Chapter 28, Problem 1CQ

To determine

To explain: The reason, why ${\theta }_1$ increases, decreases, or remains the same when the crystal volume is reduced.

Answer to Problem 1CQ

The reason why ${\theta }_1$ increases, decreases, or remains the same when the crystal volume r is reduced has been explained.

Explanation of Solution

Consider the expression of Bragg condition.

$2d\cos {\theta }_1=m\lambda$ (1)

Here,

$d$ is the spacing between the atomic planes,

${\theta }_1$ is the angle of incident,

$m$ is order of diffraction, and

$\lambda$ is the wavelength.

The crystal has been compressed which means the spacing between the atomic planes decreases. $d$ decreases resulting in an increase in the value of $\cos {\theta }_1$ . When $\cos {\theta }_1$ increases, the value of ${\theta }_1$ should decrease.

Conclusion:

Thus, the reason why ${\theta }_1$ increases, decreases, or remains the same when the crystal volume is reduced has been explained.