A metal having atomic mass 50 g `"mol"^(-1)` has a body centred cubic crystal structure.
The density of the metal is 596 g `"cm"^(-1)`. Find the volume of unit cell ?

Explanation

Atomic mass of metal, `M=50"g mol"^(-1)`
`d=5.96"g cm"^(-3)`
`N_(A)=6.023xx10^(23)"mol"^(-1)`
z (b.c.c. Lattice) = 2
As `d=(ZxxM)/(a^(3)xxN_(A))`
`rArra^(3)=(ZxxM)/(d xxN_(A))`
`=(2xx50"g mol"^(-1))/(5.96"g cm"^(-3)xx6.023xx10^(23)"mol"^(-1))`
`a^(3)=2.79xx10^(-23)"cm"^(3)`
Volume `(a^(3))` is `2.79xx10^(-23)"cm"^(3)`.