Copper has the fcc crystal structure. Assuming an atomic radius of 130 pm for copper atom (Cu = 63.54):the density of Cu is

# Copper has the fcc crystal structure. Assuming an atomic radius of 130 pm for copper atom (Cu = 63.54):the density of Cu is

1. A

2. B

3. C

4. D

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### Solution:

Expression of density:

$\rho =\frac{n×{M}_{\mathrm{m}}}{{N}_{\mathrm{A}}×{a}^{3}}$

For fcc structure, edge length is calculated as:

$\begin{array}{l}4r=\sqrt{2}a\\ a=2\sqrt{2}r\\ =2\sqrt{2}×130\mathrm{pm}=367.64\mathrm{pm}=3.67×{10}^{-8}\mathrm{cm}\end{array}$

Volume of unit cell is:

$\begin{array}{l}{a}^{3}={\left(3.67×{10}^{-8}\right)}^{3}{\mathrm{cm}}^{3}\\ =49.43×{10}^{-24}{\mathrm{cm}}^{3}\end{array}$

For FCC, Z= 4. Substitute the given values in the density expression:

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