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


2 Answers 2


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.

  • $\begingroup$ good point. I'll edit to address conservation of mass/energy too $\endgroup$
    – Paul T.
    Commented Oct 12, 2019 at 12:19
  • $\begingroup$ 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 $\endgroup$
    – From Geoff
    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.


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