Calculate the volume of unit cell of an element having molar mass 27 g mol − 1 that forms fce unit cell. [ ρ . N A = 16.0 × 1 0 23 g cm − 3 mol − 1 ] [Note: The question has been modified to get the

Question

Calculate the volume of unit cell of an element having molar mass 27 g mol − 1 that forms fce unit cell. [ ρ . N A ​ = 16.0 × 1 0 23 g cm − 3 mol − 1 ] [Note: The question has been modified to get the correct answer.]

TestHub · Accepted Answer

The density of a unit cell is given by the formula:

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

For a face-centered cubic (fcc) unit cell, the number of atoms per unit cell is $Z = 4$ .

Rearranging the formula to solve for the volume $V$ of the unit cell:

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

Substituting the given values $M = 27 g mol^{- 1}$ and $ρ \times N_{A} = 16.0 \times 1 0^{23} g cm^{- 3} mol^{- 1}$ :

$V = \frac{4 \times 27}{16.0 \times 1 0 ^{23}}$

$V = \frac{108}{16.0 \times 1 0 ^{23}}$

$V = 6.75 \times 1 0^{- 23} cm^{3}$

Answer: $6.75 \times 1 0^{- 23} cm^{3}$

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