# Total volume of atoms present in a face­-centred cubic unit cell of a metal is (r is atomic radius ) Option 1) $\frac{20}{3}\pi r^{3}$ Option 2) $\frac{24}{3}\pi r^{3}$ Option 3) $\frac{12}{3}\pi r^{3}$ Option 4) $\frac{16}{3}\pi r^{3}$

As we learnt in

Packing fraction for face centered cubic unit cell -

Pf = 0.74

-

In case of a face­centred cubic structure, since our atoms are present in a unit cell, hence volume

$V=4\left ( \frac{4}{3}\pi r^{3} \right )\frac{16}{3}\pi r^{3}$

Correct option is 4.

Option 1)

$\frac{20}{3}\pi r^{3}$

This is an incorrect option.

Option 2)

$\frac{24}{3}\pi r^{3}$

This is an incorrect option.

Option 3)

$\frac{12}{3}\pi r^{3}$

This is an incorrect option.

Option 4)

$\frac{16}{3}\pi r^{3}$

This is the correct option.

N

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