Answer to Question #253188 in Physics for Jashwanth

Question #253188

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)


1
Expert's answer
2021-10-19T15:15:47-0400

Find the 'period' of the diffraction grating - the side of the primitive unit cell using Bragg's law:


λ=2dsinθ, d=λ2sinθ, V=d3=(λ2sinθ)3=9.3 A˚3.\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.


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