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 = Z×Ma3×NA = 1×63.54(255.6×10-10)3×(6.02×1023)

  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 = 4r3 = 4×127.81.732pm = 295.15 pm

Z = 2

P = Z×Ma3×NA = 2×63.54(295.15×10-10)3×6.02×1023

 P = 8.21 g cm-3

Hence, copper atom is not body centred.

If copper atom were face-centred :

a = 22

or a = 2×1.414×127.8 pm

= 361.4 pm = 361.4×10-10 cm

P = Z×Ma3×NA = 4×63.54(361.4×10-10)3×6.02×1023

 P = 8.94 g cm-3

Hence, copper is face-centred cubic.

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