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At what angles with X-rays of wavelength $1.542\times 10^{-10}m$ undergo first order and second order reflections by planes separated by $3.5\times 10^{-10}m$?

$\begin{array}{1 1}12.73^{\large\circ},26.14^{\large\circ}\\22.73^{\large\circ},16.14^{\large\circ}\\32.73^{\large\circ},36.14^{\large\circ}\\42.73^{\large\circ},46.14^{\large\circ}\end{array} $

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Here $\lambda=1.542\times 10^{-10}m$
$d=3.5\times 10^{-10}m$
According to Bragg's equation
$2d\sin \theta=n\lambda$
$\sin \theta=\large\frac{n\lambda}{2d}$
For $n=1$
$\sin \theta=\large\frac{1\times 1.542\times 10^{-10}}{2\times 3.5\times 10^{-10}}$
$\Rightarrow 0.2203$
$\Rightarrow \theta=12.73^{\large\circ}$
For $n=2$
$\sin \theta=\large\frac{2\times 1.542\times 10^{-10}}{2\times 3.5\times 10^{-10}}$
$\Rightarrow 0.4406$
$\Rightarrow \theta=26.14^{\large\circ}$
answered Jul 31, 2014 by sreemathi.v

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