Chapter 21, Problem 21.65SP

Interpretation Introduction

Interpretation:

The reason for softer nature of copper than iron has to be explained using band energy.

Concept introduction:

Band theory:

Molecular orbital theory deals molecules with few atoms whereas cubic metallic crystal contains more atoms.  When atomic orbital combines to form molecular orbital, the number of molecular orbital is same as number of atomic orbital.  Therefore, number of molecular orbital of ${\text{Na}}_{\text{3}}$ is three, number of molecular orbital of ${\text{Na}}_4$ is four and so on.

In a cubic crystal of metal larger number of metal atoms forms molecular orbital in which electrons are delocalized throughout the crystal.  The energy difference between molecular orbitals in metal crystal decreases as metal atom increases which leads to merging of molecular orbital to form continuous energy band.  Thus, molecular orbital theory for metals are known as band theory.