# Where does the electron come from when a free neutron transforms? [duplicate]

I'm reading in Tales of the Quantum (page 68) that "Each neutron is made up of one up quark and two down quarks. In a free neutron one of the down quarks will transform into an up quark, turning the neutron into a proton and creating an electron in the process."

Where does that electron come from?

• What are you looking for as an answer here? It's created in the process, as the text says. What information exactly are you missing? Are you simply looking for a more detailed explanation of neutron decay? Mar 18, 2020 at 16:03
• Have you seen the diagram of $\beta^-$ decay here? Mar 18, 2020 at 16:17
• The process isn't just a rearrangement of existing particles into a new configuration. With enough energy, new particles can be created. I believe the OP is looking for an answer that elaborates on this. Mar 18, 2020 at 16:35
• Does this answer your question? beta decay equation balance Mar 18, 2020 at 17:01
• @foolishmuse, Re, "...or else there would be a net creation of energy." Did you mean to say, "...net creation of charge?" Of course energy also must be conserved, but that can be accounted for by the different rest energies of the particles, kinetic energies before and after, etc. Mar 18, 2020 at 17:08

Here's an analogy that might help.

When an electron jumps from a higher orbital to a lower one, it produces a photon which carries away both energy and angular momentum. This is the energy difference and angular momentum difference between these two electron orbits.

When a neutron turns into a proton, the quarks change from an udd to an uud. So a down quark is changing into an up quark. This change is similar to when the electron changed orbits, but with a couple of key differences.

In the case of a down quark turning into an up quark instead of a photon, a $$W^-$$ virtual particle is created. It's virtual because the W's have mass and there isn't enough energy in this transition to account for this mass. But quantum mechanics will let this happen in its funny way.

The $$W^-$$ carries aways some energy, angular momentum and some electric charge. The $$W^-$$ isn't stable, and so will decay into an electron and an antineutrino. The electron and neutrino have a lower mass than the difference between the d and the u quark, and so the energy of transition is able to create real versions of them.

Over the full story, the energy, angular momentum and charge are all accounted for.

There are some nuances that I've glossed over, but that is pretty close to the legit picture.

This was actually why physicists (Wolfgang Pauli, Enrico Fermi) started to think that neutrinos and antineutrinos were a thing.

On its own, the electron that is produced doesn't have enough energy to account for the change in mass from the neutron to the proton. It also doesn't the right amount of angular momentum. So there must have been some other (hard to detect) particle that was carrying away the extra energy and angular momentum.

You might check out the story of the neutrino.

https://www-numi.fnal.gov/public/story.html

• Thanks All. Very helpful. Mar 18, 2020 at 17:13
• David's answer is correct, but to elaborate on your puzzlement, the electron came from a neutrino just like the d quark came from the u. The ud current is coupled to the $\nu e^-$ current by a W boson. This structure of quark and lepton (the building blocks) currents coupled by force carrying bosons is how particles interact. Another example, the $e^-e^-$ current is coupled to another $e^-e^-$ current by a photon boson. Notice that the photon is an operator Q which doesn't change the charge on the current, but the operator $W^-$ changes u to d, and a $\nu$ to an $e^-$. Mar 18, 2020 at 18:06

It is very important to understand, and accept that the universe is set up so, that if certain laws are obeyed, certain particles and energy can be transformed into other formes of particles and energy.

There are many examples of this, like pair creation, with photons and electron positron pairs, but your case is one of these transformations too.

What needs to be obeyed is energy and momentum conservation (and other laws), but if these are obeyed, then the part of the total energy in the process might as you can see be converted into an electron.

Another example for your question is asking where the neutrino comes from in weak decay processes.

Or you could ask where does the photon come from when an electron/atom emits it.

So you are asking where the electron comes from, and the answer is that it has always been there (in a different form of energy), and it comes from the total energy in the process that is available.