Question

The number of atoms in 100 g of an fcc crystal with density 10 g cm^-3 and unit cell edge length 200 pm is equal to ______.

Options

• 1 × 10²⁴

• 3 × 10²⁴

• 2 × 10²⁴

• 5 × 10²⁴

Answer 1

The number of atoms in 100 g of an fcc crystal with density 10 g cm^-3 and unit cell edge length 200 pm is equal to 5 × 10²⁴.

Explanation:

Density = `("n" xx "M")/("a"^3 xx "N"_0)`

`10 = (4 xx "M")/((200 xx 10^-12)^3 xx 6 xx 10^23)`

M = `(10 xx 8 xx 10^-30 xx 6 xx 10^23)/4` = 12 g/mol

∴ 100 g will contain = `(6 xx 10^23 xx 100)/12 = 50 xx 10^23 = 5 xx 10^24` atoms