Verified Solution • 2025–26 Session moderate

QPages 384-386: Q46: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q46 Solution: Consider an excited hydrogen atom in state moving with a…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often apply only the classical Doppler shift ($ uapprox u_0(1- v/c)$ for forward emission) and forget that momentum conservation forces the atom to recoil, introducing the extra term $h\nu_0/(2Mc^2)$. Include the recoil energy when using energy conservation to obtain the correct frequency shift.

Consider an excited hydrogen atom in state nn moving with a velocity vv≪c)v v \ll c). It emits a photon in the direction of its motion and changes its state to a lower state mm. Apply momentum and energy conservation principles to calculate the frequency ν\nu of the emitted radiation. Compare this with the frequency ν0\nu_0 emitted if the atom were at rest.

Step-by-Step Verified Solution

**Answer:** _ = __/(1 + hv_/(2Mc_)) approximately. **Step-by-Step Explanation:** For an excited hydrogen atom moving with velocity v, the emitted photon frequency is modified by the Doppler effect and recoil. Using conservation of momentum and energy, the frequency is:
ν=ν0(1−vc+hν02Mc2)\nu = \nu_0 \left(1 - \frac{v}{c} + \frac{h\nu_0}{2Mc^2}\right)
where __ is the frequency when at rest [citation:3].

All Questions in this Chapter

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