Solid State - Result Question 10
10. At $100^{\circ} C$, copper $(Cu)$ has $FCC$ unit cell structure with cell edge length of $x Å$. 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) $\dfrac{211}{x^{3}}$
(b) $\dfrac{205}{x^{3}}$
(c) $\dfrac{105}{x^{3}}$
(d) $\dfrac{422}{x^{3}}$
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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, $a=x Å=x \times 10^{-8} cm$
density $(d)=\dfrac{Z \times M}{N _A \times a^{3}}$
$ =\dfrac{4 \times 63.55}{6.023 \times 10^{23} \times\left(x \times 10^{-8}\right)^{3}}=\dfrac{422.048}{x^{3}} g$ $ cm^{-3} $
BETA
