Question

Edge length of a cubic is 400pm. Its body diagonal is

A]566pm B]600pm

C]500pm D]693pm

Answer 1

Option: D)

Length of Body diagonal = √3 × edge length of the cube.
So, length of Body diagonal =√3 × 400= 693 pm.

Answer 2

Answer : The body diagonal of a cubic unit cell is, 693 pm

Solution :

The unit cell is simple cubic unit cell.

The relation between the edge length and body diagonal of a cubic unit cell is,

$d=\sqrt{3}\times a$

where,

d = body diagonal of a cubic unit cell = ?

a = edge length of a cubic unit cell = 400 pm

Now put all the given values in the above relation, we get the body diagonal of a cubic unit cell.

$d=\sqrt{3}\times (400pm)$

$d=692.82pm=693pm$

Therefore, the body diagonal of a cubic unit cell is, 693 pm