Video: Charged Leptons

In this video, we will learn how to describe the properties of electrons, muons, and tauons and their antiparticles.

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Video Transcript

In this video, we will be discussing charged leptons. This includes the most famous lepton that we probably already know, the electron, as well as its cousins the muon and the tauon. We will describe the properties of these particles, such as charge and mass, along with the properties of their antiparticles.

Electrons, muons, and tauons all belong to a group of particles known as leptons. More specifically, these particles are known as charged leptons as each of the particles has a charge. We should recall that an electron, as represented by the letter e, has a relative charge of negative one, meaning that the value has a magnitude of one elementary charge. So the charge would be negative 1.6 times 10 to the negative 19th coulombs. How does that compare to its cousins the muon and the tauon as represented by the mu and the tau symbol, respectively?

Both of these particles also have a relative charge of negative one, so we can say that all three of our particles have a relative charge of negative one, which is why the symbols for the electron, the muon, and the tauon each have a negative sign in the upper right-hand corner as shown here. But what about their masses? We might recall that the mass of an electron is 9.11 times 10 to the negative 31st kilograms. And how does that compare to the muon and the tauon? It turns out that their masses are a bit larger. In fact, the mass of the muon is approximately 200 times larger than the mass of the electron. And the tauon is approximately 3500 times larger than the mass of the electron.

Looking at our particles, we have listed them in ascending mass from the top of our screen to the bottom of our screen. To properly include all of the charged leptons, we must also add to our list the antiparticles of the electron, muon, and tauon. These will be called the positron, antimuon, and antitauon, respectively. Together, these six particles represent the group known as charged leptons. Each antiparticle has the same mass as their corresponding particle. The positron has a mass of 9.11 times 10 to the negative 31st kilograms. The antimuon has a mass of 1.88 times 10 to the negative 28th kilograms. And the antitauon has a mass of 3.17 times 10 to the negative 27th kilograms.

However, each of the antileptons have a relative electric charge of positive one, as represented by the positive sign in the upper right-hand corner of their symbols. For this reason, we have drawn all the negative particles in blue and all of the positive antiparticles in red. These six charged leptons interact through three of the four fundamental forces, including the electromagnetic force, the gravitational force, and the weak nuclear force. The only fundamental force not involved in their interactions is the strong nuclear force.

At this point in our studies, we should be pretty familiar with the electron, but probably not as much with the muon and the tauon. This to some extent could be based on the instability of these two leptons. In fact, muons are only around for approximately two microseconds before they decay. And tauons will decay 10 million times faster than the muon. What happens to them then? Muons and tauons will decay to lighter, more stable particles. For example, a muon will decay into an electron and two corresponding neutrinos — for the purposes of this video, we don’t need to worry about what neutrinos are, but simply that the muon decays into a more stable particle, in this case, the electron — whereas the tauon might decay into an electron and two neutrinos or a muon and two neutrinos.

Once again, we won’t worry about neutrinos for this video, but rather focus on the tauon decaying into a muon or an electron, both of which are more stable. If the tauon decays into a muon, we would then once again expect the muon to decay into an electron. Heavier particles in general decay faster than lighter particles. So the bottom line is that the electron is gonna be more stable because there is no charged lepton that is lighter than the electron. Since the antiparticles for both muons and tauons are also heavier particles, they too will decay and are considered relatively unstable when compared to the positron.

When dealing with particles and antiparticles, we need to keep in mind pair annihilation. When a particle and its antiparticle meet, they annihilate each other and release a photon. In many cases, more than one photon is released. Let’s look at what happens when an electron meets its antiparticle, the positron. After the electron and positron meet, they release two gamma-ray photons. The same concept is true in reverse. A photon that interacts with matter can create a pair production of a particle and its antiparticle. This is known as pair production. An example is a photon, in this case, a gamma-ray photon, coming in with enough energy to produce an electron and a positron pair.

Now that we’ve discussed properties of charged leptons, let’s do a few examples.

List the following particles in order from the least mass to the greatest mass: tauon, photon, proton, electron, muon, neutron.

We’ll be ranking our six particles from least mass to greatest mass. Of the six particles listed, we know that a photon is considered to be massless. Therefore, it would have the least mass out of everything. And so we can place it at the top of our list. When we compare the masses of our three charged leptons, the tauon, the electron, and the muon, the electron has the least mass and the tauon has the greatest with the muon being in the middle. In fact, the mass of the electron is so small that it comes next on our list. And the muon being 200 times greater than the electron is the third on our list, which leaves us with the three most massive particles on our list, the tauon, the proton, and the neutron.

Their masses are actually pretty close together. With the neutron slightly edging out the mass of a proton, we can put our next particle in our list. The proton is the next most massive particle. The proton is followed pretty closely by the neutron, leaving only the tauon which happens to be about twice as massive as the neutron. When ranking the particles on our list from least mass to greatest mass, it goes photon, electron, muon, proton, neutron, tauon.

Which of the following particles have an electric charge of positive one? Photon, electron, antimuon, tauon, proton, neutron, antitauon, muon.

We can begin by eliminating particles we are most familiar with, the electron and the neutron. We only want particles that have an electric charge of positive one. And we know that the electron has a charge of negative one. Therefore, this cannot be one of our particles. We also know that a neutron is neutral or has a charge of zero. Therefore, we can eliminate neutron from our list as well. Along with the electron and the neutron, we should also be very familiar with the proton. A proton has an electric charge of positive one and is therefore one of the particles we are looking for. Looking back at our list, the first particle, the photon, the particle nature of light, does not have any charge and therefore can be eliminated from our list.

This leaves us with particles that are considered the charged leptons, antimuon, tauon, antitauon, and muon. We can recall the six charged leptons. The electron, which we have already eliminated, the muon, and the tauon all have a charge of negative one. And their associated antileptons, the positron, the antimuon, and the antitauon, all have charges of positive one. Referring back to our list, all of the particles that fall under the negative one column, the tauon and the muon, can now be eliminated. The antimuon and the antitauon are charged leptons with a value of positive one charge. The particles from the list that have an electric charge of positive one are the antimuon, proton, antitauon.

Which of the following equations shows the pair production of a tauon and an antitauon from a high-energy gamma ray? (A) 𝜏 negative plus 𝜏 positive arrow to 𝛾. (B) 𝛾 arrow to 𝜏 negative plus 𝜏 positive. (C) 𝛾 arrow to 𝑡 plus anti 𝑡. (D) 𝑡 plus anti 𝑡 arrow to 𝛾. (E) 𝛾 arrow to 𝜇 negative plus 𝜇 positive.

Our problem talks about tauon, antitauon, and gamma ray. Therefore, we can eliminate any answer choice that does not include these three particles. We need to recall that a tauon is represented by the symbol 𝜏 with a negative in the upper right-hand corner. And the antitauon is represented by 𝜏 with a positive symbol in the upper right-hand corner. Each of the answer choices has a gamma ray represented by the symbol 𝛾. We could eliminate answer choices (C), (D), and (E) as none of the three of these have a tauon or antitauon in them.

The problem tells us our equation is a pair production that takes a high-energy gamma ray and turns it into a tauon and an antitauon. Looking at our remaining two equations, only answer choice (B) has a gamma ray being turned into a tauon and an antitauon. In fact, answer choice (A) is what we would call a pair annihilation, where a tauon and an antitauon meet and release a gamma-ray photon. Of the listed equations, the only one that shows a pair production of a tauon and an antitauon from a high-energy gamma ray is answer choice (B).

Key Points

The electron, muon, tauon, and their antiparticles are known as the charged leptons. The electron, muon, and tauon have a relative charge of negative one. The electron has a mass of 9.11 times 10 to the negative 31st kilograms. The muon has a mass of 1.88 times 10 to the negative 28th kilograms. And the tauon has a mass of 3.17 times 10 to the negative 27th kilograms.

The antiparticles, the positron, the antimuon, and the antitauon, all have a relative charge of positive one. The muon, tauon, and their antiparticles are unstable and decay into lighter particles. Pair annihilation between a particle and antiparticle produces a photon. A photon can pair produce a particle–antiparticle pair. Charged leptons interact via the electromagnetic force, weak nuclear force, and gravity.

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