GATE 2020 PH – Question 22

Atomic and Molecular Physics · Rotational and vibrational spectra of diatomic molecules · 1 mark · Multiple choice

A diatomic molecule consists of identical atoms. Let $E_v$ and $E_e$ be characteristic vibrational nuclear and electronic energies, with electron mass m and nuclear mass M. The ratio $E_v/E_e$ scales as

$(m/M)^{1/2}$
$m/M$
$(m/M)^{3/2}$
$(m/M)^2$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $(m/M)^{1/2}$

Explanation

The electronic energy scale is $E_e\sim\hbar^2/(ma^2)$ for molecular length a. A molecular bond has force constant of order $K\sim E_e/a^2$, giving nuclear vibration $E_v\sim\hbar\sqrt{K/M}$. Dividing by $E_e$ and substituting the electronic scale yields $E_v/E_e\sim\sqrt{m/M}$. Numerical reduced-mass factors do not change this scaling. Select A.

More Rotational and vibrational spectra of diatomic molecules questions

GATE 2024 PH Q15 – The mean distance between atoms in HD is r, with hydrogen mass m H. The difference between…
GATE 2025 PH Q28 – Potential energy of two diatomic molecules P and Q of the same reduced mass is shown in…
GATE 2026 PH Q62 – A diatomic molecule has rotational lines spaced by 20.0 cm−1 and moment of inertia I…
GATE 2022 PH Q50 – For molecular mass M, electron mass m, and electronic, rotational, vibrational energies…

All Rotational and vibrational spectra of diatomic molecules questions →