Question

An atomic substance A of molar mass 12 g mol$^{-1}$ has a cubic crystal structure with edge length of 300 pm. The no. of atoms present in one unit cell of A is _____ (Nearest integer)

Hint:

The number of atoms in a unit cell can be calculated using the formula $Z = \frac{N_A \times M}{d \times a^3}$.

Answer 1

Correct Answer: 4

Given:
- Molar mass $M = 12$ g mol$^{-1}$
- Density $d = 3.0$ g mL$^{-1}$
- Edge length $a = 300$ pm $= 300 \times 10^{-12}$ m
- Avogadro's number $N_A = 6.02 \times 10^{23}$ mol$^{-1}$

Formula for number of atoms in one unit cell: $$Z = \frac{N_A \times M}{d \times a^3}$$ Substitute values: $$Z = \frac{6.02 \times 10^{23} \times 12}{3.0 \times (300 \times 10^{-12})^3}$$ $$Z = 40.635 \times 10^{21} = 6$$ Thus, the number of atoms present in one unit cell is 6. The correct answer is (4).