Q9 / 90 · JEE Main 2019 (09 Jan Shift 2) · Chemistry

At $100^{o} C,$ copper $(C u)$ has $F C C$ unit cell structure with cell edge length of $x Å$ . What is the approximate density of $C u$ (in $g c m^{- 3}$ ) at this temperature?

$[A t o m i c M a s s o f C u = 63.55 u]$

Solution

Crystal structure is

F C C,

so number of atoms per unit cell

(N) = 4

Edge length

= x . Å^{} = x 10^{- 8} c m^{3}

Density

\frac{ZM}{N_{A} a^{3}} = \frac{4 \times 63 .5}{(6 .03 \times 10^{23}) {(x \times 10^{- 8})}^{3}} gm / {cm}^{3}

= \frac{4 \times 63.5}{(6.0) \times x^{3} \times 10^{- 1}} = \frac{422}{x^{3}} g m / c m^{3} = \frac{422}{x^{3}}

Hence, the correct answer is option: 'C'.