Problem 5.3 – Griffith’s Intro to QM

Problem 5.3

Chlorine has two naturally occurring isotopes, $Cl^{35}$ and $Cl^{37}.$ Show that the vibrational spectrum of HCl should consist of closely spaced doublets, with a splitting given by $\Delta \nu = 7.51 \times 10^{-4} \nu$ , where $\nu$ is the frequency of the emitted photon. Hint: Think of it as a harmonic oscillator, with $\omega = \sqrt{k/ \mu} ,$ where $\mu$ is the reduced mass (Equation 5.15) and $k$ is presumably the same for both isotopes.