Nick Connor

What is Isospin

In particle physics and nuclear physics, isospin, I or I₃,  is a quantum number related to the strong nuclear force. Isospin is associated with a conservation law which requires strong interaction decays to conserve isospin. This term was derived from isotopic spin, but physicists prefer the term isobaric spin, which is more precise in meaning.

Isospin was introduced by a German theoretical physicist and one of the key pioneers of quantum mechanics Werner Karl Heisenberg in 1932 as a way of distinguishing between protons and neutrons. It must be added, the concept of isospin was introduced before the development of the quark model, in the 1960s, which provides our modern understanding.

The observations have showed that the strong interaction does not distinguish between these nucleon. The strength of the strong interaction between any pair of nucleons is the same, independent of whether they are interacting as neutrons or as protons. Instead of regarding protons and neutrons as totally different species, as far as strong interactions are concerned, they are regarded as being different isospin states of the same underlying nucleon particle. This particle is called the nucleon. Similarly, the three pions, π⁰,  π⁺ and π^–, seem to be only three different states of the same particle, when only a strong nuclear force interacts. Isospin is mathematically similar to spin, though it has nothing to do with angular momentum. The spin term is tacked on because the addition of the isospins follows the same rules as spin.

The proton has isotopic spin ½ as the neutron has isotopic spin ½, but in case of proton the spin is pointing upwards and the spin of neutron is pointing downwards.

In general, each multiplet is assigned a isospin number I that is a positive integer or half an odd positive integer. Isospin may be considered to be a vector not in coordinate space (x, y, z). The third component, T₃, may take on any one of the values T, T − 1, T − 2, . . ., −T in a fashion similar to the values of the z component of angular momentum. Two other components, T₁ and T₂ can be ignored. Each of T₃ values corresponds to a different member of the multiplet. There are 2T + 1 particles in the multiplet. This result follows from counting the possible values of T₃. Thus singlets have T = 0, doublets have T = 1/2, and triplets have T = 1.

Total isospin for a collection of particles is computed in the same manner as for ordinary spin. , The maximum value of system isospin is the sum of the individual particle’s isospins. For example if one considers π⁺ – p scattering, T_max = 3/2 and T₃ = 3/2 so T can only have the value 3/2. For π⁻ − p scattering, T_max = 3/2 and T₃ = −1/2 so T can be either 3/2 or 1/2. In fact, measurement of T for π − -p sometimes produces T = 3/2 and sometimes T = 1/2 but always T₃ = −1/2.

See also:

Fundamental Particles

What is Isospin

In particle physics and nuclear physics, isospin, I or I₃,  is a quantum number related to the strong nuclear force. Isospin is associated with a conservation law which requires strong interaction decays to conserve isospin. This term was derived from isotopic spin, but physicists prefer the term isobaric spin, which is more precise in meaning.

Isospin was introduced by a German theoretical physicist and one of the key pioneers of quantum mechanics Werner Karl Heisenberg in 1932 as a way of distinguishing between protons and neutrons. It must be added, the concept of isospin was introduced before the development of the quark model, in the 1960s, which provides our modern understanding.

The observations have showed that the strong interaction does not distinguish between these nucleon. The strength of the strong interaction between any pair of nucleons is the same, independent of whether they are interacting as neutrons or as protons. Instead of regarding protons and neutrons as totally different species, as far as strong interactions are concerned, they are regarded as being different isospin states of the same underlying nucleon particle. This particle is called the nucleon. Similarly, the three pions, π⁰,  π⁺ and π^–, seem to be only three different states of the same particle, when only a strong nuclear force interacts. Isospin is mathematically similar to spin, though it has nothing to do with angular momentum. The spin term is tacked on because the addition of the isospins follows the same rules as spin.

The proton has isotopic spin ½ as the neutron has isotopic spin ½, but in case of proton the spin is pointing upwards and the spin of neutron is pointing downwards.

In general, each multiplet is assigned a isospin number I that is a positive integer or half an odd positive integer. Isospin may be considered to be a vector not in coordinate space (x, y, z). The third component, T₃, may take on any one of the values T, T − 1, T − 2, . . ., −T in a fashion similar to the values of the z component of angular momentum. Two other components, T₁ and T₂ can be ignored. Each of T₃ values corresponds to a different member of the multiplet. There are 2T + 1 particles in the multiplet. This result follows from counting the possible values of T₃. Thus singlets have T = 0, doublets have T = 1/2, and triplets have T = 1.

Total isospin for a collection of particles is computed in the same manner as for ordinary spin. , The maximum value of system isospin is the sum of the individual particle’s isospins. For example if one considers π⁺ – p scattering, T_max = 3/2 and T₃ = 3/2 so T can only have the value 3/2. For π⁻ − p scattering, T_max = 3/2 and T₃ = −1/2 so T can be either 3/2 or 1/2. In fact, measurement of T for π − -p sometimes produces T = 3/2 and sometimes T = 1/2 but always T₃ = −1/2.

Conservation of Isospin

The benefit of introducing isospin is that it vastly simplifies the problems of strong interactions. Thus for a interaction of two nucleons, instead of dealing with four charge states (neutron-neutron, proton-proton, proton-neutron, neutron-proton) we are concerned with only two isospin states, I = 1 and I = 0. The isospin concept tells us why certain strong interactions are forbidden on account of violation of isospin I. Isospin is associated with a conservation law which requires strong interaction decays to conserve isospin. For weak interactions neither T₃, nor T need be conserved.

See also: J. Christman,  (2001, December 11). ISOSPIN: CONSERVED IN STRONG INTERACTIONS. Retrieved from http://www.physnet.org/modules/pdf_modules/m278.pdf

See also:

Law of Conservation

Hadrons

In general, particles that do participate in strong interactions are called hadrons: protons and neutrons are hadrons. The hadrons are further sub-divided into baryons and mesons, according to the number of quarks they contain. Protons and neutrons each contain three quarks; they belong to the family of particles called the baryons. Other baryons are the lambda, sigma, xi, and omega particles. On the other hand mesons bosons and they are composed of two quarks: a quark and an antiquark. Besides charge and spin (1/2 for the baryons), two other quantum numbers are assigned to these particles: baryon number (B) and strangeness (S). Baryons have a baryon number, B, of 1, while their antiparticles, called antibaryons, have a baryon number of −1. A nucleus of deuterium (deuteron), for example, contains one proton and one neutron (each with a baryon number of 1) and has a baryon number of 2.

Since baryons make up most of the mass of ordinary atoms, the everyday matter is often referred to as baryonic matter.

The conservation of baryon number is an important rule for interactions and decays of baryons. No known interactions violate conservation of baryon number.

See also:

Fundamental Particles

Baryon Number

In particle physics, the baryon number is used to denote which particles are baryons and which particles are not. Each baryon has a baryon number of 1 and each antibaryon has a baryon number of -1. Other non-baryonic particles have a baryon number of 0. Since there are exotic hadrons like pentaquarks and tetraquarks, there is a general definition of baryon number as:

where n_q is the number of quarks, and n_q is the number of antiquarks.

The baryon number is a conserved quantum number in all particle reactions. The term conserved means that the sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction. A slight asymmetry in the laws of physics allowed baryons to be created in the Big Bang.

Examples of Baryon Numbers

For example, the following reaction has never been observed:

even if the incoming proton has sufficient energy and charge, energy, and so on, are conserved. This reaction does not conserve baryon number since the left side has B =+2, and the right has B =+1.

On the other hand, the following reaction (proton-antiproton pair production) does conserve B and does occur if the incoming proton has sufficient energy (the threshold energy = 5.6 GeV):

As indicated, B = +2 on both sides of this equation.

From these and other reactions, the conservation of baryon number has been established as a basic principle of physics.

This principle provides basis for the stability of the proton. Since the proton is the lightest particle among all baryons, the hypothetical products of its decay would have to be non-baryons. Thus, the decay would violate the conservation of baryon number. It must be added some theories have suggested that protons are in fact unstable with very long half-life (~10³⁰ years) and that they decay into leptons. There is currently no experimental evidence that proton decay occurs.

See also:

Baryons

What is Baryon

Baryon is any fermion that undergo strong interactions. In general, particles that do participate in strong interactions are called hadrons: protons and neutrons are hadrons. The hadrons are further sub-divided into baryons and mesons, according to the number of quarks they contain. Protons and neutrons each contain three quarks; they belong to the family of particles called the baryons. Other baryons are the lambda, sigma, xi, and omega particles. On the other hand mesons bosons and they are composed of two quarks: a quark and an antiquark. Besides charge and spin (1/2 for the baryons), two other quantum numbers are assigned to these particles: baryon number (B) and strangeness (S). Baryons have a baryon number, B, of 1, while their antiparticles, called antibaryons, have a baryon number of −1. A nucleus of deuterium (deuteron), for example, contains one proton and one neutron (each with a baryon number of 1) and has a baryon number of 2.

Since baryons make up most of the mass of ordinary atoms, the everyday matter is often referred to as baryonic matter.

The conservation of baryon number is an important rule for interactions and decays of baryons. No known interactions violate conservation of baryon number.

Baryon Number

In particle physics, the baryon number is used to denote which particles are baryons and which particles are not. Each baryon has a baryon number of 1 and each antibaryon has a baryon number of -1. Other non-baryonic particles have a baryon number of 0. Since there are exotic hadrons like pentaquarks and tetraquarks, there is a general definition of baryon number as:

where n_q is the number of quarks, and n_q is the number of antiquarks.

The baryon number is a conserved quantum number in all particle reactions. The term conserved means that the sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction. A slight asymmetry in the laws of physics allowed baryons to be created in the Big Bang.

Law of Conservation of Baryon Number

In analyzing nuclear reactions, we apply the many conservation laws. Nuclear reactions are subject to classical conservation laws for, momentum, angular momentum, and energy (including rest energies).  Additional conservation laws, not anticipated by classical physics, are electric charge, lepton number and baryon number. Certain of these laws are obeyed under all circumstances, others are not.

Baryon number is a generalization of nucleon number, which is conserved in nonrelativistic nuclear reactions and decays. The law of conservation of baryon number states that:

The sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction.

For example, the following reaction has never been observed:

even if the incoming proton has sufficient energy and charge, energy, and so on, are conserved. This reaction does not conserve baryon number since the left side has B =+2, and the right has B =+1.

On the other hand, the following reaction (proton-antiproton pair production) does conserve B and does occur if the incoming proton has sufficient energy (the threshold energy = 5.6 GeV):

As indicated, B = +2 on both sides of this equation.

From these and other reactions, the conservation of baryon number has been established as a basic principle of physics.

This principle provides basis for the stability of the proton. Since the proton is the lightest particle among all baryons, the hypothetical products of its decay would have to be non-baryons. Thus, the decay would violate the conservation of baryon number. It must be added some theories have suggested that protons are in fact unstable with very long half-life (~10³⁰ years) and that they decay into leptons. There is currently no experimental evidence that proton decay occurs.

See also:

Fundamental Particles

What is Baryon

Baryon is any fermion that undergo strong interactions. In general, particles that do participate in strong interactions are called hadrons: protons and neutrons are hadrons. The hadrons are further sub-divided into baryons and mesons, according to the number of quarks they contain. Protons and neutrons each contain three quarks; they belong to the family of particles called the baryons. Other baryons are the lambda, sigma, xi, and omega particles. On the other hand mesons bosons and they are composed of two quarks: a quark and an antiquark. Besides charge and spin (1/2 for the baryons), two other quantum numbers are assigned to these particles: baryon number (B) and strangeness (S). Baryons have a baryon number, B, of 1, while their antiparticles, called antibaryons, have a baryon number of −1. A nucleus of deuterium (deuteron), for example, contains one proton and one neutron (each with a baryon number of 1) and has a baryon number of 2.

Since baryons make up most of the mass of ordinary atoms, the everyday matter is often referred to as baryonic matter.

The conservation of baryon number is an important rule for interactions and decays of baryons. No known interactions violate conservation of baryon number.

Baryon Number

In particle physics, the baryon number is used to denote which particles are baryons and which particles are not. Each baryon has a baryon number of 1 and each antibaryon has a baryon number of -1. Other non-baryonic particles have a baryon number of 0. Since there are exotic hadrons like pentaquarks and tetraquarks, there is a general definition of baryon number as:

where n_q is the number of quarks, and n_q is the number of antiquarks.

The baryon number is a conserved quantum number in all particle reactions. The term conserved means that the sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction. A slight asymmetry in the laws of physics allowed baryons to be created in the Big Bang.

Law of Conservation of Baryon Number

In analyzing nuclear reactions, we apply the many conservation laws. Nuclear reactions are subject to classical conservation laws for, momentum, angular momentum, and energy (including rest energies).  Additional conservation laws, not anticipated by classical physics, are electric charge, lepton number and baryon number. Certain of these laws are obeyed under all circumstances, others are not.

Baryon number is a generalization of nucleon number, which is conserved in nonrelativistic nuclear reactions and decays. The law of conservation of baryon number states that:

The sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction.

For example, the following reaction has never been observed:

even if the incoming proton has sufficient energy and charge, energy, and so on, are conserved. This reaction does not conserve baryon number since the left side has B =+2, and the right has B =+1.

On the other hand, the following reaction (proton-antiproton pair production) does conserve B and does occur if the incoming proton has sufficient energy (the threshold energy = 5.6 GeV):

As indicated, B = +2 on both sides of this equation.

From these and other reactions, the conservation of baryon number has been established as a basic principle of physics.

This principle provides basis for the stability of the proton. Since the proton is the lightest particle among all baryons, the hypothetical products of its decay would have to be non-baryons. Thus, the decay would violate the conservation of baryon number. It must be added some theories have suggested that protons are in fact unstable with very long half-life (~10³⁰ years) and that they decay into leptons. There is currently no experimental evidence that proton decay occurs.

See also:

Laws of Conservation

Lepton Number

In particle physics, the lepton number is used to denote which particles are leptons and which particles are not. Each lepton has a lepton number of 1 and each antilepton has a lepton number of -1. Other non-leptonic particles have a lepton number of 0. The lepton number is a conserved quantum number in all particle reactions. A slight asymmetry in the laws of physics allowed leptons to be created in the Big Bang.

The conservation of lepton number means that whenever a lepton of a certain generation is created or destroyed in a reaction, a corresponding antilepton from the same generation must be created or destroyed. It must be added, there is a separate requirement for each of the three generations of leptons, the electron, muon and tau and their associated neutrinos.

Example: Electron Capture

Consider the electron capture mode. The reaction involves only first generation leptons: electrons and neutrinos:

The antineutrino cannot be emitted, because in this case the conservation law would not be fulfilled. The particle emitted with the neutron must be a neutrino.

Example: Neutron Decay

Consider the decay of the neutron. The reaction involves only first generation leptons: electrons and neutrinos:

Since the lepton number must be equal to zero on both sides and it was found that the reaction is a three-particle decay (the electrons emitted in beta decay have a continuous rather than a discrete spectrum),  the third particle must be an electron antineutrino.

Example: Muon Decay

The observation of the following decay reaction leads to the conclusion that there is a separate lepton number for muons which must also be conserved.

This is in fact the most common decay mode of the ^–.

See also:

Leptons

What is Lepton

A lepton is an elementary, half-integer spin (spin  1⁄2) particle that does not undergo strong interactions. Particles that do participate in strong interactions are called hadrons.

There are six leptons in the present structure, the electron, muon, and tau particles and their associated neutrinos. Leptons are said to be elementary particles; that is, they do not appear to be made up of smaller units of matter. They behave as point-like particles. All leptons are fermions, i.e. leptons are spin- 1⁄2 particles and thus that they are subject to the Pauli exclusion principle. This fact has key implications for the building up of the periodic table of elements.

Any of the six elementary particles that (with their antiparticles) are not quarks are leptons. Two main classes of leptons exist:

• Charged leptons. Charged leptons can combine with other particles to form various composite particles such as atoms and positronium.
  • Electron. The electron is a negatively charged particle with a mass that is approximately 1/1836 that of the proton. Electrons are located in an electron cloud, which is the area surrounding the nucleus of the atom. The electron is only one member of a class of elementary particles, which forms an atom.
  • Muon. The muon is an elementary particle similar to the electron, with an electric charge of −1 e and a spin of ½. Muons are heavier, having more than 200 times as much mass as electrons. The muon is an unstable subatomic particle with a mean lifetime of 2.2 µs.
  • Tau. The tau (τ), also called the tau lepton, tau particle, or tauon, is an elementary particle similar to the electron, with an electric charge of −1 e and a spin of ½. Taus are approximately 3,700 times more massive than electrons. Tau leptons have a lifetime of 2.9×10⁻¹³ s.
• Neutral leptons (better known as neutrinos) are electrically neutral particles that rarely interact with anything, and are consequently rarely observed. A neutrino is an elementary subatomic particle with infinitesimal mass (less than 0.3 eV..?) and with no electric charge. Neutrinos are weakly interacting subatomic particles with ½ unit of spin.
  • Electron neutrino. The electron neutrino is a subatomic lepton elementary particle which has the symbol ν_e. It has no net electric charge and a spin of ½. Together with the electron it forms the first generation of leptons, hence the name electron neutrino.
  • Muon neutrino. The muon neutrino is a subatomic lepton elementary particle which has the symbol  ν_μ. It has no net electric charge and a spin of ½. Together with the muon it forms the second generation of leptons, hence the name muon neutrino.
  • Tau neutrino. The tau neutrino is a subatomic lepton elementary particle which has the symbol  ν_τ. It has no net electric charge and a spin of ½. Together with the tauon it forms the third generation of leptons, hence the name tau neutrino.

Law of Conservation of Lepton Number

In particle physics, the lepton number is used to denote which particles are leptons and which particles are not. Each lepton has a lepton number of 1 and each antilepton has a lepton number of -1. Other non-leptonic particles have a lepton number of 0. The lepton number is a conserved quantum number in all particle reactions. A slight asymmetry in the laws of physics allowed leptons to be created in the Big Bang.

The conservation of lepton number means that whenever a lepton of a certain generation is created or destroyed in a reaction, a corresponding antilepton from the same generation must be created or destroyed. It must be added, there is a separate requirement for each of the three generations of leptons, the electron, muon and tau and their associated neutrinos.

Example: Electron Capture

Consider the electron capture mode. The reaction involves only first generation leptons: electrons and neutrinos:

The antineutrino cannot be emitted, because in this case the conservation law would not be fulfilled. The particle emitted with the neutron must be a neutrino.

Example: Neutron Decay

Consider the decay of the neutron. The reaction involves only first generation leptons: electrons and neutrinos:

Since the lepton number must be equal to zero on both sides and it was found that the reaction is a three-particle decay (the electrons emitted in beta decay have a continuous rather than a discrete spectrum),  the third particle must be an electron antineutrino.

Example: Muon Decay

The observation of the following decay reaction leads to the conclusion that there is a separate lepton number for muons which must also be conserved.

This is in fact the most common decay mode of the ^–.

See also:

Fundamental Particles

What is Lepton

A lepton is an elementary, half-integer spin (spin  1⁄2) particle that does not undergo strong interactions. Particles that do participate in strong interactions are called hadrons.

There are six leptons in the present structure, the electron, muon, and tau particles and their associated neutrinos. Leptons are said to be elementary particles; that is, they do not appear to be made up of smaller units of matter. They behave as point-like particles. All leptons are fermions, i.e. leptons are spin- 1⁄2 particles and thus that they are subject to the Pauli exclusion principle. This fact has key implications for the building up of the periodic table of elements.

Any of the six elementary particles that (with their antiparticles) are not quarks are leptons. Two main classes of leptons exist:

• Charged leptons. Charged leptons can combine with other particles to form various composite particles such as atoms and positronium.
  • Electron. The electron is a negatively charged particle with a mass that is approximately 1/1836 that of the proton. Electrons are located in an electron cloud, which is the area surrounding the nucleus of the atom. The electron is only one member of a class of elementary particles, which forms an atom.
  • Muon. The muon is an elementary particle similar to the electron, with an electric charge of −1 e and a spin of ½. Muons are heavier, having more than 200 times as much mass as electrons. The muon is an unstable subatomic particle with a mean lifetime of 2.2 µs.
  • Tau. The tau (τ), also called the tau lepton, tau particle, or tauon, is an elementary particle similar to the electron, with an electric charge of −1 e and a spin of ½. Taus are approximately 3,700 times more massive than electrons. Tau leptons have a lifetime of 2.9×10⁻¹³ s.
• Neutral leptons (better known as neutrinos) are electrically neutral particles that rarely interact with anything, and are consequently rarely observed. A neutrino is an elementary subatomic particle with infinitesimal mass (less than 0.3 eV..?) and with no electric charge. Neutrinos are weakly interacting subatomic particles with ½ unit of spin.
  • Electron neutrino. The electron neutrino is a subatomic lepton elementary particle which has the symbol ν_e. It has no net electric charge and a spin of ½. Together with the electron it forms the first generation of leptons, hence the name electron neutrino.
  • Muon neutrino. The muon neutrino is a subatomic lepton elementary particle which has the symbol  ν_μ. It has no net electric charge and a spin of ½. Together with the muon it forms the second generation of leptons, hence the name muon neutrino.
  • Tau neutrino. The tau neutrino is a subatomic lepton elementary particle which has the symbol  ν_τ. It has no net electric charge and a spin of ½. Together with the tauon it forms the third generation of leptons, hence the name tau neutrino.

Law of Conservation of Lepton Number

In particle physics, the lepton number is used to denote which particles are leptons and which particles are not. Each lepton has a lepton number of 1 and each antilepton has a lepton number of -1. Other non-leptonic particles have a lepton number of 0. The lepton number is a conserved quantum number in all particle reactions. A slight asymmetry in the laws of physics allowed leptons to be created in the Big Bang.

The conservation of lepton number means that whenever a lepton of a certain generation is created or destroyed in a reaction, a corresponding antilepton from the same generation must be created or destroyed. It must be added, there is a separate requirement for each of the three generations of leptons, the electron, muon and tau and their associated neutrinos.

Conservation of Lepton Number – Electron Capture

Consider the electron capture mode. The reaction involves only first generation leptons: electrons and neutrinos:

The antineutrino cannot be emitted, because in this case the conservation law would not be fulfilled. The particle emitted with the neutron must be a neutrino.

Conservation of Lepton Number – Neutron Decay

Consider the decay of the neutron. The reaction involves only first generation leptons: electrons and neutrinos:

Since the lepton number must be equal to zero on both sides and it was found that the reaction is a three-particle decay (the electrons emitted in beta decay have a continuous rather than a discrete spectrum),  the third particle must be an electron antineutrino.

Conservation of Lepton Number – Muon Decay

The observation of the following decay reaction leads to the conclusion that there is a separate lepton number for muons which must also be conserved.

This is in fact the most common decay mode of the ^–.

See also:

Laws of Conservation

Law of Conservation of Electric Charge

In physics, there are two very important principles concerning the electric charge.

First is the law of conservation of electric charge. This law states that:

The algebraic sum of all the electric charges in any closed system is constant.

The only way to change the net charge of a system is to bring in charge from elsewhere, or remove charge from the system.

Charge can be created and destroyed, but only in positive-negative pairs.

Conservation of charge is thought to be a universal conservation law. No experimental evidence for any violation of this principle has ever been observed. In particle physics, charge conservation means that in elementary particle reactions that create charged particles, equal numbers of positive and negative particles are always created, keeping the net amount of charge unchanged. Even in high-energy interactions in which particles are created and destroyed, such as the creation of positron-electron pairs, the total charge of any closed system is exactly constant.

The second important principle is:

The magnitude of charge of the electron or proton is a natural unit of charge.

We say that charge is quantized. That is, every observable amount of electric charge is always an integer multiple of this basic unit. This unit is called the elementary charge, e, approximately equal to 1.602×10⁻¹⁹ coulombs (except for particles called quarks, which have charges that are integer multiples of  ¹⁄₃e).

Conservation of Charge in Nuclear Reactions

Important examples of the law of conservation of electric charge occur in nuclear reactions such as the radioactive decay of nuclei and the nuclear fission.  In these reactions a nucleus transforms into a different type of nucleus or nuclei.

Consider a typical fission reaction such as the one listed below.

Typically, when uranium 235 nucleus undergoes fission, the nucleus splits into two smaller nuclei (triple fission can also rarely occur), along with a few neutrons (the average is 2.43 neutrons per fission by thermal neutron) and release of energy in the form of heat and gamma rays. From these reactions we find that in the fission the parent nucleus:

• ²³⁵U contains 92 protons (a charge of +92e),
• incident neutron is electrically neutral.

The fission fragments:

• ¹³⁹Ba contains 56 protons (a charge of +56e),
• ⁹⁴Ba contains 36 protons (a charge of +36e)

We see that the total charge is 92e before and after the reaction; thus, charge is conserved. It is noteworthy, the total number of nucleons before and after a reaction are also the same.

Conservation of Charge in Positron-Electron Pair Production

The law of conservation of electric charge can be demonstrated also on positron-electron pair production. Since a gamma ray is electrically neutral and sum of the electric charges of electron and positron is also zero, the electric charge in this reaction is also conserved.

Ɣ → e^– + e⁺

It must be added, in order for electron-positron pair production to occur, the electromagnetic energy of the photon must be above a threshold energy, which is equivalent to the rest mass of two electrons. The threshold energy (the total rest mass of produced particles) for electron-positron pair production is equal to 1.02MeV (2 x 0.511MeV) because the rest mass of a single electron is equivalent to 0.511MeV of energy. If the original photon’s energy is greater than 1.02MeV, any energy above 1.02MeV is according to the conservation law split between the kinetic energy of motion of the two particles. The presence of an electric field of a heavy atom such as lead or uranium is essential in order to satisfy conservation of momentum and energy. In order to satisfy both conservation of momentum and energy, the atomic nucleus must receive some momentum. Therefore a photon pair production in free space cannot occur.

Conservation of Electric Charge in Neutrino Discovery

In 1931, Pauli proposed that another particle must be emitted in the beta decay process, because the electrons emitted in beta decay have a continuous rather than a discrete spectrum appeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus. This another particle was later named by Fermi the neutrino. It was clear, this particle must be highly penetrating and that the conservation of electric charge requires the neutrino to be electrically neutral. This would explain why it was so hard to detect this particle. The term neutrino comes from Italian meaning “little neutral one” and neutrinos are denoted by the Greek letter ν (nu). In the process of beta decay the neutrino carries the missing energy and also in this process the law of conservation of energy remains valid.

See also:

Laws of Conservation