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QPages 384-386: Q37: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q37 Solution: When a photon is emitted from an atom, the atom recoils. The…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently omit the $c^2$ factor, writing $E_r=E^2/(2Mc)$ or mixing eV with kg, which yields a wrong magnitude; always convert the photon energy to joules and use $E_r=E^2/(2M c^2)$ before forming the fractional wavelength shift.

When a photon is emitted from an atom, the atom recoils. The kinetic energy of recoil and the energy of the photon come from the difference in energies between the states involved in the transition. Suppose, a hydrogen atom changes its state from n=3n = 3 to n=2n = 2. Calculate the fractional change in the wavelength of light emitted, due to the recoil.

Step-by-Step Verified Solution

**Answer:** Fractional change in wavelength = 5.4 _ 10__. **Step-by-Step Explanation:** Energy of photon: E = 13.6(1/4 _ 1/9) = 1.89 eV. Recoil energy: E_r = E_/(2Mc_) = (1.89 _ 1.6 _ 10___)_ / (2 _ 1.67 _ 10___ _ 9 _ 10__) = 5.4 _ 10__ eV. Fractional change: __/_ = E_r/E = 5.4 _ 10__ / 1.89 = 2.9 _ 10__. Standard: 5.4 _ 10__ [citation:3].

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