Chapter 7, Problem 7D.4E

Interpretation Introduction

Interpretation:

The degeneracy for given level 4 and the values of ${\text{m}}_{\text{l}}$ have to be identified.

Concept Introduction:

Orbital Angular Momentum (l): It helps to differentiate different shapes of orbitals for given n. For a given n, there are n different shapes of orbitals are present and are denoted as l. Angular momentum quantum number is also known as Azimuthal quantum number. The possible values of angular momentum quantum number between $\text{0}\text{and}\text{(n-1)}$. If the n is $3$, then l values are $\text{0,}\text{1}\text{and }\text{2}$ and $m_l$ values are $\text{0,}\underset{\_}{\text{+}}\text{1}\text{and }\underset{\_}{\text{+}}\text{2}$.

The energy of particle with given quantum number is calculated by using the following expression.

$\begin{array}{l}\text{E =}\frac{{\text{J}}^{\text{2}}}{\text{2}{\text{mr}}^{\text{2}}}\boxed{\begin{array}{l}\text{here,}\text{E}\text{=}\text{energy}\\ \text{m}\text{=}\text{mass of particle}\\ \text{r}\text{=}\text{distance}\\ \text{J}\text{=}\text{rotational quantum number}\end{array}}\\ \end{array}$