that has 3 neutrons. Is it possible for helium-1 exist? and if not why not?

Not exactly.

Helium, of course, by definition has exactly 2 protons, and can vary with the number of neutrons.

Here is a list of the

helium isotopes.Helium-4 is ([tex]^4_2[/tex]He) is the most common form of helium on Earth since it is a nuclear decay product. It has 2 neutrons and 2 protons for a molecular weight of 4.

Helium-3 ([tex]^3_2[/tex]He) is also stable, it has 1 neutron, and 2 protons for a molecular weight of 3.

Helium-2 (diprotium), ([tex]^2_2[/tex]He) has no neutrons, and 2 protons. It is very unstable, and decays almost immediately to deuterium, or Hydrogen-2 ([tex]^2_1[/tex]H).

[tex]^2_2[/tex]He → [tex]^2_1[/tex]H + e

^{+} + ν

_{e} + Energy, where e

^{+} is a positron (antimatter), and ν

_{e} is an

electron neutrino.

By definition, one can not have a Helium-1 because that would mean 2 protons and (-1) neutrons for a molecular weight of 1.

Helium with more neutrons is unstable, with a half-life of less than a second.

Helium-5 ([tex]^5_2[/tex]He) would have 2 protons, 3 neutrons, and decays with a half-life of about 700 ×10

^{−24} s