Question

How many unit cells can be made out of an 18-carat pure 197 g sample of gold? (gold has fcc structure, atomic mass of gold = 197 u)?

Answer 1

given, mass of gold = 197g

atomic mass of gold = 197 g/mol

so, number of mole of sample = 197/197 = 1

but it is given that, 18 carat pure gold.

so, percentage of pure gold in sample = (18/24) × 100 = 75%

[ note : you know,24 carat means 100% pure gold ]

so, number of mole of pure gold = 75% of 1mole = 0.75 mole

now, number of atoms of gold = 0.75 × 6.023 × 10²³

= 4.51 × 10²³

gold has face - centered cubic lattice.

so, number of atoms per unit cell = 4

number of unit cell = number of atoms of gold/4

= 4.51 × 10²³/4

≈ 1.27 × 10²³

hence, number of unit cell = 1.27 × 10²³