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  4. Copper (atomic mass = 63.5) crystallises in a fee lattice and has density 8.93 g cm 3. The radius of copper atom is closest to

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Q. Copper (atomic mass $= 63.5$) crystallises in a fee lattice and has density $8.93 \,g cm^ 3.$ The radius of copper atom is closest to

KVPYKVPY 2016The Solid State

Solution:

Given, density of copper lattice $= 8.93\, g cm^-3$
Number of atoms in fee lattice, $Z = 4$
As we know, $\rho =\frac{M\times N}{N_A\times \alpha ^3}$
$\alpha^{3}=\frac{\rho\times N_{A}}{M\times N}=\frac{8.93 \times 6.023 \times 12^{23}}{4 \times 63.5}$
$\alpha=\left(47.2\times10^{-24}\right)^{1 3}$
$\alpha=3.61\times10^{-10} m$
$=361\,pm$
Also, in fee lattice
$\alpha=2\sqrt{2}R$
$r=\frac{\alpha}{2\sqrt{2}}=\frac{361}{2\sqrt{2}}=127.8\, pm $