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unscientific
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Homework Statement
In rotations of diatomic molecules such as HCL, the hamiltonian is found to be:
[tex] \hat H = \frac{\hat L^2}{2\mu a^2} [/tex]
where ##\mu## is the reduced mass, a is the separation.
(a) Find the energy levels and separation.
(b) Explain why rotational spectra of HCl due to emission or absorption of electric dipole radiation consists of equally spaced lines. Given spacing ##20.57cm^{-1}##, calculate the separation ##a##.
Homework Equations
The Attempt at a Solution
Part(a)
[tex]E = \frac{l(l+1)\hbar^2}{2\mu a^2}[/tex]
[tex] \Delta E = E_l - E_{l-1} = \frac{l(l+1) - l(l-1)}{2\mu a^2}\hbar^2 = \frac{l\hbar^2}{\mu a^2}[/tex]
Part (b)
By dipole transition selection rules, ##\Delta l = \pm 1##.
m not sure why it would be equally spaced, since spacing depends on ##l##. I tried letting ##l \rightarrow \infty##, which implies spacing goes to zero as ##l(l+1) − l(l−1) \approx l^2−l^2 = 0##.