Question

A certain solid metallic element has a density 7.87 g/cm^3 and a molar mass of 55.85 g/mol. It crystallizes in one of the cubic unit cells with an edge length of 286.7 pm. Calculate the number of atoms per unit cell.

Answer 1

We are given density molar mass and edge of crystal we can use it to get its number of atoms per unit cell

We use following formula

Density = ( Z. M / a³ x N_A)

Here z is number atoms in unit cell. M is molar mass , a is edge , N_A is Avagadro number.

Lets convert edge to cm

1 cm = 1 E pm

So edge in cm = 286.7 pm x 1 cm / 1 E 10 pm

= 2.857E-8 pm

Lets plug all given values to get the value of Z

Z = Density x ( a³N_A / M)

So the number of atoms in unit cell = 2