Vibrational spectra — UPSC Physics Optional CSE 2026 Paper II

The fundamental and 2^{\text{nd}} harmonic transitions of {}^{14}\text{N}^{16}\text{O} are recorded at 1876\cdot 06\text{ cm}^{-1} and 3724\cdot 2\text{ cm}^{-1}, respectively. Calculate the equilibrium vibrational frequency, the anharmonicity constant and the zero-point energy of the molecule.

{[Given : Mass of {}^{14}\text{N} = 23\cdot 25 \times 10^{-27}\text{ kg}, Mass of {}^{16}\text{O} = 26\cdot 56 \times 10^{-27}\text{ kg}]}