An element crystallizes in a structure having fcc unit cell of an edge 200 pm. Calculate the density if 200 g of this element contains `24 xx 10^(23)` atoms.

Explanation

Edge length = 200 pm
Volumne of the unit cell `= (200 xx 10^(-10) cm)^(3)`
`= 8 xx 10^(-24) cm^(3)`
In a fcc unit cell there are four atoms per unit cell.
Mass of unit cell = `(200 xx 4)/(24 xx 10^(23))`
`= 33.3 xx 10^(-23)` g
Density `= ("Mass of unit cell")/("Volume of unit cell")`
`= (33.3 xx 10^(-23) g)/(8 xx 10^(-24) cm^(3))`
= 41.6 g `cm^(-3)`