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

Jun 13, 2015

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 $2.7 {\text{kg/dm}}^{3}$.

#### Explanation:

The formulas to use are

$\text{Density" = "mass"/"volume}$ 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 $\text{53 pm}$ 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