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 .

Options

A. 4.6
B. 7.5
C. 5.38
D. 3.36

Answer

C

Explanation

As the uncleus is massive, recoil momentum of the atom can be ignore. We can assume that the entire energy of tranition is transferred to the augar 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 `n^th` stae is
`E_n=-(RchZ^2)/(n^2)` when R is hydberg constant.
In the transition form `n=2` to `n=1`, energy released ,
`DeltaE=-RhcZ^2((1)/(4)-1)=(3)/(4)RhcZ^2`
The energy rquired to eject ` n=4` electron
`=RhcZ^2((1)/4)^2=(RhcZ^2)/(16)`
`therefore` KE of augar electron `=(3RhcZ^2)/(4)-(RhcZ^2)/(16)`
`KE=RhcZ^2((3)/(4)-(1)/(16))=(11)/(16)RhcZ^2`
`(11)/(16)(13.6eV)xx24xx24=5385.6eV=5.38keV`
`[because Rhc=13.6eV]`