1.

Calculate the ratio of separation between successive (1 0 0), (11 0) and (111) lattice planes in a cubic cell.

Answer»

Solution :We have,
`d=a/sqrt(h^(2) + K^(2) + l^(2))`
THUS, `d_(100) = a/sqrt(1^(2) + 0^(2) + 0^(2)) =a`
`d_(110) = a/sqrt(1^(2) + 1^(2) + 0^(2)) = a/sqrt(2)`
and `d_(111) = a/sqrt(1^(2) + 1^(2) + 1^(2)) = a/sqrt(3)`
Hence, `d_(100): d_(110): d_(111) =a:a/sqrt(2) : a/sqrt(3) =1: 1/sqrt(2) : 1/sqrt(3)`


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