Question

An element crystallizes in a structure having FCC unit cell of an edge length $200$ pm. If $200$ g of this element contains $24\times 10$ ${}^{23}$ atoms, the density (in g/cc) of the element is :

• A. $50.3$
• B. $63.4$
• C. $41.6$
• D. $34.8$

Answer 1

The correct option is C $41.6$

It is given that an element crystallizes in a structure having FCC unit cell of an edge length $200$ pm.

$200$ gm of the element contains $24\times {10}^{23}$ atoms, which implies $6.022\times {10}^{23}$ atoms are present in $50$ gm, which is its molecular weight.

Since, the lattice is FCC, $z=4$

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

$d=\frac{4\times 50}{{6\times 10}^{23}\times {(200\times {10}^{-10})}^3}=41.6$ g/cc