by anearthling

Question by doodlesthemonkey: How do I calculate the densities of a hydrogen nucleus and a hydrogen atom?
Using the mass of the proton (1.67e-27 kg), the mass of the electron (9.11e-31 kg), and the sizes of the nucleus and the atom, calculate the densities of a hydrogen nucleus and a hydrogen atom. (Radius of hydrogen atom is 1e8 cm and I thnk the diameter of the nucleus is 1e-13 cm)
density of hydrogen nucleus
? g/cm3
density of hydrogen atom
? g/cm3

There is another question just like this already on answers but when I tried it out it did not work.

Best answer:

Answer by Maxime J
You will very well understand with the following paragraph. (Source at the bottom.)

“The nucleus occupies only a tiny fraction of the volume of an atom (the radius of the nucleus being some 10,000 to 100,000 times smaller than the radius of the atom as a whole), but it contains almost all the mass. An idea of the extreme density of the nucleus is revealed by a simple calculation. The radius of the nucleus of hydrogen is on the order of 10-13 cm so that its volume is on the order of 10-39 cm3 (cubic centimeter); its mass is about 10-24 g (gram). Combining these to estimate the density, we have 10-24 g/10-39 cm3 approximately 1015 g/cm3, or about a thousand trillion times the density of matter at ordinary scales (the density of water is 1 g/cm3).”

Now, if I try with what you provided as numbers, I get the following:
The nucleus is made of one proton, so it weights
1.67*10^-27 kg or 1.67*10^-24 g
Diameter of the nucleus : 1*10^-13 cm
Radius : 5*10^-14 cm or 5*10^-16 m
Volume of a sphere : 4/3*pi*r³
Volume of the H nucleus : 4/3 * pi * (5*10^-16 m)³ = 5.236*10^-46 m³

Then you have a density (in SI units) of
1.67*10^-27 kg / 5.236*10^-46 m³ = 3.189*10^18 kg/m³
using google : convert 3.189*10^18 kg/m^3 to g/cm^3
I get 3.189*10^15 g/cm³

That’s not exactly what they say on the site, but I also didn’t use the same numbers.

Same idea for the whole atom.

Hope this helps!

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