Chapter 2, Problem 2F.20E

Interpretation Introduction

Interpretation:

The normalization constant $\left(\text{N}\right)$ for the below hybrid orbital has to be determined.

  $h_1=\text{s}+{\text{p}}_x+{\text{p}}_y+{\text{p}}_z$

Concept Introduction:

Hybrid orbitals are formed by the mixture of atomic orbitals overlapped on each other of different proportions. The four hybrid orbitals of ${\text{sp}}^3$ that are formed by the linear combination of four atomic orbitals are denoted as $h$ and are given as:

$\begin{array}{l}{h}_1=\text{s}+{\text{p}}_x+{\text{p}}_y+{\text{p}}_z\\ h_2=\text{s}-{\text{p}}_x-{\text{p}}_y+{\text{p}}_z\\ h_3=\text{s}-{\text{p}}_x+{\text{p}}_y-{\text{p}}_z\\ h_4=\text{s}+{\text{p}}_x-{\text{p}}_y-{\text{p}}_z\end{array}$

The two orbitals are orthogonal when there is no interaction between the atomic electrons and another atom. The addition of probabilities to 1 is defined as normalization of hybrid orbitals.