Chapter 8, Problem 8A.4BE

Interpretation Introduction

Interpretation:

The $\text{3s}$ radial wave function has three extrema in its amplitude has to be shown and the position of two extrema has to be located.

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 $\text{3s}$ orbital of hydrogen atom is shown below.

    $R_{3,0}=\frac{1}{{243}^{1/2}}{\left(\frac{1}{a_{\text{ο}}}\right)}^{3/2}\left(6-\frac{6r}{a_{\text{ο}}}+{\left(\frac{r}{a_{\text{ο}}}\right)}^2\right){\text{e}}^{-r/2a_{\text{ο}}}$