The ratio of inner planar distancess of three types of planes d100,d110,d111for simple cubic lattice are

The ratio of inner planar distancess of three types of planes $(d_{100}, d_{110}, d_{111})$ for simple cubic lattice are

A
$1 : \frac{1}{\sqrt{2}} : \frac{1}{\sqrt{3}}$
B
$\frac{1}{\sqrt{3}} : \frac{1}{\sqrt{2}} : 1$
C
$\sqrt{3} : \sqrt{2} : 1$
D
$1 : \sqrt{2} : \sqrt{3}$

Solution:

$d_{hkl} = \frac{a}{{(h^{2} + k^{2} + l^{2})}^{1 / 2}}$
hence $d_{100} = 1, d_{110} = \frac{1}{\sqrt{2}}, d_{111} = \frac{1}{\sqrt{3}}$

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