An element crystallizes into structure which may be described by a cube type of unit cell having one atom on each corner of the cube and two atoms on one of its diagonals. If the volume of this unit cell is 24 xx 10^(-24) cm^3 and density of the element is 7.2 g cm^(-3), calculate the number of atoms present in 200 g of the element.

An element crystallizes into structure which may be described by a cub

1.	An element crystallizes into structure which may be described by a cube type of unit cell having one atom on each corner of the cube and two atoms on one of its diagonals. If the volume of this unit cell is 24 xx 10^(-24) cm^3 and density of the element is 7.2 g cm^(-3), calculate the number of atoms present in 200 g of the element.
Answer» Solution :We know that a simple CUBIC UNIT cell has atoms=1 Volume of element= `("Mass of element")/("density of element") = (200g)/(7.2 g CM^(-3))= 27.78 cm^3` Number of unit CELLS= `("Volume of element")/("Volume of unit cell")=(27.78 cm^3)/(24xx10^(-24)cm^3)= 1.157 xx 10^(24)` Number of atoms present in the given unit cell = 1+2 (given) = 3 `:.` Number of atoms present in `1.157 xx 10^(24)` unit cells = `3 xx 1.157 xx 10^(24) = 3.471 xx 10^(24)`