Chapter 41, Problem 10CQ

To determine

The reason that the $1s$ radial probability density is maximum at $r=a_B$ and is zero at $r=0$.

Introduction: The radial probability density of the hydrogen atom is a function of a distance from the nucleus.

Formula to calculate the $1s$ radial probability density for a hydrogen atom is,

$\text{Prob}\left(r_{\min }\le r\le r_{\max }\right)={{\displaystyle {\int }_{r_{\max }}^{r_{\min }}{r}^2\left|R_{1s}\left(r\right)\right|}}^{2}dr$

• $\left|R_{1s}\left(r\right)\right|$ is the radial wave function.

• $r$ is the radial distance from the nucleus.