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Hydrogen Nucleus

Nucleus of any atom will comprise of protons and neutrons and hydrogen is no exception but hydrogen atom that we consider the most stable has no neutrons and only one proton which gives it a unique place in the entire periodic table. The isotopic forms of hydrogen atom do have neutrons and thus give a different mass number, density as well as radius.

Hydrogen with a standard mass 1.0078 u has naturally occurring three isotopes (1H 2H 3H). Other than these isotopic forms there are other highly unstable nuclei’s 4H 7H which are not found in nature but synthesised in laboratory. The most heavily unstable nuclei are tritium which has a half-life of 12.32 years whereas other heavier isotopes have a half-life less than 10-21 seconds or zepto seconds.

Of all elements only Hydrogen has different names for its isotopes which are in common use today. The deuterium or 2H isotope and tritium 3H with symbols D and T are the naturally occurring isotopes which are used generally for studies and lab practices. The ordinary isotope of hydrogen which has no neutron is also known as protium.

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Hydrogen Nucleus Mass

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The hydrogen atom having only one proton in the nucleus has a mass of 1.6726 $\times$ 10-27 Kg. the mass of electron is negligible and hence covers only 0.05% of the mass.
Mass number (A) = Z + N 

Where, Z is the atomic number which equals the number of protons in nucleus. N is the neutron number which equals the number of neutrons in nucleus.

Hydrogen species 
Hydrogen -1 or Protium 1.00782 u or 1.6726 x 10-27 Kg 
Hydrogen -2 or Deuterium 2.014 u or 3.34432563 × 10-27 kg 
Hydrogen – 3 or Tritium 3.016 u or 5.00818575 × 10-27 Kg 
Hydrogen – 4 or Quadrium 
4.0278 u or 6.68831915 × 10-27 Kg 

Hydrogen Nucleus Charge

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The nucleus charge of Hydrogen atom is positive as the proton carries a positive charge. Proton was discovered in 1919 by Rutherford and its formal charge as put as positive as there is only one proton inside the Hydrogen nucleus and hence both the atomic mass and number are equal to 1.

In other isotopic forms of Hydrogen although the presence of neutrons give a different mass number but the nucleus charge still remains positive as neutrons carry no charge.

Hydrogen Nucleus Diameter

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The diameter of Hydrogen nucleus is found to be 1.6 $\times$ 10-15 m or 0.0000016 nm approximately.

Protium or Hydrogen - 1

$^{1}\textrm{H}$ is the most common hydrogen isotope with an abundance of more than 99.98% and the formal name of protium is mainly because this isotope has only one proton.

Deuterium or Hydrogen – 2

The other stable hydrogen isotope $^{2}\textrm{H}$ known as deuterium which contains one proton and one neutron in its nucleus is not radioactive and does not have high toxicity as well. Water which is enriched in deuterium instead of the normal form of hydrogen is termed as heavy water which is used in nuclear plants as neutron moderator and coolant. These are also considered as potential fuel for commercial nuclear fusion.

Tritium or Hydrogen – 3

$^{3}\textrm{H}$ known as tritium which contains one proton and two neutrons in its nucleus is radioactive and decays into Helium-3 through the beta particle decay with a 12.32 years half-life. These are used in all kinds of thermonuclear fusion type of weapons, used as tracer in isotopic geochemistry and are used as self-powered lighting devices.

Quadrium or Hydrogen - 4

This has one proton and three neutrons and is highly unstable isotope of hydrogen which is synthesized in lab and decays through neutron emissions with a half-life of 1.39 $\times$ 10-22 seconds.

Muonic Helium or Hydrogen – 4.1

The Muonic helium is created by substituting a Muon for one of the electrons in Helium-4. As the Muon orbits very close to nucleus than electron and hence could be regarded as an isotope which has a nucleus consisting of two protons, two neutrons and one Muon. This has a single electron orbiting the nucleus. This can bond with other atoms and behave as hydrogen atom unlike the Helium atom.

Hydrogen – 5

This isotopic form is very unstable and has a nucleus with a proton and four neutrons. This is synthesized in lab and decays through double neutron emission with a half-life of 9.1 $\times$ 10-22 seconds.

Hydrogen – 6

This isotopic form has a nucleus consisting of one proton and five neutrons. This has a half-life 2.9 $\times$ 10-22 seconds. This decays through triple neutron emission.

Hydrogen Nucleus Volume

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The hydrogen nucleus has a radius of around 8.41 $\times$ 10-16 m approximately and hence the volume could be calculated as $(\frac{4}{3})$ $\pi$ $radius^{3}$

Volume of hydrogen nucleus: (1.33 $\times$ 3.142) $\times$ (8.41 $\times$ 10-16 m)3 = (1.33 $\times$ 3.142) $\times$ (5.94 x 10-46 m3) = 24.91 $\times$ 10-46 m3 = 2.49 $\times$ 10-45 m3

The volume of any nucleus could be ascertained in terms of nucleus mass (A) by the formula as mentioned below:

Volume (nucleus) = $(\frac{4}{3})$ $\times$ $\pi$ $\times$ r3  OR $(\frac{4}{3})$ $\times$ a3 A

Hydrogen Nucleus Density

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In a Hydrogen atom, the nucleus consists of just one proton with a mass of 1.6726 $\times$ 10-27 Kg. Along with this the size of the atom is about 0.8768 $\times$ 10-15 meters.

Density = ${mass}{volume}$

$\rho$ = $\frac{m (nucleus)}{V (nucleus)}$ = $\frac{Am}{\frac{4}{3} \pi a^3 A}$
Density $(\rho)$ = (1.67 $\times$ 10-27 Kg) / (2.49 $\times$ 10-45 m3) = 6.7 $\times$ 1017 Kg per m3
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