Question

How can I calculate the densities of a hydrogen nucleus and a hydrogen atom?

Answer 1

You use the formula for density and the published radii to calculate the densities. The values are `6.70 × 10^14"kg/dm"^3` and `2.7"kg/dm"^3`.

Explanation:

The formulas to use are

`"Density" = "mass"/"volume"` or `ρ = m/V` and

`V = (4/3)πr^3`

Hydrogen nuclei

A hydrogen nucleus is a proton, and the mass of a proton is `1.67 × 10^(-27)"kg"`.

The most recent value for the radius of a proton is `8.41 × 10^(-16)"m"`.

`V = (4/3)πr^3 = (4/3)π(8.41 × 10^-16"m")^3 = 2.49 × 10^(-45)"m"^3`

`ρ = m/V = (1.67 × 10^(-27)"kg")/(2.49 × 10^(-45)"m"^3)= 6.70 × 10^17"kg/m"^3 = 6.70 × 10^14"kg/dm"^3`

H atoms

The mass of a hydrogen atom is `1.67 × 10^(-27)"kg"`.

The radius of a hydrogen atom, calculated using self-consistent field functions, is `"53 pm"` or `53 × 10^(-12)"m"`.

`V = (4/3)πr^3 = (4/3)π(53 × 10^(-12)"m")^3 = 6.24 × 10^(-31)"m"^3`

`ρ = m/V = (1.67 × 10^(-27)"kg")/(6.24 × 10^(-31)"m"^3) = 2.7 × 10^3"kg/m"^3 = "2.7 kg/dm"^3`