Question

A nucleus of mass M emits a γ-ray photon of frequency 'v'. The loss of internal energy by the nucleus is ______.

Options

• 0

• `hν[1 + (hν)/(2Mc^2)]`

• hν

• `hν[1 - (hν)/(2Mc^2)]`

Answer 1

A nucleus of mass M emits a γ-ray photon of frequency 'v'. The loss of internal energy by the nucleus is `bbunderline(hν[1 + (hν)/(2Mc^2)])`.

Explanation:

Use momentum conservation;

`vecp_gamma + vecp_"Nu" = 0`

`vecp_"Nu"` → momentum of decayed nuclei

The momentum of γ ray [p_γ] = `(hν)/c`

The energy of γ ray = hν

K.E. of nuclei = `(P_{Nu})^2/(2M) = 1/(2M)[(hν)/c]^2`

Loss in internal energy = E_γ + K.E_Nu

= `hν + 1/(2M)[(hν)/c]^2`