A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is `8 g cm^(-3)`, then the number of atoms present in 256g of the crystal is `N xx 10^(24)`. The value of `N` is

Answer

2

Explanation

Volume of unit cell = `(400 xx 10^(-10))^(3) cm^(3)`
Mass of element 256 g
Density of element = `8 g cm^(-3)`
Volume of 256 g of element = `(256)/8 = 32 cm^3`
No. of unit cells = `32/((400 xx 10^(-10))^3) = 5 xx 10^(23)` unit cells
Since the structure is fcc, number of atoms present in a unit cell = 4.
No. of atoms in 256 g ` = 5 xx 10^(23) xx 4`
`= 2 xx 10^(24)` atoms .