Verified Solution • 2025–26 Session moderate

QPages 384-386: Q23: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q23 Solution: Find the temperature at which the average thermal kinetic…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently mistake the average thermal kinetic energy for $kT$ instead of the correct $ rac{3}{2}kT$ for a monatomic ideal gas. Ensure you use the full translational degrees of freedom factor when equating thermal energy to excitation energy.

Find the temperature at which the average thermal kinetic energy is equal to the energy needed to take a hydrogen atom from its ground state to n=3n = 3 state. Hydrogen can now emit red light of wavelength 653.1 nm. Because of Maxwellian distribution of speeds, a hydrogen sample emits red light at temperatures much lower than that obtained from this problem. Assume that hydrogen molecules dissociate into atoms.

Step-by-Step Verified Solution

**Answer:** Temperature = 9.4 _ 10_ K. **Step-by-Step Explanation:** Energy to take hydrogen from ground state to n = 3: E = 13.6(1 _ 1/9) = 12.09 eV. Average thermal kinetic energy = (3/2)kT = 12.09 eV. T = 2 _ 12.09 / (3 _ 8.62 _ 10__) = 9.35 _ 10_ K � 9.4 _ 10_ K [citation:14].

All Questions in this Chapter

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