Question

The number of atoms in $100$ g of fcc crystal with density equal to $10$ g cm${}^{-3}$ and edge length of $200$ pm is:

• A. $1\times$ ${10}^{25}$
• B. $5\times$ ${10}^{24}$
• C. $5\times$ ${10}^{26}$
• D. $5\times$ ${10}^{20}$

Answer 1

The correct option is B $5\times$ ${10}^{24}$

The expression for density is given below:

$d=\frac{zM}{N_A{a}^3}$

$10=\frac{4\times M}{{6\times 10}^{23}\times {(200\times {10}^{-10})}^3}$ $⟹M\approx 12$ g mol${}^{-1}$

Number of moles of element, $n=\frac{100}{12}=8.33moles$

Number of atoms $=N_a\times 8.33$ $=5\times {10}^{24}atoms$