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.

Options

A. `4.16 g cm^(-3)`
B. `41.6 g cm^(-3)`
C. `20.8 g cm^(-3)`
D. `10.4g cm^(-3)`

Answer

B

Explanation

Volume of unit cell `= ( 200 xx 10^(-10))^(3)`
`= 8 xx 10^(-24) cm^(3)`
Mass of unit cell
`=( 4 xx 200)/( 24 xx 10^(23)) = 33.3 xx 10^(-23) g `
Density `= ( 33.3 xx 10^(-23))/(8 xx 10^(-24)) = 41.6 g cm^(-3)`