Diamond has face-centred cubic lattice. There are two atoms at `(0, 0, 0)` and `((a)/(4), (a)/(4), (a)/(4))` coordinates. The ratio of the carbon-carbon bond distance to the edge of the unit cell is

Options

A. `sqrt((3)/(16))`
B. `sqrt((1)/(4))`
C. `(1)/(4)`
D. `(1)/(sqrt2)`

Answer

A

Explanation

a. Distance between `(0, 0, 0)` and `((a)/(4), (a)/(4), (a)/(4)) = 2r`
`implies 2r = (sqrt3a)/(4)`
`implies (2r)/(a) = sqrt((3)/(16))`, where `2r =` bond distance