Question

The density of metal which crystallises in bcc lattice with unit cell edge length 300 pm and molar mass 50 g mol-1 will be

• A. 6.15 g cm^-3
• B. 9.31 g cm-3
• C. 10.0 g cm^-3
• D. 14.2 g cm^-3

Answer 1

The correct option is A

6.15 g cm^-3

The explanation for the correct answer:-

Option (A) $6.15\mathrm{g}{\mathrm{cm}}^{-3}$

Step 1: Given data

In a body-centred cubic unit cell, the number of atoms in a unit cell, z is equal to two.

Unit Cell is the smallest part (portion) of a crystal lattice. It is the simplest repeating unit in a crystal structure.

The entire lattice is generated by the repetition of the unit cell in different directions.

$n=2$ and Unit cell edge length$\mathrm{a}=300\times {10}^{-10}\mathrm{cm}$

$M=50g$

Step 2: Formula used

$\mathrm{\rho }=\frac{\mathrm{nM}}{{\mathrm{N}}_{\mathrm{o}}{\mathrm{a}}^3}\mathrm{g}/{\mathrm{cm}}^3$

Step 3: Deriving theoretical density

The density of unit cell = $2\times {\mathrm{Ma}}^3\times {\mathrm{N}}_{\mathrm{A}}$

$$\begin{gathered} \mathrm{\rho }=\frac{2\times 50}{6.022\times {10}^{23}\times {300}^3\times {\left({10}^{-10}\right)}^3} \\ \mathrm{\rho }=6.15\mathrm{g}/{\mathrm{cm}}^3 \end{gathered}$$

Hence, option (A) is the correct answer.