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Welcome to our Physics lesson on Elementary Particles and Laws of Conservation, this is the fifth lesson of our suite of physics lessons covering the topic of Particles and Antiparticles - Interaction and Laws of Conservation, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
From all elementary particles discussed so far, only the particles proton, electron, positrons, neutrino, antineutrino and photon (gamma quant) are stable while the other particles are radioactive. Thus, while the lifespan of neutron is 12 minutes, that of zero pion (π0) particle is about 10-16 s. According to the law of energy conservation, an isolated particle can split only in lighter particles. The balance of energies (or masses) is ensured by means of kinetic energy of fission products. However, particles like neutrino, antineutrino and photon have a zero rest mass, hence they cannot experience any fission. Likewise, electron (e-) and positron (e+) as the two lightest charged particles, are stable too (electric charge can neither increase nor decrease during the fission process).
In order to explain the stability of proton and antiproton from the experimental point of view, scientists associated a nucleonic number otherwise known as baryon charge B to each particle, in analogy with the electric charge e discussed in Electrostatics section. Baryon charge represents the amount of nucleons' attraction inside the atomic nucleus, i.e. it characterizes the strength of nucleons as sources of nuclear field. Hence, there is a full similarity between the baryon charge that produces the nuclear field and electric charge that produces the electric field.
The conservation of baryon charge implies the conservation of the number of baryons in a nucleus. Baryons are not only neutrons and protons but also some heavier elementary particles discovered recently (>Λ, Σ, ΞΩ - hyperons) which contain nuclear charge. In other words, the conservation of baryon charge also implies the conservation of nuclear material.
Each baryon bears a baryon number B as follows:
Knowing the baryon number of each particle or antiparticle helps us understand whether a certain nuclear reaction can occur or not (not all combinations of elementary particles are possible). It is not sufficient to have the law of electric charge conservation applied but the law of baryon charge conservation must also be applied for a nuclear reaction to occur. Let's clarify this point through an example.
Determine whether the following nuclear reaction are possible or not.
Thus, this nuclear reaction cannot occur, as the baryon charge is not conserved. The law of conservation of baryon charge is so far universal. It is similar to all laws of conservation such as the law of conservation of mass, energy, momentum, moment of impulse, electric charge etc.
Since there exist particles and antiparticles such as neutrino, antineutrino, mesons etc., which have neither electric nor baryon charge, this implies that these two types of charge are not the only that make the distinction between matter and antimatter. Obviously, neutrino and antineutrino must have other properties that make them different from (and opposite to) each other. For example, we see that in beta decay process, antineutrino is associated with electron while neutrino with positron. This is not a casual combination. It is impossible to find neutrino and antineutrino alone in space. This fact brought scientists in the conclusion that there exist another charge besides the electric and baryon ones in elementary particles as well as the law governing its behavior. This is known as a lepton charge - a type of charge that is also conserved in various nuclear reactions and radioactive decay processes.
The term "lepton" derives from Greek language (leptos = lightweight). The category of leptons (lightweight particles) includes electrons and positrons (e- and e+), muons and antimuon (μ- and μ+), tau particles - elementary particles similar to the electron, with negative electric charge and a spin of 1/2 (τ+ and τ-) and the three types of neutrinos (νμ, νe and μτ) each of them having in correspondence an antineutrino as well. In total, there are six leptons and six antileptons. All leptons have a spin of 1/2. The tau particles and muons are unstable; each tau particle splits into one muon and two neutrinos while one muon splits into one electron and two neutrinos. Tau particles have a large mass (1784 MeV/c2, i.e. about 3491 times heavier than electron). They belong to the category of leptons only because they don't produce a strong interaction.
As we discussed earlier, leptons obey to the laws of conservation. There are 3 lepton numbers according to the type of corresponding leptons (Le, Lμ and Lτ). Thus, electron e- and electronic neutrino νe have L = + 1 as well as μ-meson μ- and muon neutrino νμ (L = +1) while their antiparticles have L = -1. In all types of interaction, the lepton charge must be conserved in order to have a valid reaction. Let's explain this point through an example.
Prove that the μ-meson reaction
does not violate the laws of conservation, hence it can occur.
We must see whether all three laws of charge conservation (of electric, baryon and lepton charge) are applied in this reaction. Thus, since the μ-meson (μ-) and electron (e-) have both a positive charge -q while the other two particles don't have any electric charge, we obtain:
Thus, the electric charge is conserved. Now, let's check for the baryon charge. Since all the above elementary particles have a baryon charge equal to zero (only protons, neutrons and their corresponding antiparticles have a baryon charge different from zero, we have:
Hence, the baryon charge is also conserved in this reaction. At last, we have to check whether lepton charge is conserved or not. Thus, based on the lepton numbers given earlier, we have
Hence, the lepton charge is also conserved. Thus, since all three types of charge are conserved, this reaction can occur as it obeys the laws of conservation.
You have reached the end of Physics lesson 21.2.5 Elementary Particles and Laws of Conservation. There are 6 lessons in this physics tutorial covering Particles and Antiparticles - Interaction and Laws of Conservation, you can access all the lessons from this tutorial below.
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