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(C) According to Bragg's equation,$n \lambda = 2 d \sin 	heta$. For the $(100)$ plane,the interplanar spacing is $d_{100} = \frac{a}{\sqrt{1^2+0^2+0^

Vedclass · Accepted Answer

$30$

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(C) According to Bragg's equation,$n \lambda = 2 d \sin 	heta$. For the $(100)$ plane,the interplanar spacing is $d_{100} = \frac{a}{\sqrt{1^2+0^2+0^2}} = a = 6 \mathring{A}$. Given $n=2, \lambda=3 \mathring{A}, 	heta=30^{\circ}$,the equation holds: $2 	imes 3 = 2 	imes 6 	imes \sin 30^{\circ} = 6 	imes 1 = 6$. For the $(200)$ plane,the interplanar spacing is $d_{200} = \frac{a}{\sqrt{2^2+0^2+0^2}} = \frac{a}{2} = \frac{6}{2} = 3 \mathring{A}$. For the first order diffraction $(n=1)$ with the same wavelength $\lambda = 3 \mathring{A}$,we have $1 	imes 3 = 2 	imes 3 	imes \sin 	heta$. $3 = 6 \sin 	heta$ $\Rightarrow \sin 	heta = 0.5$ $\Rightarrow 	heta = 30^{\circ}$.

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