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 Δν=7.51×10−4ν, where ν is the frequency of the emitted photon. Hint: 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.