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

Options

A. `1 xx 10^(24)`
B. `1 xx 10^(22)`
C. `1 xx 10^(20)`
D. `1 xx 10^(25)`

Answer

D

Explanation

Edge length of the unit cell `=2Å=2 xx 10^(-8)cm` Volume of unit cell `=(2 xx 10^(-8))^(3)= 8 xx 1^(-24)cm^(3)` Mass of one unit cell= volume `xx` density `=8xx 10^(-24) xx 2.5`
Number of unit cell in 200g of metal `=("mass of the metal")/("mass of one unit cell")= (200)/(8xx 10^(-24)xx 2.5)=1 xx 10^(25)`