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I wondered whether there is a maximum number of neutrons in an isotope. Or is there no maximum number? So, can an H-75 atom exist?

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Effectively there is a maximum number, or rather producing more and more neutron-rich isotopes requires energy.

You can think of it this way. Identical particles are affected by the Pauli exclusion principle; this applies to neutrons in the nucleus. Therefore a stack of neutrons will fill up the lowest energy states, but will then have to occupy higher energy states. However, it could then be the case that it is more energetically favourable for a neutron in a higher energy state to beta decay into a proton and an electron (and anti-neutrino). The proton would occupy a lower energy level in the nucleus. But produce too many protons and they fill their possible low-lying energy states and then the possible decay proton has nowhere to go - the beta decay is blocked and instead inverse beta decay can become favourable.

In this way there is a locus of stability for the ratio of neutrons to protons as a function of the total mass number of the nucleus. See also this question. If there are too many neutrons then they are unstable to beta decay; too few neutrons and they are unstable to electron capture (inverse beta decay).

The plot below indicates this line of stability (taken from the wikipedia page on beta stability isobars).

Beta stability

However, this is a "low density" approximation. It is possible to produce extremely neutron-rich isotopes in the ultra-dense crust regions of neutron stars. Here the nuclei are surrounded by ultra-relativistic degenerate electrons and, at very high densities, degenerate neutrons. The requirement that beta decay electrons cannot be created below the Fermi energy of the electron gas shifts the beta equilibrium towards more neutron rich nuclei. A crude calculation (the Harrison-Wheeler treatment) suggest that $n/p$ can reach 3 or more at densities above $10^{15} kg/m^{3}$. However the most stable nuclei at these densities must have atomic masses of 200 or more, so your suggestion of Hydrogen 75 is not on the cards.

At even higher densities, the individual nuclei lose their identity and form very neutron-rich structures (often called nuclear pasta) and then even to a nucleon fluid dominated by neutrons; but these could not be considered nuclei in the sense you mean.

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Maybe I should add that nuclei which are unstable to beta decay can still exist for quite some time. However, beyond the limit of beta-stability, there comes a point at which it is energetically favorable for a nucleus to decay by emitting a neutron. Another way of putting this is that the last neutron is not bound within the nucleus. This point in an isotopic chain is called the neutron dripline (there is also a corresponding proton dripline). In the case of hydrogen, 1H and 2H are stable, 3H is unstable to beta decay with a half-life of 12.32 years, and 4H is unstable to neutron decay and decays essentially instantaneously.

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