If a metal crystallises in a face-centred cubic structure with metallic radius of 25 pm, the number of unit cells in `1 cm^(3)` of lattice is :

Options

A. `2.828 xx 10^(28)`
B. `1.414xx10^(28)`
C. `1.414xx10^(24)`
D. `2.828xx 10^(24)`

Answer

D

Explanation

`asqrt(2)=4r`
`axx 1.414=4xx25`
`a=70.72` pm `=70.72xx10^(-10)` cm
Volume of one unit cell `=a^(3)=(70.72xx10^(-10))^(3)`
`=3.536xx10^(-25) cm^(3)`
Number of unit cells in `1 cm^(3)` lattice `=(1)/(3.536xx10^(-25))`
`=2.828xx10^(24)`