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QPages 384-386: Q36: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q36 Solution: When a photon is emitted by a hydrogen atom, the photon carries …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often plug the photon momentum directly into $KE = \frac{p}{2M}$, forgetting that kinetic energy requires the momentum squared: $KE = \frac{p^{2}}{2M}$. Always square the momentum (and convert the wavelength to metres before using $p = h/\lambda$) to avoid a factor‑of‑$10^{9}$ error.

When a photon is emitted by a hydrogen atom, the photon carries a momentum with it. a) Calculate the momentum carries by the photon when a hydrogen atom emits light of wavelength 656.3 nm. b) With what speed does the atom recoil during this transition? Take the mass of the hydrogen atom = 1.67×10−27 kg1.67 \times 10^{-27} \text{ kg}. c) Find the kinetic energy of recoil of the atom.

Step-by-Step Verified Solution

**Answer:** (a) p = 1.01 _ 10___ kg m/s (b) v = 0.6 m/s (c) KE = 3 _ 10___ J. **Step-by-Step Explanation:** (a) p = h/_ = 6.63 _ 10___ / (656.3 _ 10__) = 1.01 _ 10___ kg m/s. (b) Recoil speed: v = p/M = 1.01 _ 10___ / 1.67 _ 10___ = 0.605 m/s. (c) KE = p_/(2M) = (1.01 _ 10___)_ / (2 _ 1.67 _ 10___) = 3.05 _ 10___ J [citation:3].

All Questions in this Chapter

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