Molecular vibration: The vibrational frequency of an HF molecule is 8.72 × 10¹³ Hz and the reduced mass of the molecule is 1.589 × 10^-27 kg. What is the ground state vibrational energy of an HF molecule? (1 eV = 1.60 × 10^-19 J, ħ = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s) A) 0.12 eV B) 0.18 eV C) 0.24 eV D) 0.30 eV E) 0.36 eV

Question

Quizplus · Accepted Answer

The ground state vibrational energy (E) of a molecule can be calculated using the formula $E = \frac{1}{2}h\nu$, where $h$ is Planck's constant and $\nu$ is the vibrational frequency. Given $h = 6.626 \times 10^{-34}$ J·s and $\nu = 8.72 \times 10^{13}$ Hz, $E = \frac{1}{2} \times 6.626 \times 10^{-34} \times 8.72 \times 10^{13} = 2.89 \times 10^{-20}$ J. Converting to eV using $1 \text{ eV} = 1.60 \times 10^{-19}$ J, $E = \frac{2.89 \times 10^{-20}}{1.60 \times 10^{-19}} = 0.18$ eV.

Molecular Vibration: the Vibrational Frequency of an HF Molecule Is