The unit cell of metal contains four particles. Calculate the volume of the unit cell if the molar mass of metal is $192\ \text{g mol}^{-1}$ .
[ $\rho \times N_A = 1.5 \times 10^{25}\ \text{g cm}^{-3}\text{mol}^{-1}$ ]

Question

The unit cell of metal contains four particles. Calculate the volume of the unit cell if the molar mass of metal is 192\ g mol^ -1 . [ × N_A = 1.5 × 10^ 25 \ g cm^ -3 mol^ -1 ]

Quantrex Academy · Accepted Answer

Correct answer: A. 5.12 × 10^ -23 \ cm^3

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

\rho = \dfrac{Z \times M}{N_A \times V}

Rearranging for the volume

V

of the unit cell:

V = \dfrac{Z \times M}{\rho \times N_A}

Given:

Z = 4

M = 192\ \text{g mol}^{-1}

\rho \times N_A = 1.5 \times 10^{25}\ \text{g cm}^{-3}\text{mol}^{-1}

Substituting the values into the formula:

V = \dfrac{4 \times 192}{1.5 \times 10^{25}}

V = \dfrac{768}{1.5} \times 10^{-25}

V = 512 \times 10^{-25}\ \text{cm}^3

V = 5.12 \times 10^{-23}\ \text{cm}^3

Answer:

5.12 \times 10^{-23}\ \text{cm}^3

The unit cell of metal contains four particles. Calculate the...

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