Question

Copper crystallizes in a face-centered cubic cell. Copper's density is 8.92 g?cm3, and its molar mass is 63.55 g/mol. Determine the radius (in pm) of a copper atom.

Answer 1

since the cubic cell is Face Centred Cubic, the value of Z=4

Molar mass = 63.55 g/mol

d = (Z*M)/(a^3*NA)

8.92 = (4*63.55)/(a^3*(6.022*10^23))

a^3 = 4.732*10^-23 cm^3

a = 3.617*10^-8 cm

a = 361.7 pm

for FCC:

length of face diagonal = sqrt(a^2+a^2)

length of face diagonal = a*sqrt(2)

use:

For FCC Lattice

length of face diagonal = 4*r

a*sqrt(2) = 4*r

361.7*sqrt(2) = 4*r

r = 128 pm

Answer: 128 pm