Question

Calculate the number of unit cells in 1 cm³ volume of metal if it forms сср structure
\[\begin{bmatrix} a=3.5\times10^{-8} & cm \end{bmatrix}\]

Options

• 4.211 × 10²²

• 3.281 x 10²²

• 1.451 x 10²²

• 2.332 × 10²²

Answer 1

2.332 × 10²²

Explanation:

\[\begin{aligned} & \mathrm{Number~of~unit~cells~in~volume~(V)~of~metal} \\ & =\frac{\text{Given volume}}{\text{Volume of a unit cell}}=\frac{\mathrm{V}}{\mathrm{a}^{3}} \end{aligned}\]
\[\begin{aligned} \therefore & \text{Number of unit cells in l cm}^3\mathrm{of~metal} \\ & =\frac{1.00}{\left(3.5\times10^{-8}\right)^3}=2.332\times10^{22} \end{aligned}\]