Question

An element crystallizes in fcc structure with a cell edge length of $500$ pm. Its density and atomic mass are $4.2$ g cm${}^{-3}$ and $90$ g respectively. The value of Avogadro's number $\left(N_A\right)$ will be:

• A. $6.86\times {10}^{23}$
• B. $6.16\times {10}^{23}$
• C. $6.66\times {10}^{23}$
• D. $6.82\times {10}^{23}$

Answer 1

The correct option is A $6.86\times {10}^{23}$

density $=\frac{zM}{N_a\times (a\times {10}^{-10}{)}^3}$

For fcc structure z=4

$4.2=\frac{4\times 90}{N_a\times (500\times {10}^{-10}{)}^3}$

$N_A=6.86\times {10}^{23}$

Hence, the correct option is $\text{A}$