##\epsilon = k\theta_r J (J+1)##

where k = boltzmann constant, and J is the rotational quantum number.

The degeneracy is 2J+1.

Let's assume the constant quantity ##k\theta_r## = 1 and that the energy level is 2Joules.

Thus 2 = J(J+1) => J = +/- 1. The only physical solution is J = 1.

Thus degeneracy is 3 for J = 1.

Here is where I am confused. I thought degeneracy is when you have an energy level that DOES NOT consist of a unique set of quantum numbers. So if the degeneracy is 3, doesn't that mean I should have 3 different J values that can give me an energy level of 2 Joules?

I think I am understanding this incorrectly, because for 2 joules, the only solution is J = 1. Doesn't that mean the degenearcy is 1?