Question

The no. Of atoms in 100 g of a fcc crystal with density and edge length as 100 pm is

Answer 1

Explanation:

d = Z x M/a3 x NA

where, a is edge of unit cell

NA = Avogadro number (6.022 × 1023)

M = Molar mass

Z = number of atoms per unit cell

For fcc, Z = 4

From the given data we can calculate the Molar mass of given substance as:

M = d x a3 x NA /z

Number of atoms = givan mass / molar mass(M) x NA

Putting the vaue of M in above equation we get

Number of moles = given mass x z x NA / d x a3 x NA

Number of atoms = given mass x z / d x a3

putting the values we get:

Number of atoms = 100 g x 4 / 10 gcm-3 x (200 x 10-10 cm)3 = 400 / 80 x 10-24 = 5 x 1024 atoms