A metal (atomic mass = 50 ) has a body centred cubic crystal structure. If the density of the metal is 5.96 g `cm^(-3)`, calculate the volume of the unit cell.

Explanation

If a is the edge length of the unit cell, then volume of unit cell , `V = a^3`
Density of unit cell, `rho = 5.96 g cm^(-3)`
Atomic mass of the metal , `M = 50 g mol^(-1)`
No. of atoms per unit cell, `Z = 2 ("bcc")`
Now, Density = `(Z xx M)/(a^3 xx N_A)`
or `" " rho = (Z xx M)/(V xx N_A)`
or `" " V = (Z xx M)/(rho xx N_A)`
`:. " Volume " = (2 xx (50 g mol^(-1)))/((5.96 g cm^(-3)) xx (6.022 xx 10^(23) mol^(-1)))`
`=27.86 xx 10^(-24) cm^(3)`.