Question

Certain planes of a crystal of halite have a spacing of 0.399 mm. The crystal is irradiated by a beam of x-rays. First order constructive interference occurs when the beam makes an angle of 20

Answer 1

The condition for diffraction maxima at a crystal lattice is, \(2 d \sin \theta=m \lambda\)

Here, \(d\) is the slit seperation, \(\theta\) is the angle of diffraction, \(m\) is the order and \(\lambda\) is the wavelength

$$ \begin{aligned} \lambda &=\frac{2 d \sin \theta}{m} \\ &=\frac{2(0.399 \mathrm{~nm}) \sin 20}{1} \\ &=0.27 \mathrm{~nm} \end{aligned} $$

The diffraction angle at which the second order is observable is,

$$ \begin{aligned} \theta &=\sin ^{-1}\left(\frac{m \lambda}{2 d}\right) \\ &=\sin ^{-1}\left(\frac{(2)(0.27 \mathrm{~nm})}{2(0.399 \mathrm{~nm})}\right) \\ &=43^{\circ} \end{aligned} $$