An x-ray beam of wavelength 3 *10^-11 m is incident on a calcite crystal of lattice spacing 0.3 nm.The smallest angle between crystal planes and the x-ray beam which will result in constructive interference is: A)2.9° B)5.7° C)12° D)23° E)none of these

Question

Quizplus · Accepted Answer

The smallest angle for constructive interference in a crystal is given by Bragg's law: $n\lambda = 2d\sin\theta$, where $n$ is the order of reflection (here, $n=1$ for the first order), $\lambda$ is the wavelength of the x-ray, $d$ is the lattice spacing, and $\theta$ is the angle between the x-ray beam and the crystal planes. Rearranging for $\theta$, we get $\theta = \sin^{-1}\left(\frac{\lambda}{2d}\right)$. Given $\lambda = 3 \times 10^{-11}$ m and $d = 0.3 \times 10^{-9}$ m (or 0.3 nm), we find $\theta = \sin^{-1}\left(\frac{3 \times 10^{-11}}{2 \times 0.3 \times 10^{-9}}\right) = \sin^{-1}\left(\frac{1}{20}\right)$, which is approximately 2.9°.

An X-Ray Beam of Wavelength 3 *10-11 M Is Incident

An X-Ray Beam of Wavelength 3 *10^-11 M Is Incident