Question

An element crystallizes in bcc structure. The edge length of its unit cell is $288$ pm. If the density of the crystal is $7.2$ g cm${}^{-3}$. what is the atomic mass (in g/mol) of the element?

• A. $51.8$
• B. $103.6$
• C. $25.9$
• D. $207.2$

Answer 1

The correct option is A $51.8$

The expression for the density of the unit cell is given below:

$d=\frac{n\times M}{a^3\times N_A}$

Given that,

$a=288$ pm $=288\times {10}^{-10}$ cm

$d=7.2$ g cm${}^{-3}$

$n=2$

Substituting values in the above expression, we get

$7.2=\frac{2\times M}{(288\times {10}^{-10}{)}^3\times 6.023\times {10}^{23}}$

$⟹M=\frac{7.2\times (288\times {10}^{-10}{)}^3\times 6.023\times {10}^{23}}{2}=51.8$

Hence, the atomic mass of the element is $51.8$ g/mol.