One of the most amazing of all substances, Hydrogen is the lightest of all diatomic gases available in earth system and perhaps in entire Universe. But we never know. This gas has no odour, taste or colour. This atom has the simplest of all nucleus and fills out only proton or couple of neutrons at max but under special conditions.
When the discussion is revolving around hydrogen nucleus, we are invariably looking at the nucleus composition and perhaps the isotopes which are existing for hydrogen. The first of the isotopic kind has only one proton and no neutron, whereas the other two isotopic forms have one and two neutrons in nucleus apart from one proton. This makes the isotopic forms little heavier than the prevalent one. Let us discuss more about this element. Hydrogen with only one proton and no neutron in nucleus is termed as protium, while the one with one neutron and one proton is called deuterium and finally we have the third of the species having two neutrons and single proton called tritium.

The mass of hydrogen nucleus depends upon the number of particles that occupy the space. Since we get to see three isotopic forms of hydrogen atom, we will have three different nuclear mass as well. For any element the atomic mass or nuclear mass is the combined mass order of proton and neutron and hence, the mass of hydrogen atom or hydrogen nucleus should also follow through.
The first of the kind having only one proton and no neutron shows a mass number of 1 u (atomic mass unit). The second of the type having one proton and one neutron shows a mass number of 2 u (atomic mass unit). Finally the third of the isotopes having one proton and two neutron shows a mass number of 3 u (atomic mass unit).
Protium: 1 u (1 p + 0 n)
Deuterium: 2 u (1 p + 1 n)
Tritium: 3 u (1 p + 2 n).
For any element the charge of nucleus is positive and hence hydrogen without any exception would have the same charge. This is mainly because the proton carrying the positive charge shows the overall characteristics of nucleus as the other particle neutron doesn’t carry any charge and this results in positive charge of Hydrogen nucleus.
If we consider the effective nuclear charge, then it is basically the attraction of outer electrons by the nucleus countered by the repulsion by inner electrons. For hydrogen there’s no such things as there is only one electron.
Nucleus radius for any element is considered from its nucleus center to its edge of electron cloud. The total electron cloud that surrounds an atomic nucleus is kind of indefinite as there’s no distinct edge or even boundary. Isolating even a single atom and measuring the diameter is difficult and hence to calculate the diameter we need to look at its immediate environment and also the interaction with surrounding atoms.
So basically we calculate values for atomic radius by estimating the distance between the atomic centres between adjacent atoms of same species. Hydrogen has atomic diameter of 1.75 fermi or 1.75 x 10^{15} m.
Once we know the radius of an element we can easily calculate the volume of the same as we consider the atoms to be spherical in shape. The radius of Hydrogen is found to be 1.75 x 1015 m and hence we can use the volume of sphere formula to calculate the volume.
Volume of sphere = (4 / 3) * π r^{3}
Volume of Hydrogen = (4 / 3) * 3.14 * (0.875 x 10^{15})^{3} m^{3}
Volume of Hydrogen = 1.1667 x 10^{45} m^{3}
For any material the density is calculated from its mass and volume. The density is the ratio that exists between mass of the substance against the space or volume it occupies. For Hydrogen, the nucleus has three isotopic forms.
Protium density:
(Mass of protium / Volume of protium) = (1.6735 * 10 27 Kg) / (2.79 x 1045 m3) = 5.99 x 1017 Kg / m3
Deuterium density:
(Mass of deuterium / Vol. of deuterium) = (3.34 * 1027 Kg) / (2.79 x 1045 m3) = 1.19 x 1018 Kg / m3
Tritium density:
(Mass of Tritium / Vol. of Tritium) = (5.0081 * 1027 Kg) / (2.79 x 1045 m3) = 1.79 x 1018 Kg / m3