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Copper crystallises in a face-centred cu...

Copper crystallises in a face-centred cubic lattice. Molar mass and density of copper are `63.5g*mol^(-1)and8.9g*cm^(-3)` respectively. Calculate the edge length of a unit cell in copper lattice and the radius of a copper atom.

Text Solution

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We know, `rho=(ZxxM)/(Nxxa^(3))`
In case of a face-centred cubic unit cell, Z = 4
Given: `rho=8.9g*cm^(-3)andM=63.5g*mol^(-1)`
Thus, `8.9=(63.5xx4)/(6.022xx10^(23)xxa^(3))` or, `a^(3)=4.739xx10^(-23)cm^(3)`
or, `a^(3)=3.622xx10^(-8)cm=3.618Å`
Copper forms a face-centered cubic unit cell. In this type of unit cell, we have the relationship, a (edge length of the cell) `=2sqrt2r` (radius of particle)
`therefore" "r=a/(2sqrt2)=3.618/(2sqrt2)Å=1.279Å`.
Therefore, the radius of a copper atom is 1.279Å.
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