At \(T(\mathrm{~K})\), copper (atomic mass \(=635 \mathrm{u}\) ) has fcc unit cell structure with edge…

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? \(\left(N_A=6.0 \times 10^{23} \mathrm{~mol}^{-1}\right)\)
  1. \(\frac{42.3}{x^3}\)
  2. \(\frac{423}{x^3}\)
  3. \(\frac{423}{x^3}\)
  4. \(\frac{212}{x^3}\)

Solution

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.

Asked in: AP EAMCET 2019 (20 Apr Shift 1)

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