AP EAMCET · PHYSICS · Atomic Physics
A stationary hydrogen atom undergoes a transition from \(n=5\) to \(n=4\). Recoil speed of the atom is \((R=\) Rydberg constant, \(h=\) Planck's constant and \(m=\) mass of the proton).
- A \(\frac{R h}{m}\)
- B \(\frac{9 m}{400 R h}\)
- C \(\frac{9 R h}{400 m}\)
- D \(\frac{7 R h}{400}\)
Answer & Solution
Correct Answer
(C) \(\frac{9 R h}{400 m}\)
Step-by-step Solution
Detailed explanation
For transition \(5 \rightarrow 4\), Momentum of photon, \(p=\frac{h}{\lambda}=h R\left(\frac{1}{16}-\frac{1}{25}\right)\) and recoil speed, \(v=\frac{p}{m}=\frac{h R\left(\frac{1}{16}-\frac{1}{25}\right)}{m}=\frac{9 h R}{400 m}\)
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