Question

A hypothetical metal crystallizes with the face-centered cubic unit cell. The radius of the metal atom is 184 picometers and its molar mass is 195.08 g/mol. Calculate the density of the metal in g/cm3.

Answer 1

Here r = 184.0 pm

r = 1.84*10^-8 cm

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

length of face diagonal = a*sqrt(2)

we have below equation to be used:

For FCC Lattice

length of face diagonal = 4*r

a*sqrt(2) = 4*r

Given: r = 1.84*10^-8 cm

So,

a = 2*sqrt(2)*1.84*10^-8 cm

a = 5.204*10^-8 cm

Molar mass = 195.08 g/mol

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

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

d = (4*195.08)/((5.204*10^-8)^3*(6.022*10^23))

d = 9.19 g/cm^3

Answer: 9.19 g/cm^3