The correct statement from the following set (i) to (iv) is (i) if q is the displacement from equilibrium for harmonic motion, the potential energy is proportional to q (ii) if the vibrational frequency $(v)$ of HCl is $2990 \mathrm{cm}^{-1}$, its zero point energy will be $1495 \mathrm{cm}^{-1}$ (iii) the correct order of vibrational frequency of $\mathrm{O}-{ }^{1} \mathrm{H}\left(\mathrm{X}_{1}\right), \mathrm{O}-{ }^{2} \mathrm{H}\left(\mathrm{X}_{2}\right)$ and $\mathrm{O}-{ }^{3} \mathrm{H}\left(\mathrm{X}_{3}\right)$ is $\mathrm{X}_{1}>\mathrm{X}_{2}>\mathrm{X}_{3}$ (iv) the fundamental vibrational transition of a diatomic molecule appears at $1880 \mathrm{cm}^{-1}$. Its first overtone will be at $940 \mathrm{cm}^{-1}$ (assuming anharmonicity constant as zero)
(a)i, ii, iii only
(b)i, ii, iii, iv
(c)ii, iii only
(d)i, ii, iv only
Answer
Answer: C ✓ checked by 4AB · confidence high
Explanation
(ii) The zero-point energy is ½ν = 1495 cm⁻¹. (iii) Frequency falls with reduced mass, so O–¹H > O–²H > O–³H. (i) is false because V ∝ q², and (iv) is false because the first overtone lies near 2ν, not ν/2. ii and iii (c).