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).