The first order reflection of a beam of X-rays of wavelength $1.54 \circ A$ from the $(100)$ face of a crystal of the simple cubic type occurs at an angle of ${11.29}^{\circ}$ . Calculate the length of the unit cell.

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Solution

Applying Bragg's equation,
$2 d sin θ = n λ$
Given, $θ = {11.29}^{\circ}, n = 1, λ = 1.54 \circ A = 1.54 \times 10^{- 8} c m$
$d = \frac{1.54 \times 10^{- 8}}{2 \times sin {11.29}^{\circ}} = \frac{1.54 \times 10^{- 8}}{2 \times 0.1957} = 3.93 \times 10^{- 8} c m$
$d_{h k l} = \frac{a}{\sqrt{h^{2} + k^{2} + l^{2}}} = a$
$a = 3.93 \times 10^{- 8} c m =$ length of the unit cell.

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The first order reflection of a beam of X-rays of wavelength 1.54∘A from the (100) face of a crystal of the simple cubic type occurs at an angle of 11.29∘. Calculate the length of the unit cell.

Applying Bragg's equation,2d sinθ=nλGiven, θ=11.29∘,n=1,λ=1.54∘A=1.54×10−8cmd=1.54×10−82×sin11.29∘=1.54×10−82×0.1957=3.93×10−8cmdhkl=a√h2+k2+l2=aa=3.93×10−8cm= length of the unit cell.

The first order reflection of a beam of X-rays of wavelength $1.54 \circ A$ from the $(100)$ face of a crystal of the simple cubic type occurs at an angle of ${11.29}^{\circ}$ . Calculate the length of the unit cell.