Chapter 10, Problem 1CQ

To determine

To Explain:The energies in the lower band and upper bandis roughly equal to that of the $n=1$ and $n=\text{2}$ atomic states respectively

Explanation of Solution

Introduction:

An electron’s kinetic energy for $n=1$ or $n=\text{2}$ atomic state in an individual well is a fixed number.There exists two atomic states at $n=1$ or $n=\text{2}$ in case of two wells.

The separation is large for an electron at molecular state $n=\text{2}$ which converges to subtraction or addition or of two $n=\text{2}$ atomic states. Since kinetic energy of two $n=\text{2}$ atomic states is same, energy of linear combination of these states will be same as that of $n=\text{2}$ atomic state. The separation is large for an electron at molecular state $n=1$

Conclusion:

The energy of molecular state and energy of $n=1$ atomic state is roughly equal.