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.

Explanation

Number of atoms contributed in onne unit cell.
= one atom from the eight corners = one atom from the two faces diagonals.
=1+1=2 atoms.
Mass of one unit cell = volume x its density
`=24 xx 10^(-24) cm^(3) xx 7.2 gm cm^(3)`
`=172.8 xx 10^(-24)` gm
`therefore 172.8 xx 10^(-24) gm` is the mass of one - unit cell i.e., 2 atoms.
`therefore 200` gm is the mass `=(2 xx 200)/(172.8 xx 10^(-24))` atoms `=2.3148 xx 10^(24)` atoms.