Question

How many atoms of sodium are in a cube of sodium that is 1.0 in on a side?

Answer 1

We know that, sodium has a density of 0.968 g/cm³

Give that a unit cell side length (a) of 1.0 in

1) First calculate the average mass of one atom of Na:

22.99 g mol¯¹ ÷ 6.022 x 10²³ atoms mol¯¹ = 3.82 x 10¯²³ g/atom

2) Then calculate the volume of the unit cell:

1.00 in = 2.54 cm

(2.54)³ = 16.4 cm³

3) Density = mass/ volume

Mass = density * volume

Mass of cube = 0.968 g/cm³ *16.4 cm³

= 15.8752 g

4) Now calculate the number of sodium atom :

Total mass of cube ÷ the average mass of one atom of Na

15.8752 g ÷ 3.82 x 10¯²³ g/atom

= 4.16 x 10²³ atoms Na