Question

If the atomic radius of potassium is 227 pm and potassium crystallizes in a body-centered cubic shape, What is the volume in cm3 of a unit cell of potassium to 3 sig figs

Answer 1

Solution :-

Lets first calculate the edge length using the radius

Edge length = [(16/3)*r^2]^0.5

                       = [(16/3)*227 pm^2]^0.5

                       = 524.234 pm

Now lets calculaete the volume

V= [edge length ]^3

V = [524.234 pm]^3

V= 1.44*10^8 pm3

Now lets convert pm to cm3

1pm3 = 1*10^-30 cm3

1.44*10^8 pm 3 * 1*10^-30 cm3 / 1 pm3 = 1.44*10^-22 cm3

So the volume of the unit cell = 1.44*10^-22 cm3