The nucleus of a hydrogen atom is a single proton, which has a radius of about 1.2 * 10-15 m. The single electron in a hydrogen atom orbits the nucleus at a distance of 5.3 * 10-11 m. What is the ratio of the density of the hydrogen nucleus to the density of the complete hydrogen atom?

Answer: 0.86 * 10^14

Explanation:

Given the following:

Radius of proton = 1.2 * 10-15 m

Radius of hydrogen atom = 5.3 * 10-11 m

Density of proton could be calculated thus:

Mass of proton = 1.67 * 10^-27 kg

Using the formula:

(4/3) * pi * r^3

(4/3) * 3.142 * (1.2 * 10^-15) ^3 = 7.24 * 10^-45

Density = mass / volume

Density = (1.67 * 10^-27) / (7.24 * 10^-45)

= 0.2306 * 10^18

Density of hydrogen atom:

Mass of hydrogen atom = 1.67 * 10^-27 kg

Using the formula:

(4/3) * pi * r^3

(4/3) * 3.142 * (5.3 * 10^-11) ^3 = 6.24 * 10^-31

Density = mass / volume

Density = (1.67 * 10^-27) / (6.24 * 10^-31)

= 0.2676 * 10^4

Ratio is thus:

Density of proton / density of hydrogen atom

0.2306 * 10^18 / 0.2676 * 10^4 = 0.8617 * 10^14