Calculate the volume of unit cell of an element having molar mass 63.5 g mol − 1 . that forms fce structure [ ϱ × N A = 5.5 × 1 0 24 g cm − 3 mol − 1 ]

Question

Calculate the volume of unit cell of an element having molar mass 63.5 g mol − 1 . that forms fce structure [ ϱ × N A ​ = 5.5 × 1 0 24 g cm − 3 mol − 1 ]

TestHub · Accepted Answer

The density of a unit cell is given by:

$ρ = \frac{Z \times M}{N _{A} \times V}$

Rearranging for the volume of the unit cell $V$ :

$V = \frac{Z \times M}{ρ \times N _{A}}$

For an fcc structure, the number of atoms per unit cell is $Z = 4$ .

Substituting the given values $M = 63.5 g mol^{- 1}$ and $ρ \times N_{A} = 5.5 \times 1 0^{24} g cm^{- 3} mol^{- 1}$ :

$V = \frac{4 \times 63.5}{5.5 \times 1 0 ^{24}}$

$V = \frac{254}{5.5 \times 1 0 ^{24}}$

$V = 46.18 \times 1 0^{- 24} cm^{3}$

$V = 4.618 \times 1 0^{- 23} cm^{3}$

Answer: $4.618 \times 1 0^{- 23} cm^{3}$

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