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The density of copper metal is 8.95g*cm^...

The density of copper metal is `8.95g*cm^(-3)`. If the radius of copper atom is 127.8 pm, is the copper unit cell a simple cube, a body-centred or a face-centred cubic structure?
[Given: Atomic mass of copper: `63.54g*mol^(-1), N_(A)=6.022xx10^(23)mol^(-1)`]

Text Solution

Verified by Experts

`rho=(ZxxM)/(Nxxa^(3))`
`rho=8.95g*cm^(-2)`,
`M=63.54g*mol^(-1),N=6.022xx10^(23)mol^(-1)`
`thereforea^(3)=(Zxx63.54)/(8.95xx6.022xx10^(23))=1.18xx10^(-23)Zcm^(3)`
or, `a=2.276xx10^(-8)cmxxZ^(1//3)`
If Z = 4, then `a=3.613xx10^(-8)cm`
Z = 4, means the unit cell is face-centred cubic. For this cell,
`r=a/(2sqrt2)=(3.613xx10^(-8))/(2sqrt2)cm=1.277xx10^(-8)cm`
= 127.7 pm
Considering Z = 4, it gives a value of r which is the same as the value of r given in question. So, the unit cell will be face-centred cubic.
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