X Rays and the Ordering of the Elements — Question 9

Question 9

A nonradiative Auger channel partitions a core binding-energy difference

Use a simplified independent-binding model with $B_K=8.0\,\mathrm{keV}$ and $B_L=1.0\,\mathrm{keV}$. An L electron fills a K vacancy and transfers the released energy to a second L electron, ejecting it. Ignore rearrangement, recoil, and work-function effects.

1. Find the Auger electron kinetic energy.

2. Compare with the $K_\alpha$ photon energy from a radiative alternative and account for the difference.

Question 9 - Solution

A nonradiative Auger channel partitions a core binding-energy difference

(a) Method and calculation

$$E_{\mathrm{fill}}=B_K-B_L=8.0-1.0=7.0\,\mathrm{keV}.$$$$K_A=E_{\mathrm{fill}}-B_L=B_K-2B_L=\boxed{6.0\,\mathrm{keV}}.$$

(b) Interpretation and further calculation

$$\boxed{E_{K\alpha}=B_K-B_L=7.0\,\mathrm{keV}}.$$$$\boxed{E_{K\alpha}-K_A=B_L=1.0\,\mathrm{keV}}.$$

Physical check

The Auger channel leaves two outer vacancies instead of one. In real atoms the energies require configuration-dependent binding and relaxation corrections; this exercise states its simplified accounting model.