Pearson Edexcel Physics

Unit 4: Further Mechanics, Fields and Particles

4.5 Nuclear and Particle Physics

Pearson Edexcel Physics

Unit 4: Further Mechanics, Fields and Particles

4.5 Nuclear and Particle Physics

Candidates will be assessed on their ability to::
111. Understand what is meant by nucleon number (mass number) and proton number (atomic number)
112. Understand how large-angle alpha particle scattering gives evidence for a nuclear model of the atom and how our understanding of atomic structure has changed over time
113. Understand that electrons are released in the process of thermionic emission and how they can be accelerated by electric and magnetic fields
114. Understand the role of electric and magnetic fields in particle accelerators (linac and cyclotron) and detectors (general principles of ionization and deflection only)
115. Be able to derive and use the equation [math]r = \frac{P}{BQ}[/math] for a charged particle in a magnetic field
116. Be able to apply conservation of charge, energy and momentum to interactions between particles and interpret particle tracks
117. Understand why high energies are required to investigate the structure of nucleons
118. Be able to use the equation [math]∆E = c^2 ∆m[/math] in situations involving the creation and annihilation of matter and antimatter particles
119. Be able to use MeV and GeV (energy) and MeV/c2, GeV/c2 (mass) and convert between these and SI units
120. Understand situations in which the relativistic increase in particle lifetime is significant (use of relativistic equations not required)
121. Know that in the standard quark-lepton model particles can be classified as:

–          Baryons (e.g. neutrons and protons), which are made from three quarks

–          Mesons (e.g. pions), which are made from a quark and an antiquark

–          Leptons (e.g. electrons and neutrinos), which are fundamental particles

–          Photons

and that the symmetry of the model predicted the top quark
122. Know that every particle has a corresponding antiparticle and be able to use the properties of a particle to deduce the properties of its antiparticle and vice versa
123. Understand how to use laws of conservation of charge, baryon number and lepton number to determine whether a particle interaction is possible
124. Be able to write and interpret particle equations given the relevant particle symbols.

  • 111) Understand what is meant by nucleon number (mass number) and proton number (atomic number)

  • ⇒ Nuclear structure:
  • The nucleus contains two types of particles: protons and neutrons. In the nucleus, these particles are all known as nucleons.
  • The number of protons in a nucleus determines which element the atom will be.
  • The periodic table is a list of the elements in the order of the number of protons in each atom’s nucleus. This number is called the proton number or the atomic number (Z).
  • The number of neutrons can be different, and we call atoms of the same element with different numbers of neutrons, isotopes.
  • For small nuclei, up to about atomic number 20 (which is calcium), the number of neutrons in the nucleus is generally equal to the number of protons.
  • Above atomic number 20, to be stable, more neutrons than protons are needed in the nucleus.
  • The neutrons help to bind the nucleus together as they exert a strong nuclear force on other nucleons, and they act as a space between the positive charges of the protons which all repel each other. This means that as we progress through the periodic table to larger and larger nuclei, proportionately more and more neutrons are needed.
  • By the time we reach the very biggest nuclei, there can be over 50% more neutrons than protons. To describe any nucleus, we must say how many protons and how many neutrons there are.
  • So, the chemical symbol written below refers to the isotope of radium, which has 88 protons and 138 neutrons:
  • [math]_{88}^{226}\text{Ra}[/math]
  • The number 226, called the nucleon number or the mass number (A), refers to the total number of nucleons – neutrons and protons – in a nucleus of this isotope.
  • So, to find the number of neutrons, we must subtract the atomic number from the mass number:
  • [math]226 – 88 = 138[/math]
  • As radium must have 88 protons because that makes it radium, it is quite common not to write the 88.
  • You might call this isotope ‘radium-226’ and this will be enough information to know its proton number and neutron number.

  • 112) Understand how large-angle alpha particle scattering gives evidence for a nuclear model of the atom and how our understanding of atomic structure has changed over time

  • ⇒ A quantum mechanical atom:
  • In the 1920s, Werner Heisenberg changed the model of the atom, which had electrons in orbits like planets in a Solar System.
  • His uncertainty principle says that we cannot know the exact position and velocity of anything at a given moment.
  • Instead of specific orbits, his new version of the atom has regions around the nucleus in which there is a high probability of finding an electron, and the shapes of these ‘probability clouds’ represent what we currently refer to as the electron ‘orbitals’.
  • Figure 1 A quantum mechanical model of an atom’s structure.

  • 113) Understand that electrons are released in the process of thermionic emission and how they can be accelerated by electric and magnetic fields

  • ⇒ Electron beams:
  • Free conduction electrons in metals need a particular amount of energy if they are to escape from the surface of the metal.
  • This energy can be supplied by a beam of photons, as seen in the photoelectric effect.
  • Figure 2 Photoelectric effect
  • The electrons can also gain enough energy through heating of the metal. The release of electrons from the surface of a metal as it is heated is known as thermionic emission.
  • Figure 3 Thermionic emission
  • If, when they escape, these electrons are in an electric field, they will be accelerated by the field, moving in the positive direction.
  • The kinetic energy they gain will depend on the p.d., V, that they move through, according to the equation:
  • [math]E_k = eV[/math]
  • Where e is the charge on an electron.
  • Using thermionic emission to produce electrons, and applying an electric field to accelerate them, we can generate a beam of fast-moving electrons, known as a cathode ray.
  • If this beam of electrons passes through a further electric field or magnetic field, then the force produced on the beam of electrons will cause it to deflect.
  • If a fast-moving electron hits a screen that is painted with a particular chemical, the screen will fluoresce – it will emit light. These are the principles by which cathode ray oscilloscopes (CROs) operate.
  • The electron beam in a CRO is moved left and right, and up and down, by passing the beam through horizontal and vertical electric fields.
  • These are generated by electric plates so the strength and direction can be altered. The point on the screen which is emitting light can be changed quickly and easily.
  • Figure 4 Principle of cathode ray oscilloscope

  • 114) Understand the role of electric and magnetic fields in particle accelerators (linac and cyclotron) and detectors (general principles of ionization and deflection only)

  • 115) Be able to derive and use the equation [math]r = \frac{P}{BQ}[/math]  for a charged particle in a magnetic field

  • 116) Be able to apply conservation of charge, energy and momentum to interactions between particles and interpret particle tracks

  • ⇒ Particle Accelerators:
  • To investigate the internal structure of particles like nucleons – protons and neutrons – scientists collide them with other particles at very high speeds (very high energies).
  • It is necessary to use high energy particles because at lower energies the particles just bounce off each other, keeping their internal structure secret.
  • If we can collide particles together hard enough, they will disintegrate, and show their structure.
  • In most cases, additional particles are created from the energy of the collision. Sometimes these extra particles uncover or confirm other new physics.
  • The challenge for scientists has been to accelerate particles to high enough speeds.
  • Charged particles can be accelerated in straight lines using electric fields, and their direction changed along a curved path by a magnetic field.
  • ⇒ Accelerating particles in circles:
  • Scientists found it difficult to make linear accelerators which were longer and longer so they started to coil the accelerators up in a circle. This means that the particles could be accelerated in an electric field repeatedly in a smaller space.
  • To do this, we use the fact that charged particles moving across a magnetic field will experience a centripetal force, and so will move in a circular path.
  • We can work out the radius of this circular path, and use it to construct a circular accelerator of the right dimensions.
  • Figure 5 The circular trajectory of a charged particle moving across a magnetic field. Note that field lines can be shown coming out of a page by drawing a dot, and those going into a page (like the magnetic field here) can be shown by drawing a cross.
  • The equation for the force on a charged particle moving across a magnetic field
  • [math]F = Bqv[/math]
  • This force acts at right angles to the velocity, v, meaning that the particle will follow a circular path. Remember that the equation for the centripetal force on anything moving in a circle.
  • [math]F = \frac{mv^2}{r}[/math]
  • We can equate these two expressions:
  • [math]Bqv = \frac{mv^2}{r}[/math]
  • Dividing out the velocity from each side, and rearranging to find an expression for the radius of the circle, gives:
  • [math]r = \frac{mv}{Bq}[/math]
  • Or
  • [math]r = \frac{p}{Bq}[/math]
  • This means that for a given magnetic field, the radius of the path of a charged particle is proportional to its momentum.
  • At slow speeds, the radius is proportional to velocity (or the square root of the kinetic energy).
  • However, these experiments generally send particles at speeds approaching the speed of light, so relativistic effects need to be accounted for.
  • In particular, at these very high speeds the particle’s mass appears to increase, which would also change its momentum.
  • The overall result is that a particle increasing in speed would travel along an outwardly spiraling path.
  • ⇒ The Cyclotron:
  • In 1930, Ernest Lawrence developed the first cyclotron. This was a circular accelerator which could give protons about 1 MeV of energy.
  • In a cyclotron, there are two D-shaped electrodes (or dees), and the particles are accelerated in the electric field in the gap between them.
  • Figure 6 The structure of a cyclotron.
  • Within the dees, the particle will travel along a semicircular path because of the magnetic field, before being accelerated across the gap again; then another semicircle, another acceleration across the gap, and so on.
  • As each acceleration increases the momentum of the particle, the radius of its path within the dee increases, and so it steadily spirals outwards until it emerges from an exit hole and hits the target placed in a bombardment chamber in its path.
  • ⇒ Linear Accelerators:
  • One of the simplest ways to produce energy high enough for these particle collisions is to accelerate a beam of charged particles along a straight path.
  • However, the maximum achievable potential difference limits this. To overcome this problem, the particles are accelerated in stages (figure 7).
  • They are repeatedly accelerated through the maximum p.d., making the particle energies very high.
  • Using this principle, the 3.2 km Stanford Linear Accelerator in the USA can accelerate electrons to an energy of 50 GeV, meaning that they have effectively passed through a potential difference of 50 billion volts. ‘GeV’ means giga electron volts, or ‘x109 eV’.
  • Figure 7 The structure of a linear accelerator.
  • If the particles to be accelerated by the linear accelerator in figure 7 are electrons, they are generated by an electrostatic machine (like a Van de Graaff generator) and then put into the machine.
  • Once inside the cylinder, the electrons move in a straight line, as the electrode is equally attracting in all directions.
  • The alternating voltage supply is made to change as the electrons reach the middle of tube A, so it becomes negative.
  • This repels the electrons out of the end of tube A and on towards tube B, which now has a positive potential.
  • They accelerate towards it, and the whole process repeats as they pass through tube B and are then accelerated on towards tube C.
  • This carries on until the electrons reach the end of the line, at which point they emerge to collide with a target.
  • In order to keep accelerating particles that are moving faster and faster, the acceleration tubes must be made longer and longer as the particles travel through each successive one at a higher speed.
  • The time between potential difference flips is fixed as the alternating voltage has a uniform frequency of a few gigahertz (often referred to as radio frequency, RF).
  • Using this type of accelerator is limited by how long you can afford to build it. The whole structure must be in a vacuum so that the particles do not collide with air atoms, and it must be perfectly straight.
  • ⇒ Linac Facts:
  • The Stanford Linear Accelerator in California is still the world’s longest linear accelerator or LINAC, despite being 50 years old. However, plans for the International Linear Collider are far advanced. Most likely to be built in Japan, this would consist of two linear colliders, each over 15 km long, designed to collide electrons and positrons, initially with energies of 250 GeV, but with the design possibility of raising this to 1 TeV.

  • 117) Understand why high energies are required to investigate the structure of nucleons

  • An Electron probe:
  • Davisson and Germer showed that an electron beam can produce a diffraction pattern. This was different to the patterns found by Geiger and Marsden in Rutherford’s alpha particle scattering experiments.
  • Davisson and Germer provided the experimental evidence to prove a theory that had been suggested three years earlier by the French physicist, Louis de Broglie.
  • Light could be shown to behave as a wave sometimes, and at other times as a particle.
  • He hypothesized that this might also be the case for things which were traditionally thought to be particles.
  • De Broglie had proposed that the wavelength, A, of a particle could be calculated from its momentum (p) using the expression:
  • [math]\lambda = \frac{h}{p}[/math]
  • Where h is the Planck constant. So:
  • [math]\lambda = \frac{h}{mv}[/math]
  • The Davisson-Germer experiment proved that the diffraction pattern obtained when a cathode ray hit a crystal could only be produced if the electrons in the beam had a wavelength that was the de Broglie wavelength.
  • Because of this experimental confirmation, Louis de Broglie was awarded the 1929 Nobel Prize for Physic.
  • The idea of electrons acting as waves has enabled scientists to study the structure of crystals, the same way they do in X-ray crystallography.
  • When waves pass through a gap which is about the same size as their wavelength, they are diffracted. In other words, they spread out.
  • Figure 8 Davisson and Germer experiment
  • The degree of diffraction spreading depends on the ratio of the size of the gap to the wavelength of the wave.
  • If a beam of electrons is aimed at a crystal, the gaps between atoms in the crystal can act as a diffraction grating and the electron waves produce a diffraction pattern on a screen. Measuring the pattern allows the spacings between the atoms to be calculated.
  • Electron diffraction and alpha particle scattering both show the idea that we can study the structure of matter by probing it with beams of high energy particles.
  • The more detail (or smaller scale) the structure to be investigated has, the higher energy the beam of particles needs to be.
  • This means that very high energies are needed to investigate the structure of nucleons, as they are very, very small.
  • Accelerating larger and larger particles to higher and higher energies has been the aim of particle physicists ever since Thomson discovered the electron in 1897.
  • Example:
  • What is the wavelength of an electron in a beam which has been accelerated through 2000 V?
  • Solution:
  • [math]\begin{gather}
    E_k = eV \\
    E_k = (-1.6 \times 10^{-19})(-2000) \\
    E_k = 3.2 \times 10^{-16} \text{ J} \\
    E_k = \frac{1}{2} mv^2 \\
    E_k = 3.2 \times 10^{-16} \text{ J} \\
    v = \sqrt{\frac{2E_k}{m}} \\
    v = \sqrt{\frac{2(3.2 \times 10^{-16})}{9.11 \times 10^{-31}}} \\
    v = 2.65 \times 10^7 \ \text{m·s}^{-1} \\
    \lambda = \frac{h}{mv} \\
    \lambda = \frac{6.63 \times 10^{-34}}{(9.11 \times 10^{-31})(2.65 \times 10^7)} \\
    \lambda = 2.75 \times 10^{-11} \ \text{m}
    \end{gather}[/math]

  • 118) Be able to use the equation [math]∆E = c^2 ∆m[/math] in situations involving the creation and annihilation of matter and antimatter particles

  • The implication from most creation stories is that, from nothing, the material of the Earth was brought into being by an unexplained entity.
  • However, one of Einstein’s most important theories suggests exactly this – matter can appear where previously there was nothing but energy.
  • Matter and energy are regularly interchanged in the Universe according to his well-known equation,
  • [math]E = mc^2[/math]
  • In this equation, multiplying the mass of an object by the square of the speed of light gives the equivalent amount of energy:
  • [math]∆E = c^2 ∆m[/math]
  • Given a suitable quantity of energy, such as that in a gamma ray photon, particles can spontaneously appear and the energy disappears from existence.
  • This is so common in the Universe that it should not surprise us.
  • The reason it does is that these events only happen on a sub-atomic scale, so we cannot detect them without complex machines.
  • This reaction is known as electron-positron pair production. In momentum terms, it is just like an explosion. Initially only the photon existed so there was some linear momentum.
  • Along this initial direction, their components of momentum must sum to the same total as the photon had. Perpendicular to the initial momentum, the electron and positron that were produced must have equal and opposite components of momentum so that in this direction it will still total zero afterwards.
  • In any reaction, the total combination of matter-energy must be conserved. If we add the energy equivalent of all matter particles with the energies, before and after the reaction, the numbers must be equal.
  • Figure 9 Pair Production
  • Example:
  • A gamma ray photon converts into an electron and a positron (an anti-electron that has an identical mass to the electron). Calculate the frequency of the gamma photon.
  • Solution:
  • [math]\begin{gather}
    \text{Mass of an electron, } m_e = 9.11 \times 10^{-31} \ \text{kg} \\
    \Delta E = c^2 \Delta m \\
    \Delta E = (3 \times 10^8)^2 (9.11 \times 10^{-31}) \\
    \Delta E = 8.2 \times 10^{-14} \ \text{J}
    \end{gather}[/math]
  • This is the amount of energy needed to produce an electron or a positron so, to produce both, the energy of the photon must be double this: [math] 16.4 × 10^{-14} J[/math]
  • [math]\begin{gather}
    E = hf \\
    f = \frac{E}{h} \\
    f = \frac{16.4 \times 10^{-14}}{6.63 \times 10^{-34}} \\
    f = 2.47 \times 10^{20} \ \text{Hz}
    \end{gather}[/math]
  • ⇒ Annihilation:
  • Matter can appear spontaneously through a conversion from energy. In the same way, energy can appear through the disappearance of mass.
  • This is the source of energy in nuclear fission and fusion. In both reactions, the sum of the masses of all matter involved before the reaction is greater than the sum of all mass afterwards. This mass difference is converted into energy.
  • Figure 10 The fictional starship Enterprise was said to be powered by a matter-anti-matter annihilation reaction.
  • In a nuclear power station, we extract this energy as heat and use it to drive turbines to generate electricity.
  • If a particle and its anti-particle meet (anti-particles are the anti-matter versions of regular particles, they will disappear to be replaced by the equivalent energy: this is interaction annihilation.
  • This reaction was supposedly the main power source to drive the starship Enterprise in the science fiction series Star Trek (figure 10).
  • Annihilation reactors could not be used as a power source on Earth, as anti-matter exists so rarely. Also, if we could find a supply of anti-matter, it would annihilate on contact with matter.
  • This would most likely be before it reached the reaction chamber, we had set up to use the energy for conversion into electricity.

  • 119) Be able to use MeV and GeV (energy) and MeV/c2, GeV/c2 (mass) and convert between these and SI units

  • The electron-volt (eV) as a unit for very small amounts of energy. Remember that one electron-volt is the amount of energy gained by an electron when it is accelerated through a potential difference of one volt.
  • This is equivalent to [math]1.6 × 10^{-19}[/math] joules, so it is a very small amount of energy, even in particle physics terms. It is common for particles to have millions or even billions of electron-volts.
  • For this reason, we often use MeV and GeV as units of energy in particle interactions.
  • The atomic mass unit, u, is not an SI unit but is often used in particle interactions, as it is usually easier to understand. [math]1 u = 1.66 × 10^{-27} kg[/math].
  • As we know that energy and mass are connected by the equation [math]∆E = c^2 ∆m[/math], we can also have mass units which are measures of [math]E/c^2[/math], such as [math]MeV/c^2[/math] and [math]GeV/c^2[/math]. 1 u of mass is equivalent to about [math]931.5 Mev/c^2[/math].
  • Calculate the mass in kilograms of 1 [math]1 Mev/c^2[/math].
  • [math]\begin{gather}
    1 \ \text{MeV} = 1 \times 10^6 \times 1.6 \times 10^{-19} \\
    1 \ \text{MeV} = 1.6 \times 10^{-13} \ \text{J} \\
    \text{In SI units, } c = 3 \times 10^8 \ \text{m·s}^{-1} \\
    \frac{\text{MeV}}{c^2} = \frac{1.6 \times 10^{-13}}{(3 \times 10^8)^2} \\
    \frac{\text{MeV}}{c^2} = 1.78 \times 10^{-30} \ \text{kg}
    \end{gather}[/math]
  • This is about twice the mass of an electron.
  • No particle interactions can occur if they break any of these conservation rules:
  • momentum
  • mass-energy
  • There are also other rules that must be obeyed, but these three are critical, as all particles involved will have some of each property.

  • 120) Understand situations in which the relativistic increase in particle lifetime is significant (use of relativistic equations not required)

  • 121) Know that in the standard quark-lepton model particles can be classified as:

  • – Baryons (e.g. neutrons and protons), which are made from three quarks

  • – Mesons (e.g. pions), which are made from a quark and an antiquark

  • – Leptons (e.g. electrons and neutrinos), which are fundamental particles

  • – Photons

  • and that the symmetry of the model predicted the top quark

  • ⇒ Baryons:
  • If three quarks are combined together, the resulting particle is a baryon (fig A). Protons and neutrons are baryons.
  • A proton consists of two up quarks and a down quark, whilst a neutron is two down quarks combined with an up quark.
  • Other baryons are more obscure and have very short lives, as they decay through a strong nuclear force reaction that makes them highly unstable.
  • Yet other baryons, like the sigma, omega and lambda particles, decay via the weak nuclear force and are longer lived, with lives as long as 10-10
  • Figure 11 Three-quark baryons. Three anti-quarks in the anti-proton make it an anti-baryon.
  • ⇒ Mesons:
  • If a quark and an anti-quark are combined together, the resulting particle is known as a meson (figure 12).
  • The pion and the kaon are the most common examples of mesons.
  • A π+ meson ([math]\overline{ud}[/math]) consists of an up quark (u) combined with an anti-down ([math]\overline{d}[/math]) quark. If a meson is a combination of a quark and its anti-quark, then the meson’s charge must be zero. This is the case for the [math]J/Ψ[/math] particle, which was first discovered in 1974 by two independent researchers at separate laboratories.
  • Its slow decay, with a lifetime of [math]7.2 × 10^{-21} s[/math], occurred when it was not travelling at relativistic speeds, so was a genuine and unexpected long lifetime.
  • This did not fit the pattern generated by up, down and strange quarks, and it is thought to be a charm-anti-charm combination ([math]\overline{cc}/math]).
  • The two independent discoverers of this, Richter and Ting, shared the 1976 Nobel Prize for their discovery of the fourth quark.
  • Figure 12 Mesons are formed from quark-anti-quark combinations.
  • ⇒ Hadrons:
  • Quarks can interact via the strong nuclear force.
  • Thus, baryons and mesons can interact via the strong nuclear force. Any particle which experiences the strong force is called a hadron.
  • So, baryons and mesons are both hadrons. Leptons do not experience the strong force and so are in a separate class of particle from the hadrons.
  • ⇒ The four forces of nature:
  • There are four other particles that we have not yet mentioned here, because they are not matter particles. These are known together as exchange bosons.
  • The matter particles interact by the four forces of nature, which are gravity, the electromagnetic force, the strong nuclear force and the weak nuclear force.
  • Each force acts on particles which have a specific property, such as mass in the case of gravity, or electric charge for the electromagnetic force.
  • The process by which these forces act has been modelled by scientists as an exchange of another type of particles – the exchange bosons.
  • For example, for a proton and an electron to attract each other’s opposite charge, they pass photons backwards and forwards between each other.
  • This has been shown experimentally to be an appropriate model for the electromagnetic, strong and weak forces. In the case of gravity, the so-called graviton has been theoretically invented to complete the model, but gravitons are yet to be discovered.
  • Many experiments have been set up recently to try and detect gravitons.
  • Figure 13 Gluons ‘in combination with virtual quark anti-quark pairs’ are exchanged between quarks to hold the quarks together. In this example, the three quarks form a proton.

  • 122) Know that every particle has a corresponding antiparticle and be able to use the properties of a particle to deduce the properties of its antiparticle and vice versa

  • ⇒  Antiparticle:
  • An antiparticle is a type of particle that:
  • – Has the same mass as its corresponding particle.
  • – Has opposite charge and other quantum numbers (like lepton number, baryon number, strangeness, etc.).
  • If a particle and its antiparticle meet, they can annihilate each other, releasing energy (usually as photons).
  • Properties of Particles and Antiparticles
Property Particle Antiparticle
Mass Same Same
Electric Charge + or – Opposite
Baryon/Lepton Number +1 –1
Other quantum numbers (e.g. strangeness, charm) Specific Opposite
  • Examples of Particles and Antiparticles
Particle Symbol Charge Antiparticle Symbol Charge
Electron e− –1 Positron e+ +1
Proton p +1 Antiproton ​[math]\overline{p}[/math] –1
Neutron n 0 Antineutron [math]\overline{n}[/math] 0
Neutrino ​[math]v_e[/math] 0 Antineutrino ​[math]\overline{v_e}[/math] 0
Muon μ− –1 Antimuon μ+ +1
Quark u u +2/3 Antiquark uˉ\bar{u}uˉ [math]\overline{u}[/math] –2/3
  • ⇒  Deduce Antiparticle Properties
  • If you are given the properties of a particle, you can deduce the properties of its antiparticle by applying these rules:
    1. Mass stays the same.
    2. Electric charge is reversed.
    3. Baryon or lepton number is reversed (±1 becomes ∓1).
    4. Other quantum numbers (like strangeness, charm) are also reversed.

  • 123) Understand how to use laws of conservation of charge, baryon number and lepton number to determine whether a particle interaction is possible

  • 124) Be able to write and interpret particle equations given the relevant particle symbols.

  • ⇒ Reactions conserve properties:
  • For any particle reaction to occur, the overall reaction must conserve various properties of the particles involved.
  • The total combination of mass/energy must be the same before and after the reaction. Furthermore, momentum and charge must also be conserved.
  • Momentum and mass/energy are difficult to check. In a reaction, particles can begin or end with more kinetic energy to balance any apparent mass difference.
  • This is how accelerator collision experiments can create large mass particles: particles with high kinetic energies can have the energy converted into mass to generate many particles with less energy.
  • Reactions can also have similar flexibility to ensure momentum conservation. We will see later that particles are also assigned values called baryon number and lepton number, and these must also be conserved in reactions.
  • ⇒ Charge conservation:
  • Charge must be conserved for any particle interaction to be possible. We can quickly see if charge is conserved by checking the reaction’s equation. Consider two common nuclear reactions: alpha decay and beta-minus decay (fig A).
  • [math]\begin{gather}\text{Alpha decay:} \\
    _{92}^{235}\text{U} \to {}_{90}^{231}\text{Th} + {}_{2}^{4}\alpha \\
    \text{Charge:} \quad +92 \to +90 + +2 \\
    \text{Beta-minus decay:} \\
    _{6}^{14}\text{C} \to {}_{7}^{14}\text{N} + {}_{-1}^{0}\beta + \overline{\nu}_e \\
    \text{Charge:} \quad +6 \to +7 + (-1) + 0
    \end{gather}[/math]
  • The reaction for beta-minus decay led to the development of the theory that neutrinos and antineutrinos exist. They are almost massless and have no charge, so are almost impossible to detect.
  • If the same nuclear change produces the same single particle every time, then for mass-energy to be conserved, the beta particles would need to have the same energy every time.
  • Figure 14 Alpha and beta decay conserve mass/energy and charge.
  • This is the case for alpha particles. However, scientists found that beta particles from nuclei of the same isotope have a range of kinetic energies.
  • This suggested that another particle was flying away with some kinetic energy, so that the total kinetic energy produced was always the same.
  • ⇒ Conservation of baryon and lepton numbers:
  • We can also check on the possibility of a reaction occurring, as the reaction must conserve baryon number and lepton number. Each quark has a baryon number, B, of [math]+ \frac{1}{3}[/math], and so a baryon has a value of B = +1. Each lepton has a lepton number, L, of +1. Anti-particles have the opposite number.
  • As mesons are quark/anti-quark combinations, their total baryon number is zero ([math]+\frac{1}{3} + \frac{1}{3} = 0[/math]).
  • Particle reactions can also only occur if they conserve baryon and lepton numbers overall. This means the total for each property must be the same before and after any reaction, or else it cannot occur.
  • Let us revisit alpha and beta decay and check on conservation of these numbers.
  • [math]\begin{gather}
    \text{Alpha decay:} \\
    _{92}^{235}\mathrm{U} \to {}_{90}^{231}\mathrm{Th} + {}_{2}^{4}\alpha \\
    \text{Charge:} \quad +92 \to +90 + +2 \\
    \text{Baryon number:} \quad +235 \to +231 + +4 \\
    \text{Lepton number:} \quad 0 \to 0 + 0 \\
    \text{Beta-minus decay:} \\
    _{6}^{14}\mathrm{C} \to {}_{7}^{14}\mathrm{N} + {}_{-1}^{0}\beta + \overline{\nu}_e \\
    \text{Charge:} \quad +6 \to +7 + (-1) + 0 \\
    \text{Baryon number:} \quad +14 \to +14 + 0 + 0 \\
    \text{Lepton number:} \quad 0 \to 0 + 1 + (-1)
    \end{gather}[/math]
  • ⇒ Strangeness:
  • The strange quark adds an additional property to reactions, which must usually also be conserved. This is called strangeness, S.
  • Each strange quark has a strangeness of -1, each anti-strange quark has S = +1, and all other particles have zero strangeness. Strong and electromagnetic force interactions must conserve strangeness.
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