In the Auger process, an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer electron which may be ejected by the atom (This is called an Auger electron). Assuming the nucleus to be massive, calculate the kinetic energy of an n = 4 Auger electron emitted by Chromium by absorbing the energy from a n = 2 to n = 1 transition.

Hint: The energy acquired by the electron is equal to the energy difference of the transition levels.
Step 1: Find the energy difference of the transition levels.
The energy of the nth state, ${E}_{n}=-{Z}^{2}R\frac{1}{{n}^{2}}$ where R is the Rydberg constant and Z = 24.
The energy released in a transition from 2 to 1 is, $∆E={Z}^{2}R\left(1-\frac{1}{4}\right)=\frac{3}{4}{Z}^{2}R.$
Step 2: Find the kinetic energy of the electron.
The energy required to eject a n = 4 electron is ${E}_{4}={Z}^{2}R\frac{1}{16}.$
Thus, the kinetic energy of the Auger electron is;
$\mathrm{KE}={Z}^{2}R\left(\frac{3}{4}-\frac{1}{16}\right)=\frac{1}{16}{Z}^{2}R\phantom{\rule{0ex}{0ex}}=\frac{11}{16}×24×24×13.6\mathrm{eV}\phantom{\rule{0ex}{0ex}}=5385.6\mathrm{eV}$