In the Angular process as 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 Augar elecrons ) . Assuming the nuclesu to be massive , calculate the kinetic energy of an `n=4` Augar electron emitted by chromium by absorbing the energy from a `n=2` to `n=1` transition .

Explanation

As the nucleus is massive, recoil momentum of the atom can be ignored. We can assume that the entire energy of transition is transferred to the Auger electron.
As there is a single valence electron in chromium (Z=24), the energy states may be thought of as given by Bohr model. The energy of the nth state is `E_(n)=-(RZ^(2))/(n^(2))` where R is Rydberg constant. In the transition form n=2 to n=1, energy released, `DeltaE=-RZ^(2)(1/4-1)=3/4RZ^(2)`
The energy required to ejected a n=4 electron `=RZ^(2)xx(1/4)^(2)=(RZ^(2))/16`
`:.` KE a Auger electron=`(3RZ^(2))/4-(RZ^(2))/16`
`KE=RZ^(2)(3/4-1/16)=11/16 RZ^(2)=11/16(13.6eV)xx24xx24=5385.6 eV`