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The first order reflection of a beam of X-rays of wavelength $1.54A^{\large\circ}$ from the (1 0 0) plane of a crystal of the simple cubic type occurs at an angle of $11.29^{\large\circ}$.Calculate the length of the unit cell.

$\begin{array}{1 1}3.933\times 10^{-8}\\2.933\times 10^{-8}\\1.933\times 10^{-8}\\0.933\times 10^{-8}\end{array} $

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We have $n\lambda =2d\sin \theta$
$1\times (1.54 \times 10^{-8})=2\times d \times \sin 11.29$
$\Rightarrow d=3.933\times 10^{-8}cm$
Further $d=\large\frac{a}{\sqrt{h^2+k^2+l^2}}$
$3.933\times 10^{-8}=\large\frac{a}{1^2+0^2+0^2}$
$\therefore a=3.933\times 10^{-8}$ cm
answered Aug 1, 2014 by sreemathi.v

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