NEET Chemistry The Solid State Questions Solved

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The density of copper metal is 8.95 g cm-3. If the radius of copper atoms is 127.8 pm, is the copper unit cell a simple cubic, a body-centred cubic or a face centred cubic structure?

(Given : At. mass of Cu = 63.54 g mol-1 and NA = 6.02$×$1023 mol-1)

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Concept Questions :-

Density/Formula/packing fraction/ Semiconductors

If copper atom were simple cubic :

a = 2$×$r = 2$×$127.8 pm

= 255.6 pm = 255.6$×$10-10 cm

Z = 1

P = $\frac{Z×M}{{a}^{3}×{N}_{A}}$ = $\frac{1×63.54}{\left(255.6×{10}^{-10}{\right)}^{3}×\left(6.02×{10}^{23}\right)}$

$\therefore$ P = 6.34 g cm-3

Actual density = 8.95 g cm-3

Hence copper atom is not simple cubic.

If copper atom were body-centred :

a = $\frac{4r}{\sqrt{3}}$ = $\frac{4×127.8}{1.732}$pm = 295.15 pm

Z = 2

P = $\frac{Z×M}{{a}^{3}×{N}_{A}}$ = $\frac{2×63.54}{\left(295.15×{10}^{-10}{\right)}^{3}×6.02×{10}^{23}}$

$\therefore$ P = 8.21 g cm-3

Hence, copper atom is not body centred.

If copper atom were face-centred :

a = 2$\sqrt{2}$

or a = 2$×$1.414$×$127.8 pm

= 361.4 pm = 361.4$×$10-10 cm

P = $\frac{Z×M}{{a}^{3}×{N}_{A}}$ = $\frac{4×63.54}{\left(361.4×{10}^{-10}{\right)}^{3}×6.02×{10}^{23}}$

$\therefore$ P = 8.94 g cm-3

Hence, copper is face-centred cubic.

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