In the cubic lattice given below, the three distances between the atoms `A-B, A-C`, and `A-G` are, respectively,

Options

A. `a, sqrt2a, sqrt3a`
B. `a, sqrt3a, sqrt2a`
C. `(a)/(2), (a)/(sqrt2), (sqrt3a)/(2)`
D. `a, (sqrt3a)/(2), sqrt2a`

Answer

A

Explanation

i. Edge length `= AB = AD = BC = CD = a`
ii. AC `= sqrt((AB^(2)) + (BC)^(2)) = sqrt((a^(2)) + a^(2)) = sqrt(2)a`
iii. AG `= sqrt((AC^(2)) + (CG)^(2)) = sqrt(2a^(2) + a^(2)) = sqrt(3)a`