Question

Calculate the radius of a copper atom in cm, given that Cu has an FCC crystal structure, a density of 8.96 g/cm³, and an atomic weight of 63.55 g/mol.

Please show all steps on how to get the answer

Answer 1

Sol :-

Let edge length of cube = a cm

So, Volume of the cube = a³ cm³

We know that,

For FCC, effective number of atoms in a unit cell (Z) = 4

So,

Number of moles in one crystal or one unit cell = 4 / 6.022 x 10²³ mol

Also,

Mass of Cu (M) = No. of moles x Molar mass of cu

= 4 mol x 63.55 g/mol / 6.022 x 10²³

= 4.22 x 10^-22 g

So,

Density = Mass / Volume of the cube

8.96 g/cm³ = 4.22 x 10^-22 g / a³ cm³

a³ = 4.22 x 10^-22 g / 8.96 g/cm³

a = 3.6 x 10^-8 cm

Also, for FCC relationship between edge length a and radius r is :

a² + a² = (4r)²

2a² = 16r²

r² = 2a² / 16

r² = 2(3.6 x 10^-8)² / 16

r² = 1.62 x 10^-16

r = 1.27 x 10^-8 cm

Hence, radius of Cu atom = 1.27 x 10^-8 cm