Question

An element crystallizes in a structure having fcc unit cell of an edge length equal to $200$ pm . Calculate the density (in g cm${}^{-3}$) if $100$ g of this element contains $12\times {10}^{23}$ atoms.

• A. $41.66$
• B. $4.166$
• C. $10.25$
• D. $1.025$

Answer 1

The correct option is A $41.66$

As $12\times {10}^{23}$ atoms have a mass of $100$ g, $6\times {10}^{23}$ atoms have mass of $50$ gm and so, the molar mass is $50$ g/mol.

The formula for density is as follows:

$d=\frac{ZM}{V{N}_A}=\frac{4\times 50}{(200\times {10}^{-10}{)}^3\times 6\times {10}^{23}}=41.66$ g cm${}^{-3}$

where $Z=4$ because the element crystallizes is fcc structure.