For a simple cubic system,find the ratio of t | vedclass

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Question

(A) The interplanar distance $d$ for a cubic system is given by the formula: $d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}$For the planes $(100)$,$(110)

Vedclass · Accepted Answer

$1 : 1/\sqrt{2} : 1/\sqrt{3}$

Vedclass · Answer

(A) The interplanar distance $d$ for a cubic system is given by the formula: $d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}$For the planes $(100)$,$(110)$,and $(111)$,the distances are:$d_{100} = \frac{a}{\sqrt{1^2 + 0^2 + 0^2}} = a$$d_{110} = \frac{a}{\sqrt{1^2 + 1^2 + 0^2}} = \frac{a}{\sqrt{2}}$$d_{111} = \frac{a}{\sqrt{1^2 + 1^2 + 1^2}} = \frac{a}{\sqrt{3}}$Therefore,the ratio $d_{100} : d_{110} : d_{111}$ is:$a : \frac{a}{\sqrt{2}} : \frac{a}{\sqrt{3}} = 1 : \frac{1}{\sqrt{2}} : \frac{1}{\sqrt{3}}$

For a simple cubic system,find the ratio of the interplanar distances between the $(100)$,$(110)$,and $(111)$ planes.

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