An element (atomic mass `= 100 g//mol`) having bcc structure has unit cell edge 400 pm .Them density of the element is

Options

A. `2.144 g//cm^(3) `
B. `7.289 g//cm^(2)`
C. `5.188 g//cm^(2)`
D. `10.367 g//cm^(3)`

Answer

C

Explanation

Atomic mass of element =100 g/mol
Cell edge = 400 pm `= 400 xx 10^(-12)=4 xx 10^(-10)` and number of atoms in BCC (Z)=2 .
As the atomic mass of the metal is 100 gm/mol, therefore mass of each atom (m) `=(100)/(6.023xx10^(23))=16.6 xx 10^(-23) g ` .
The volume of unit cell `=(4 xx 10^(-8))^(3)= 64xx10^(-24)cm^(3)` .
And mass of unit cell `=Z xx m `
`= 2 xx (16.6 xx 10^(-23))= 33.2 xx 10^(-23)`g .
Therefore density of element `=("Mass of unit cell ")/("Volume of unit cell ")`
`=(33.2 xx 10^(-23))/(64 xx 10^(-24))~~5.188 g//cm^(3)` .