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

1 Answer
Jun 13, 2015

Answer:

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#