NCERT Physics Class 12 Exemplar Ch 12 Atoms Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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 H-atom when (i) , and (ii) .

Ans:

For a point nucleus in H-atom:

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