Video Transcript
The following equation shows a muon
and an antimuon being produced via pair production from a gamma-ray photon. What is the total lepton number
before the interaction takes place? What is the total lepton number
after the interaction takes place?
Looking at this equation, we indeed
see a gamma-ray photon here on the reactant side, producing a muon and an
antimuon. This is called pair production
because the muon and the antimuon are antiparticles one of another. The first part of our question
asks, what is the total lepton number before the interaction takes place, that is,
before the muon and antimuon have been generated? This is another way of asking, what
is the total lepton number of this gamma-ray photon that’s all that existed before
the interaction? When we consider the lepton number
of a particle or group of particles, the rule for that goes like this. If a particle is a lepton, then its
lepton number is positive one. If it’s an antilepton, then its
lepton number is negative one. And if the particle is neither a
lepton nor an antilepton, then its lepton number is zero.
When it comes to classifying this
photon, we can recall that all leptons, and there are six of them, have mass; that
is, none of them are massless particles. A photon, though, is massless. And from this, we can tell that
it’s not a lepton. But then it’s also not an
antilepton because these antiparticles have the same mass as their corresponding
lepton. This tells us that a photon is
neither a lepton nor an antilepton. And therefore, it has a lepton
number of zero. Since that’s the only particle
involved in our interaction before the interaction takes place, we know that the
total lepton number before that happens is therefore zero.
Part two of our question asks, what
is the total lepton number after the interaction takes place? There are two ways we could figure
this out. One is to recall that lepton number
is conserved in any nuclear equations. This means the total lepton number
before an interaction must equal the total lepton number after an interaction. A second way we could get at the
same answer is by recognizing that a muon is a lepton and therefore has a lepton
number of positive one, while an antimuon is an antilepton and therefore has a
lepton number of negative one. The total lepton number after the
interaction then would be positive one minus one or zero. So both before and after this
interaction, the total lepton number involved is zero.
