Question

An element (atomic mass $=100$ g/mol) having bcc structure has unit cell edge length $400$ pm. The density (in g cm${}^{-3}$) of the element is:

• A. $10.376$
• B. $5.188$
• C. $7.289$
• D. $2.144$

Answer 1

The correct option is B $5.188$

Given, M $=$ 100 g/mol, a $=$ 400pm

For BCC -

$n=8\times \frac{1}{8}+1=2$

As we know,

$\text{Density}=\frac{n\times M}{a^3\times N_A}$ $=\frac{2\times 100}{(400\times {10}^{-10}{)}^3\times 6.02\times {10}^{23}}$ $=5.188$ g cm${}^{-3}$

$(\because 400pm=400\times {10}^{-10}cm)$

Hence, the correct option is B.