Question

The substance cesium is found to crystallize in a cubic lattice, with an edge length of 605.0 pm. If the density of solid cesiumis 1.993 g/cm³, how many Cs atoms are there per unit cell?

Your answer should be an integer:

Answer 1

it is given that

edge length a = 605.0 pm = 605 x 10^-10 cm

atomic mass of Cesium M = 133 g mol^-1

no of atoms per unit cell = n

avagadro number = 6.023 x 10²³ mol^-1

density = 1.993 g/cm3

density = [M x n] /[ a³ x avogadro number]

1.993 g/cm3 = [ 133 g mol^-1 x n ] / [ (605 x 10^-10 cm)³ x 6.023 x 10²³ mol^-1]

n = 2

Therefore, no of Cs atoms per unit cell = 2