Solid State - Result Question 10
####10. At $100^{\circ} C$, copper $(Cu)$ has $FCC$ unit cell structure with cell edge length of $x \AA$. What is the approximate density of $Cu$ (in $g$ $cm^{-3}$ ) at this temperature?
[Atomic mass of $Cu=63.55 u$ ]
(2019 Main, 9 Jan II)
(a) $\frac{211}{x^{3}}$
(b) $\frac{205}{x^{3}}$
(c) $\frac{105}{x^{3}}$
(d) $\frac{422}{x^{3}}$
Show Answer
Answer:
Correct Answer: 10. (d)
Solution:
- For fcc, rank of the unit cell $(Z)=4$
Mass of one $Cu$-atom, $M=63.55 u$
Avogadro’s number, $N _A=6.023 \times 10^{23}$ atom
Edge length, $a=x \AA=x \times 10^{-8} cm$
density $(d)=\frac{Z \times M}{N _A \times a^{3}}$
$$ =\frac{4 \times 63.55}{6.023 \times 10^{23} \times\left(x \times 10^{-8}\right)^{3}}=\frac{422.048}{x^{3}} g cm^{-3} $$
