An element crystallises in a face -centred cubic (fcc) unit cell with cell edge a. The distance between the centre of two nearest octahedral voids in the crystal lattice is ::

Options

A. `sqrt(2)`a
B. `(a)/(sqrt(2))`
C. a
D. `(3)/(2)`a

Explanation

`cos theta = (1)/(sqrt(3))`
The distance of corner atom tetrahedral void along body diagonal = Component along any side = `(sqrt(2) a)/(4 ) xx (1)/(sqrt(3)) = (a)/(4)`
`(a - (a)/(4) - (a)/(4)) = (a)/(2)`