Diatomic molecule problem

[quantum_prince]

We have Heteronuclear diatomic molecules with atomic masses m1 and m2 and an internuclear distance R have rotational energy eigenvalues
EJ = BJ(J + 1) , J = 0, 1, 2, . . . when they are considered as a rigid rotor. The rotational constant is given by
B = h^2/2µR^2 with the reduced mass µ = m1m2/(m1 + m2) .

I need to Describe the frequency spectrum observed when photons are emitted
in a pure rotational transition J + 1 -> J .

also describe a method to estimate the internuclear distance R
from such a rotational spectrum ?.

How to proceed in this regard.

Regards.
QP.

 

[BigJDubs]

Answer:The frequency spectrum observed when photons are emitted in a pure rotational transition J + 1 -> J can be described as a series of peaks in the infrared region of the electromagnetic spectrum. The frequency of the emission line is proportional to the rotational constant B and can be determined from the equation ν = B(J + 1) - BJ. This equation can be used to estimate the internuclear distance R by measuring the frequency of the emission line and then solving for R using the rotational constant B equation.