# How can neutron be converted to proton and electron?

Since a neutron and a proton are made up of quarks and an electron is a lepton, how can a neutron yield an electron?

A neutron is made of 3 quarks, two down quarks and one up. The process you are talking about is called beta decay. It is a weak nuclear interaction the can be summarized like this:

$$(u+d+d) \rightarrow (u+d+u) + e^- + \bar{\nu}$$

One of the down quarks ($$d$$) decays producing an up quark ($$u$$), an electron ($$e^-$$), and an anti-neutrino ($$\bar\nu$$). The final baryon state has two up quarks and one down, that's a proton. This process follows a few conservation laws.

• conservation of baryon number: $$1 \rightarrow 1$$, Each quark counts for $$1/3$$ of a baryon number. The three-quark proton and neutron are each $$1$$ baryon. This maintains the same number of quarks on each side of the arrow.
• conservation of lepton number $$0 \rightarrow +1 -1$$. A neutrino is also a lepton, and an anti-particle counts as $$-1$$ of it's type. So the electron and anti-neutrino add up to zero total leptons on the right-hand-side.
• conservation of charge $$0 \rightarrow +1 -1 +0$$. The $$(udd)$$ neutron and the anti-neutrino have zero charge. The $$(uud)$$ proton has $$+1$$ charge and the electron has $$-1$$, so the charge is zero on both sides of the arrow.
• conservation of energy $$E_n \rightarrow E_p + E_e + E_\nu$$. The total energy of the particles on each side is the same.

Energy conservation is a bit more that just that. All of the particles have mass, so they have energy following following $$E=mc^2$$. Additionally, they could have kinetic energy if they are moving.

If the initial neutron is at rest, then its energy is $$E_n=(1.008664\,\mathrm{u})c^2 = 939.6$$ MeV, where $$\mathrm{u}$$ is the atomic mass unit and MeV is a mega-electron-volt, a unit of energy. A proton at rest has an energy of $$E_p = 938.3$$ MeV, and an electron at rest has $$E_e = 0.5$$ MeV. Nobody knows the rest mass of a neutrino, but it's at least a million times less than an electron. We'll call it zero, even though it's not...

When we put this together assuming everything is at rest, we get: $$939.6\,\mathrm{MeV} \rightarrow 938.3\,\mathrm{MeV} + 0.5\,\mathrm{MeV} + 0\,\mathrm{MeV}$$ But wait, the two sides aren't equal. The right-hand-side is missing $$0.8$$ MeV. To conserve energy the new particles must be moving, so they have a little bit of kinetic energy to make up the mass-Energy difference.

• good point. I'll edit to address conservation of mass/energy too Commented Oct 12, 2019 at 12:19
• First answer has a typo in that the structure of the neutron and proton are the other way around A neutron is made of 3 quarks, but it is two down quarks and one up A proton is made of 3 quarks, two up quarks and one down Then you need to change the equation appropriately (u+d+d)→(u+d+u)+e−+ν¯ here is a Q and A from Fermilab that partly covers the question fnal.gov/pub/science/inquiring/questions/antineutron.html Commented Mar 26, 2023 at 18:43

A nuclear decay is not something that already exists being pulled out of a particle. It is the creation of new particles. As long as the transition respects all of the conservation laws there is a probability of it happening.