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QPages 384-386: Q22: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q22 Solution: The average kinetic energy of molecules in a gas at temperature …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often set $\frac32kT$ equal to the hydrogen atom’s ionization energy (13.6 eV) and then conclude that H₂ will dissociate, overlooking that the relevant stability limit for a molecule is its bond‑dissociation energy (~4.5 eV). Always compare the kinetic energy to the correct binding energy for the species in question and keep unit conversions (eV, K) consistent.

The average kinetic energy of molecules in a gas at temperature T is 1.5kT1.5 k T. Find the temperature at which the average kinetic energy of the molecules of hydrogen equals the binding energy of its atoms. Will hydrogen remain in molecular form at this temperature? Take k=8.62×10−5 eV K−1k = 8.62 \times 10^{-5} \text{ eV K}^{-1}.

Step-by-Step Verified Solution

**Answer:** Temperature = 1.05 _ 10_ K. No, hydrogen will not remain molecular at this temperature. **Step-by-Step Explanation:** Binding energy of hydrogen atom = 13.6 eV. Average kinetic energy = (3/2)kT = 13.6 eV. T = 2 _ 13.6 / (3 _ 8.62 _ 10__) = 1.05 _ 10_ K. At this temperature, hydrogen molecules dissociate into atoms [citation:14].

All Questions in this Chapter

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