How do the spacings of the three planes ( 100), ( 101) and ( 111) of simple cubic lattice vary ?

Explanation

Applying the formula
`d_(hkl) = (a)/(sqrt(h^2 + k^2 +1^2))`
`d_((100)) = (a)/(sqrt(1^2 + 0 + 0)) = a`
`d_((110)) = (a)/(sqrt(1^2 + 1^2 + 0)) = (a)/(sqrt2)`
`d_((111)) = (a)/(sqrt(1^2 +1^2 +1^2)) = (a)/(sqrt3)`
Thus `d_((100) : d_((110)) : d_((111)) = 1 : 1// sqrt2 : 1// sqrt3`
`= 1 : 0.707 : 0.577`