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

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Answer 1 · 2015-06-13T19:28:06

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 $2.7"kg/dm"^3$ .

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 $53 × 10^(-12)"m"$ .

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

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