In a rotating atomic nucleus shaped like a football the quantized rotational energy levels have angular momentum values l = 0,2,4,6,8,etc.Given that the energy of each level is equal to a constant times l $\times$ (l + 1),calculate the ratio of the l = 4 to l = 2 energy levels.
A)4.0
B)0.3
C)2.0
D)0.5
E)3.3

Question

Quizplus · Accepted Answer

The energy of each level is proportional to $l(l + 1)$. For $l = 4$, the energy is proportional to $4 \times 5 = 20$. For $l = 2$, the energy is proportional to $2 \times 3 = 6$. The ratio of the $l = 4$ to $l = 2$ energy levels is $20/6 = 10/3 = 3.3$.

In a Rotating Atomic Nucleus Shaped Like a Football the Quantized