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Question

The density of copper metal is 8.95 gm cm3. If the radius of copper atom is 127.8 pm, Will the copper unit cell be a simple cubic, a body-centred cubic or a face centred cubic? (At mass of Cu=63.54g mol1 and NA =6.02×1023mol1)

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Solution

Density of metal (ρ)=Z×MNA×a3
For, simple cubic, a=2r,Z=1
ρ=1×63.54(2×127.8×1010)3×6.02×1023=6.31 g/cm3
For BCC, Z=2,a=43r
ρ=2×63.54(43×127.8×1010)3×6.02×1023=8.2 g/cm3
For FCC, Z=4,a=42r
ρ=4×63.54(42×127.8×1010)3×6.02×1023=8.92 g/cm3
The density of copper metal is 8.95 g/cm3 which is nearest to FCC. Therefore, the copper unit cell is face centre cubic.

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