Chapter 8, Problem 8A.5BE

(i)

Interpretation Introduction

Interpretation:

The radius where the radial distribution function of hydrogen atom will be $50\%$ of its maximum value has to be calculated.

Concept introduction:

Radial distribution function is the probability of finding an electron at a distance $r$ from the nucleus.  The surface where the radial probability density becomes zero is known as the radial node.  The radial distribution function of the ground state of hydrogen atom is shown below.

    $\text{R}\left(\text{r}\right)\text{=}\frac{\text{2}}{{\text{a}}_{\text{ο}}^{\text{3}/\text{2}}}{\text{e}}^{\text{-r}/{\text{a}}_{\text{ο}}}$

(ii)

Interpretation Introduction

Interpretation:

The radius where the radial distribution function of hydrogen atom will be $75\%$ of its maximum value has to be calculated.

Concept introduction:

Refer to part (i).