Hydrogen chloride's bond absorbs infrared light in a band centred near

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · Wave mechanics in one dimension

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch The harmonic oscillator

Problem

2886\ \mathrm{cm^{-1}}

. Idealising this as a single line, and treating the chlorine atom as fixed (it is about

35

times heavier than hydrogen, so it barely moves), find the vibrational quantum

\hbar\omega

in eV, the angular frequency

\omega

, and the effective stiffness

m_H\omega^2

of the bond, using

m_H = 1.673\times10^{-27}

kg.