Chapter 5, Problem 6P

Using Table 5.2, write down the mathematical expression for the $\text{2}{p}_x$ wave function for an electronically excited H atom. Estimate the probability of finding the $\text{2}{p}_x$ electron if you look in a cubical box of volume of $0.\text{8 }{\left(\text{pm}\right)}^{\text{3}}$ centered at a distance of $0.\text{5}00\times \text{1}{0}^{-\text{1}0}\text{m}$ in the $\theta =\pi \text{/}2$ , $\varphi =0$ direction. Does this probability change as you change $\varphi$ ? At what $\varphi$ angles is the probability of finding the electron smallest and at what $\varphi$ angles is the probability the largest? (Note that $\varphi =2\pi$ is the same location as $\varphi =0$ , so don’t double count.)