MHTCET 11 Apr 2026 Shift 1 Paper

Concept:$$Z$$ is the number of formula units per unit cell, which is used in the density relation $$\rho = \frac{ZM}{N_{A}V}$$.Explanation:Anions are present at the eight corners of the cubic unit cell.Each corner particle contributes $$\frac{1}{8}$$ to the unit cell.So, number of anions per unit cell is $$8 \times \frac{1}{8} = 1$$.The cation is at the body centre and belongs completely to the unit cell.So, number of cations per unit cell is $$1$$.Hence, one unit cell contains one formula unit of the ionic compound.Therefore, $$Z = 1$$.The density of the unit cell is given by $$\rho = \frac{ZM}{N_{A}V}$$.Rearranging for volume: $$V = \frac{ZM}{\rho N_{A}}$$.Substituting the values: $$V = \frac{1 \times 168.6}{4 \times 6.022 \times 10^{23}}$$.$$V = \frac{168.6}{24.088 \times 10^{23}}$$.$$V \approx 7.0 \times 10^{-23} \,\mathrm{cm^{3}}$$.Answer:The volume of the unit cell is $$7.0 \times 10^{-23} \,\mathrm{cm^{3}}$$.Correct option: Option C.