Chapter 11, Problem 11.91E

Interpretation Introduction

Interpretation:

The value of $\langle r\rangle$ for ${\Psi }_{1s}$ and the reason as to why $\langle r\rangle$ is not equal to $0.529\stackrel{\circ }{\text{A}}$ for ${\Psi }_{1s}$ are to be stated.

Concept introduction:

For calculating the average value, the operator is taken as multiplication in between the two wave functions, the product of the wave functions is integrated over the entire limits. It is expressed by the equation as given below.

${\displaystyle \underset{0}{\overset{\infty }{\int }}{\Psi }_m\widehat{x}{\Psi }_n}$

Where, ${\Psi }_m$ and ${\Psi }_n$ are two different wave functions and $\widehat{x}$ is the operator.