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 (

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 (

He) is also stable, it has 1 neutron, and 2 protons for a molecular weight of 3.
Helium-2 (diprotium), (

He) has no neutrons, and 2 protons. It is very unstable, and decays almost immediately to deuterium, or Hydrogen-2 (

H).

He →

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 (

He) would have 2 protons, 3 neutrons, and decays with a half-life of about 700 ×10
−24 s