Chlorine has two naturally occurring isotopes, Cl³⁵ and Cl³⁷. Show that the vibrational spectrum of HCl should consist of closely spaced doublets, with a splitting given by ^v = 7.51 x 10^-4 v, where ν is the frequency of the emitted photon. Think of it as a harmonic oscillator, with ω = √k/μ, where μ is the reduced mass (Equation 5.15) and k is presumably the same for both isotopes.

Equation 5.15

Transcribed Image Text:

m im!2 כ + ד m (5.15)