Question

Silver crystallizes with a face centeredd cubic unit cell. the radius of silver atom is 0.144 nm. Calculate the density of solid silver ? Answer: 10.6 g/ml

Answer 1

Given, Radius of silver atom = 0.144 nm

Unit cell = Face centered

density = ?

The density of face centered cubic unit cell can be calculated using equation as follows :

d = Z M / (a^3 N_A)..................... (1)

Z = number of atoms contribution per unit cell = 4

a = edge length, this can be calculated using radius of silver atom = 0.144 nm by following equation

a 2 = 4 r

a = 4 r / 2

a = (4 x 0.144 x 10^-9) / 2

a = 4.0729 x 10^10 m = 4.0729 x 10^12 cm

  M = molecular weight of silver = 63.5 g/mol

N_A = 6.022 x 10^23 mol^-1

Substituting all the above values in equation (1)

d = 4 x 63.5 / [(4.0729 x 10^12)^3 x (6.022 x 10^23)]

d = 254 / (4.068 x 10^61)

d = 6.24 x 10^-60 g/cm^3