Chapter 16, Problem 16.10E

Interpretation Introduction

Interpretation:

The maximum splitting of the ${}^2{\text{P}}_{3/2}$ state of the hydrogen atom due to earth’s magnetic field, having a value of $0.6$ gauss is to be stated.

Concept Introduction:

The change in energy $\left(\Delta E\right)$ of the state depends on the strength of the magnetic field $\left(B\right)$ and the z-component quantum number $\left(M_L\right)$ in the presence of magnetic field. The expression for the change in energy $\left(\Delta E\right)$ is written below.

$\Delta E={\text{μ}}_B\cdot M_L\cdot B$

The value of $\left(M_L\right)$ can be positive, negative or zero. Hence, the change in energy $\left(\Delta E\right)$ can be positive, negative or zero. The change in energy $\left(\Delta E\right)$ of the state is equal to the amount of splitting.