Question

Gold crystallizes in the face-centred cubic lattice. The number of unit cells in 1 g of gold (atomic mass = 197 u) will be

• A. $6.02 \times 10^{23}$
• B. $7.64 \times 10^{20}$
• C. $3.82 \times 10^{20}$
• D. $15.28 \times 10^{20}$

Answer 1

Answer: (B)

$7.64 \times 10^{20}$

Answer 2

1 Mole of gold $= 197 \, g = 6.02 \times 10^{23}$ atoms $\therefore$ 1 g gold $= \frac{6.02 \times 10^{23}}{197}$ atoms As fee contains 4 atoms per unit cell, therefore, number of unit cells $= \frac{6.02 \times 10^{23}}{197 \times 4}$ $= 7.64 \times 10^{20}$