The cubic unit cell of a metal (molar mass = 63.55g `mol^(-1)`) has an edge length of 362 pm. Its density is 8.92 g `cm^(-3)`. The type of unit cell is

Options

A. Primitive
B. Face centred
C. Body centred
D. End centred

Answer

b

Explanation

`M = 63.55 gmol^(-1), a = 362 pm = 362xx10 ^(-10)m`
`d = 8.92 g cm^(-3), N = 6.022 x 10^(23)`
`d=(MZ)/(N_(o)a^(3))`
`8.92=(63.55xxZ)/( 6.022 x 10^(23)xx(362xx10^(-10))^(3))`
`z=(8.92 xx6.022 x 10^(23)xx(362xx10^(-10))^(3))/(63.55)`Since, the number of atoms per unit cell (Z)=4, the metal has face centred unit cell.