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At \(T(\mathrm{~K})\), copper (atomic mass \(=635 \mathrm{u}\) ) has fcc unit cell structure with edge length of \(x Å\). What is the approximate density of \(\mathrm{Cu}\) in \(\mathrm{g} \mathrm{cm}^{-3}\) at that temperature?
\(\left(N_A=6.0 \times 10^{23} \mathrm{~mol}^{-1}\right)\)
Options:
\(\left(N_A=6.0 \times 10^{23} \mathrm{~mol}^{-1}\right)\)
Solution:
2779 Upvotes
Verified Answer
The correct answer is:
\(\frac{423}{x^3}\)
Given,
fcc unit cell is present, \(Z=4\)
Edge length \(=x Å\)
Atomic weight \(=63.5 \mathrm{~g} \mathrm{~mol}^{-1}\)
\(\because \text { Density, } d=\frac{Z \times \text { atomic weight }}{a^3 \times N_A}\)
where, \(\quad a=\) edge length
\(\begin{aligned}
d & =\frac{Z \times \text { atomic weight }}{x^3 \times 6.023 \times 10^{23} \times\left(10^{-8}\right)^3} \\
& =\frac{4 \times 63.5}{x^3 \times 6.023 \times 10^{23} \times 10^{-24}} \\
d & =\frac{423.0}{x^3}
\end{aligned}\)
Hence, option (3) is correct.
fcc unit cell is present, \(Z=4\)
Edge length \(=x Å\)
Atomic weight \(=63.5 \mathrm{~g} \mathrm{~mol}^{-1}\)
\(\because \text { Density, } d=\frac{Z \times \text { atomic weight }}{a^3 \times N_A}\)
where, \(\quad a=\) edge length
\(\begin{aligned}
d & =\frac{Z \times \text { atomic weight }}{x^3 \times 6.023 \times 10^{23} \times\left(10^{-8}\right)^3} \\
& =\frac{4 \times 63.5}{x^3 \times 6.023 \times 10^{23} \times 10^{-24}} \\
d & =\frac{423.0}{x^3}
\end{aligned}\)
Hence, option (3) is correct.
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