How many times larger is a potassium atom than the potassium nucleus in terms of volume?

Question

The nucleus of a potassium atom has a diameter on the order of 1x10^-5 nm. A potassium atom has a diameter of approximately 0.5 nm. In terms of volume, how many times larger is the potassium atom than the potassium nucleus?

Please help me solve this. Thanks!

Answer 1

Let's assume both the atom and its nucleus are spheres. The volume of a sphere is: V = 4/3 π r³. Since we are taking the ratios of the volumes of the spheres, it is not necessary to to actually calculate the volumes, all we need to do is take the ratio of the cubes of the radii, which are half of the given diameters.

(0.5x10^-5 nm)³ / (0.25 nm)³ = 1.25x10^14

Obvously, the vast majority of the volume of an atom is empty space, while the vast majority of the mass of the atom is in a very small place (the nucleus).