Chapter 12, Problem 73E

Interpretation Introduction

Interpretation:Value of ${\psi }_{2p_{\text{z}}}{}^2$ at $0°$ and at $90°$ is to be calculated.

Concept introduction:The square of wave function ${\psi }^2$ is used to denote region of maximum probability around the particular orbital. It essentially represents the region that has highest probability to locate an electron. For instance if the different location is to be compared on the basis of the relative probability to locate electron then ratio can be found as follows:

  $\frac{{\left[\psi \left(r_1,{\theta }_1,{\varphi }_1\right)\right]}^{2}dv}{{\left[\psi \left(r_2,{\theta }_2,{\varphi }_2\right)\right]}^{2}dv}=\frac{N_1}{N_2}$

Where,

• $\psi \left(r_1,{\theta }_1,{\varphi }_1\right)$ denotes wave function of location 1.
• $\psi \left(r_2,{\theta }_2,{\varphi }_2\right)$ denotes wave function of location 2.
• $N_1\text{/}{N}_2$ denotes ratio of probabilities at two locations