A rotating diatomic molecule in its l = 1 quantum state has energy E.What is the energy of the same molecule in its l = 2 quantum state?

Question

Quizplus · Accepted Answer

The energy levels of a rotating diatomic molecule are given by the formula $E_l = \frac{l(l+1)\hbar^2}{2I}$, where $l$ is the quantum number, $\hbar$ is the reduced Planck's constant, and $I$ is the moment of inertia of the molecule. For $l = 1$, the energy is $E_1 = \frac{1(1+1)\hbar^2}{2I} = \frac{2\hbar^2}{2I}$. For $l = 2$, the energy is $E_2 = \frac{2(2+1)\hbar^2}{2I} = \frac{6\hbar^2}{2I}$. Thus, $E_2 = 3E_1$, making the correct answer 3E.

A Rotating Diatomic Molecule in Its L = 1 Quantum