Now consider a Rigid Rotator-Harmonic oscillator model for the HD molecule at te

Question

Now consider a Rigid Rotator-Harmonic oscillator model for the HD molecule at temperature T=3 K. a) Where is each nuclei located relative to the center of mass in nm? b) What is the fraction of molecules in the first 5 rotational states in the vibrational ground state? c) Assuming that transition probabilities are independent of the rotational quantum number J, i.e., it only depends on the fraction/number of molecules in each J level, plot the rotational-vibrational spectrum as a function of wavelength for the n=0 to the n=1 vibrational transition, showing the rotational P and R branches for J=0 to 4 in the vibrational ground state? d) What is the average rotational energy assuming that only J=0 to 4 levels are populated in the vibrational ground state n=0? Please don't just copy+paste online pulications...teach me how to do this problem, I appreciate for a thorough answer to this problem! thanks.

Explanation / Answer

for part a

calculate the reduced mass of HD
randa*T=2.9*10^-3
get frequency
calculate inertia
use these relationship calculate the total length of HD bond
and then use m1*l1=m2*l2 relationship to get l1 and l2

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