Question

At $T( K )$, copper (atomic mass $=63.5\, u$ ) has fcc unit cell structure with edge length of $x \mathring {A}$. What is the approximate density of $Cu$ in $g \,cm ^{-3}$ at that temperature? $\left(N_{A}=6.0 \times 10^{23} mol ^{-1}\right)$

• A. $\frac{42.3}{x^3}$
• B. $\frac{4.23}{x^3}$
• C. $\frac{423}{x^3}$
• D. $\frac{212}{x^3}$

Answer 1

The Correct Option is C

Given,

fcc unit cell is present, $Z=4$

Edge length $=x\, ?$

Atomic weight $=63.5 \,g \,mol ^{-1}$
$\because$ Density, $d=\frac{Z \times \text { atomic weight }}{a^{3} \times N_{A}}$

where, $a=$ edge length

$d =\frac{Z \times \text { atomic weight }}{x^{3} \times 6.023 \times 10^{23} \times\left(10^{-8}\right)^{3}} $
$=\frac{4 \times 63.5}{x^{3} \times 6.023 \times 10^{23} \times 10^{-24}}$
$d =\frac{423.0}{x^{3}}$