Question

An element crystallizes in fcc type of unit cell. The volume of one unit cell is 24.99 × 10^-24 cm³ and density of the element 7.2 g cm^-3, Calculate the number of unit cells in 36 g of pure sample of element?

विकल्प

• 2.0 × 10²³

• 1.25 × 10²¹

• 2.0 × 10²¹

• 2.0 × 10²⁴

Answer 1

2.0 × 10²³ 

Explanation:

Volume (a³) = 24.99 × 10^-24 cm³

Density (d) = 7.2 g cm^-3

Mass of metal (m) = 36 g

Mass of one unit cell = volume × density

= 24.99 × 10^-24 × 7.2

= 179.928 × 10^-24 

∴ Number of unit cells in 36 g metal.

Unit cell = `"Mass of metal"/"Mass of one unit cell"`

`= 36/(179.928 xx 10^-24)`

`= 0.200080 xx 10^24`

`= 2.0 xx 10^23`