1CQ The left diagram in FIGURE 10.1 ... [FREE SOLUTION]

Chapter 10: 1CQ (page 413)

The left diagram in FIGURE 10.1 might represent a two atom crystal with two bands. Basing your argument on the kinetic energy inside either individual well, explain why both energies in the lower band should be roughly equal to that of the $n = 1$ atomic state and why both energies in the upper should roughly equal that of the $n = 2$ atomic state

Short Answer

Expert verified

Both energies in the lower band should be roughly equal to that of $n = 1$ atomic state because the two $n = 2$ atomic states have the same kinetic energy, the linear combination of these states will also have the same energy as of $n = 2$ state.

Step by step solution

Understanding the Concept

For an individual well, the kinetic energy of an electron for $n = 1$ atomic state or $n = 2$ atomic state is a fixed number. When there are two wells, there are two atomic states at $n = 1$ or $n = 2$ .

Understanding Why Kinetic Energy is the same

An electron at $n = 2$ molecular state has large separation, and so converges to the addition or subtraction of the two $n = 2$ atomic states. Since the two $n = 2$ atomic states have the same kinetic energy, the linear combination of these two states will also have the same energy as that of $n = 2$ atomic state.

Hence, an electron at $n = 1$ molecular state has small separation, and so the energy of the molecular state is only roughly equal to energy for $n = 1$ atomic state.