Chapter 28, Problem 1CQ

To determine

Whether the diffraction angle increase or decrease when the crystal is compressed

Answer to Problem 1CQ

The diffraction angle decrease decreases

Explanation of Solution

Write the Bragg’s condition for the constructive interference of first order x-ray diffraction.

    $2d\cos {\theta }_m=m\lambda$

Here, $d$ is the interplanar distance, ${\theta }_m$ is the angle with which the x-rays are incident on the plane, $\lambda$ is the wavelength of x-rays and $m=1,2,\mathrm{3...}$

Conclusion:

The compressing of the crystal leads to a decrease in the interplanar distance, $d$ of the crystal.

From Bragg’s condition, as $d$ decreases, $\cos {\theta }_m$ increases so that the left hand side of the equation remains constant. Also, $\cos \theta$ value decreases from $1$ to $0$ as $\theta$ increases from $0°$ to $90°$ Therefore, when the crystal is compressed, the diffraction angle $\theta$ also decreases.