Question

An X-ray scattering experiment is performed on a crystal whose atoms form planes separated by 0.440 nm. Using an X-ray source of wavelength 0.548 nm, what is the angle (with respect to the planes in question) at which the experimenter needs to illuminate the crystal in order to observe a first-order maximum?

Answer 1

To observe 1st order maximum, using Braggs consition

$2d\sin\theta=n\lambda\Rightarrow \sin\theta=\frac{n\lambda}{2d}=\frac{1\times0.548\times10^{-9}}{2\times0.440\times10^{-9}}=0.623\\ \Rightarrow \theta=\sin^{-1}(0.623)=38.5^o$