Normal hydrogen will not have neutrons in its nucleus probably because it is a very small atom. It will not have enough space for a neutron anymore. It will only come with one electron and one proton. The fact that it only has one proton is the reason why it does not have a neutron.
It should be remembered that the main goal of the neutron is to make sure that the atom will be stable. Since hydrogen only has one proton, it will not react to other potential protons in the nucleus because there isn’t any other proton available. If you would remove the electron from the hydrogen atom, it will become an ion.
The tiny nucleus of the hydrogen atom does not have any neutrons within its nucleus. The hydrogen atom is the tiniest of atoms and has only one electron and one proton. Thus you can take out the electron and it will make an ion, but the neutrons cannot be removed from this atom.
The number of neutrons impact the weight of the atom. One neutron weigh as much as an electron and proton put together. Thus the weight of the hydrogen atom is so mimimal because of this phenomon of not haveing a neutron. This is what causes the seemingly weightless property of the hydrogen atom.
Hydrogen does not have neutron since it is the smallest atom and would mean that it also has the smallest nuclei just enough room for a proton. It does not need any neutron to be stable as it has one proton and one electron that cancel out their charges.
Meaning, hydrogen has no charge and a neutron would not be needed to stabilize a chargeless atom. Neutrons balance the movement of the protons inside the nuclei so the protons will not bump into each other and create an explosion and since hydrogen has only one proton, the atom is safe and stable. If there are two protons in nuclei and no neutron present, this atom will be unbalanced.