In body-centred cubic lattice given below, the three disntances `AB, AC`, and `AA'` are

Options

A. `a, sqrt2a, (sqrt3a)/(2)`
B. `a,(sqrt3a)/(2), sqrt2a`
C. `(sqrt3a)/(2), sqrt2a, a`
D. `a, (a)/(sqrt2a), (sqrt3a)/(2)`

Answer

A

Explanation

i. Edge length `= AB = AD = BC = CD = a`
ii. `AC = sqrt(2)a`
iii. `AG` (body diagonal) `= sqrt(3)a`
Therefore `AA' = AG//2 = (sqrt(3))/(2)a`