When scattering 0.328 nm x-rays off a crystal, the first interference maximum occurs at an angle of 23.0 degrees relative to the crystal surface. At what angle does the second maximum occur?
A) 51.4°
B) 46.0°
C) 34.5°
D) There is no second maximum.

Question

Quizplus · Accepted Answer

The angle for the second maximum can be found using Bragg's law, $n\lambda = 2d\sin(\theta)$, where $n$ is the order of the maximum, $\lambda$ is the wavelength of the x-rays, $d$ is the spacing between the planes in the crystal, and $\theta$ is the angle of incidence. Given that the first maximum occurs at 23.0 degrees, we can solve for $d$ using $n=1$. For the second maximum ($n=2$), we solve for $\theta$ using the same equation with the found value of $d$. The angle that satisfies this condition for the second maximum is larger than the first, and among the given options, 51.4° is the only one that is plausible and follows the trend of increasing angle with increasing order of maximum.

When Scattering 0