A metallic element has a cubic lattice. Each edge of the unit cell is 2 Å. The density of the metal is `2.5 g cm^(–3)` . The number of unit cells in 200 g of the metal will be:

Options

A. `1times10^(25)`
B. `1times10^(24)`
C. `1times10^(22)`
D. `1times10^(20)`

Answer

A

Explanation

Edge length of the unit cell =2Å
`=2times10^(-8)cm`
Volume of the unit cell `=(2times10^(-8))^(3)cm^(3)`
`=8times10^(-24)cm^(3)`
Mass of unit cell =`"Volume"times"density"`
`=8times10^(-24)times2.5 g`
No. of unit cells in 200 g of the metal
`="Mass of metal"/"Mass of unit cell"=200/(8times10^(-24)times2.5)=1times10^(25)`