Question

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 1

To determine the density ratio of a hydrogen nucleus to the entire hydrogen atom, the volumes of both must be calculated using their radii. Once the volumes are found, their densities can be calculated since the mass of a hydrogen atom is almost entirely due to the mass of the proton. The density ratio is the density of the nucleus divided by the density of the whole atom.

Step-by-step explanation:

The question is asking for the ratio of the density of a hydrogen nucleus to that of the entire hydrogen atom. To find this ratio, we need to calculate the volumes of the nucleus and the entire atom and then use their respective masses to find the densities.

The volume (V) of a sphere is given by V = 4/3 π r^3, where r is the radius of the sphere. The radius of the proton, which acts as the hydrogen nucleus, is 1.2 × 10^-15 m, and the radius of the hydrogen atom is roughly 5.3 × 10^-11 m.

We'll use the mass of a proton for the nucleus, which is approximately 1.67 × 10^-27 kg, and for the whole atom, it's essentially the same since the electron's mass is negligible compared to that of the proton.

First, calculate the volume of the nucleus (V_nucleus), then calculate the volume of the atom (V_atom). The density (ρ) is mass divided by volume, so we'll calculate the density of the nucleus (ρ_nucleus) and of the entire atom (ρ_atom). Finally, find the ratio (ρ_nucleus / ρ_atom).

The density ratio is very large because the nucleus is much denser than the atom as a whole since the nucleus contains nearly all the mass of the atom but occupies a very small volume compared to the atom's volume.

Answer 2

Answer: 0.86 × 10^14

Step-by-step 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