NCERT Physics Class 12 Exemplar Ch 12 Atoms Part 4
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26 If a proton had a radius R and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a Hatom when (i) , and (ii) .
Ans:
For a point nucleus in Hatom:
Ground state:
Potential energy
For an spherical nucleus of radius R,
If same result.
If : the electron moves inside the sphere with radius
new Bohr radius).
Charge inside
27 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 Auger electron emitted by Chromium by absorbing the energy from a to transition.
Ans:

As the nucleus is massive, recoil momentum of the atom may be neglected and the entire energy of the transition may be considered transferred to the Auger electron.

As there is a single valence electron in Cr, the energy states may be thought of as given by the Bohr model.
The energy of the nth state where R is the Rydberg constant and .
The energy released in a transition from 2 to 1 is
The energy required to eject a electron is
Thus the kinetic energy of the Auger electron is