Chapter 7, Problem 7D.3E

Interpretation Introduction

Interpretation:

The angular momentum quantum number for given system with given magnitude angular momentum value has to be calculated.

Concept Introduction:

The energies are quantized for particle in sphere and are generally expressed as follows,

$\begin{array}{c}\text{E}=l\left(l+1\right)\frac{{\hslash }^2}{2m{r}^2}\\ l=0,1,2,\mathrm{...}\\ m_l=0,\underset{\_}{+}1,\underset{\_}{+}2,\mathrm{...}\\ here,l=orbitalangularmomentum\text{quantum number}\\ m=mass\\ r=spheresurfaceradius\\ \hslash =\frac{h}{2\pi },hisPlanck\text{'}s\text{constant}\end{array}$

The angular momentum magnitude value is obtained by using following formula.

$\begin{array}{c}J=l\left(l+1\right){\hslash }^2\\ l=0,1,2,\mathrm{...}\\ here,J=orbitalangularmomentummagnitude\\ \hslash =\frac{h}{2\pi },hisPlanck\text{'}s\text{constant}\end{array}$