Answer to Question #253189 in Physics for Jashwanth

Question

A metal with body centered cubic (bcc) structure shows the first (i.e. smallest angle) diffraction peak at Bragg angle of θ=30∘. The wavelength of X-ray used is 2.1Å. The volume of primitive unit cell of the metal is :

26.2(Å3)

13.1(Å3)

9.3(Å3)

4.6(Å3)

Answer 1

Determine the length of the side of the primitive unit cell with Bragg's law:

$$\lambda=2d\sin\theta,\\\space\\ d=\frac\lambda{2\sin\theta},\\\space\\ V=d^3=\bigg(\frac\lambda{2\sin\theta}\bigg)^3=9.3\text{ Å}^3.$$