A crystal is irradiated with x-rays with a wavelength of $0.120 \mathrm {~nm}$. The atomic planes in the crystal are separated by $0.21 \mathrm {~nm}$. At what angles of incidence with respect to the normal will the $x$-rays reflect from the crystal?
A) only $73 ^ { \circ }$
B) only $55 ^ { \circ }$
C) $73 ^ { \circ } , 55 ^ { \circ } , 31 ^ { \circ }$
D) only $73 ^ { \circ }$ and $31 ^ { \circ }$

Question

Quizplus · Accepted Answer

The angles of incidence can be found using Bragg's law, $n\lambda = 2d\sin\theta$, where $\lambda$ is the wavelength of the x-rays, $d$ is the distance between the atomic planes, and $n$ is an integer representing the order of the reflection. Given $\lambda = 0.120 \, \mathrm{nm}$ and $d = 0.21 \, \mathrm{nm}$, we can solve for $\theta$ for different values of $n$. For $n=1$, $n=2$, and higher, we find angles that satisfy the equation, indicating multiple angles of reflection are possible, including $73^\circ$, $55^\circ$, and $31^\circ$.

A Crystal Is Irradiated with X-Rays with a Wavelength Of 0.120