Chapter 8, Problem 8A.3ST

Interpretation Introduction

Interpretation:

The most probable distance of a $2\text{s}$ electron from the nucleus in a hydrogenic atom 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 $2\text{s}$ orbital of hydrogen atom is shown below.

    $R_{2,0}=\frac{1}{8^{1/2}}{\left(\frac{1}{a_{\text{ο}}}\right)}^{3/2}\left(2-\frac{r}{a_{\text{ο}}}\right){\text{e}}^{-r/2a_{\text{ο}}}$