If the atoms of an element have the radius r, then in a primitive cubic unit cell, calculate
(a) the length of the face diagonal. (b) the lenth of the body diagonal.

Explanation

In the Fig, AC is the face diagonal and CD is the body diagonal.
` Delta ABC` , right angled at B.
` AC = sqrt(AB^(2) +BC^(2)) = sqrt((2r)^(2) + (2r)^(2)) = sqrt(8r) = 2sqrt2 r,`
In ` Delta ACD ,` right angled at A,
` CD = sqrt(AC^(2) + AD^(2)) = sqrt((2sqrt3 r)^(2) + (2r)^(2)) = sqrt(12r^(2)) = 2 sqrt3 r`
` (##PR_CHE_V01_XII_C01_E17_001_S01.png" width="80%">