, meaning that is has a magnitude as well as a direction in space. The magnitude is called speed. I assume that in the question the ion and the electron were travelling in the same direction, with the electron about to overtake the ion when it was captured. If M1 is the mass of the ion and M2 the mass of the electron, the combined momentum of the two was M1V1 + M2V2. By the law of conservation of momentum, this is then also the momentum of the ion+electron after capture. For all practical purposes, their combined mass equals M12 = M1 + M2. The new velocity V12 has to satisfy M12V12 = M1V1 + M2V2. By elementary algebra, we find that
 * V12 = V1 + (V2 − V1) × M2 / M12.
 * If V2 > V1, the term after the plus sign is greater than zero, so also V12 > V1. --Lambiam 01:08, 29 July 2022 (UTC)
 * And how does the orbital energy of the electron come into play? Malypaet (talk) 08:04, 30 July 2022 (UTC)


 * During capture, some energy is released, which is typically carried away by a photon. How much depends on the relative velocities and the binding energy after capture. The photon has some momentum too. PiusImpavidus (talk) 08:15, 29 July 2022 (UTC)
 * The ionization energy is not zero, but negligible compared to the masses of the particles, which is why I wrote "For all practical purposes". The momentum of the photon, which has no preferred direction anyway, is negligible too. --Lambiam 11:02, 29 July 2022 (UTC)
 * It is worth noting that making quantitative calculations will in many cases require taking note of relativistic effects. PianoDan (talk) 16:51, 29 July 2022 (UTC)