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A nucleus of mass M emits a photon of frequency ν and the nucleus recoils. The recoil energy will be

1. Mν² − hν
2. hν² / 2Mc²
3. zero
4. hν

Correct answer: hν² / 2Mc²

Solution

The recoil energy of the nucleus is derived from the conservation of momentum and energy. The photon carries momentum p = hν/c, and the nucleus recoils with an equal and opposite momentum. The recoil energy is given by p²/2M = (hν)² / (2Mc²).

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