Question

The recoil speed of a hydrogen atom after it emits a photon in going from $ \overline{P}\overline{Q}\overline{R}\overline{S} $ to $ (P+Q)(R+S) $ state is

• A. $ \overline{PQRS} $
• B. $ 2v\,\tan \phi $
• C. $ v\,\tan \phi $
• D. $ v\,\cot \phi $

Answer 1

Answer: (C)

(c.)We can write $ \pi \sqrt{\frac{{{a}^{2}}}{2G\lambda }} $ Momentum of photon emitted $ 2\pi \sqrt{\frac{{{a}^{2}}}{2G\lambda }} $ Recoil momentum of H-atom $ 2\pi \sqrt{\frac{2{{a}^{2}}}{G\lambda }} $ $ \frac{\sqrt{2}}{\pi }\times \frac{1}{\sqrt{15LC}} $ $ \frac{1}{\sqrt{2}}\pi \times \frac{1}{\sqrt{15LC}} $ $ \frac{2\sqrt{2}}{\pi }\times \frac{1}{\sqrt{15LC}} $ $ \frac{\pi }{2}\times \frac{1}{\sqrt{15LC}} $