A metallic element crystallizes in simple cubic lattice. Each edge length of the unit cell is 3 Å.The density of the element is `8g//c c`. Number of unit cells in 108 g of metal is

Options

A. `1.33times10^(20)`
B. `2.7times10^(22)`
C. `5times10^(23)`
D. `2times10^(24)`

Answer

C

Explanation

Edge lengthh of the unit cell =3Å
`=3times10^(-8)cm`
Volume of the unit cell =`("edge length")^(3)`
`=(3times10^(-8))^(3)=27times10^(-24)cm^(3)`
Mass of unit cell `=27times10^(-24)times8g`
Number of unit cells in 108 g of metal
`=108/(27times10^(-24)times8)=5times10^(23)`