Particles

Question 1

1. What is the charge and mass (given on the formula sheet) of the proton, neutron and electron in SI and relative units?
2. Define nucleon and nuclide

Answer 1

1. Particle charge
   Proton: actual charge, 1.6 x 10^-19, relative charge +1
   Neutron: charge 0
   Electron: actual charge, -1.6 x 10^-19, relative charge -1

Particle mass (actual mass in kg)
Proton: actual mass, 1.67 x 10^-27, approximate mass 1.0
Neutron: actual mass, 1.67 x 10^-27, approximate mass 1.0
Electron: actual mass, 9.11 x 10^-31, approximate mass, 0.00055
2. Nucleon: a particle in the nucleus — can only be a proton or neutron.
Nuclide: a nucleus with specific numbers of neutrons and protons.

Question 2

1. Define isotope
2. What is isotopic data and what are the applications for isotopic data?
3. What is specific charge and the formula?

Answer 2

1. Isotope: nuclei that have the same number of protons but different numbers of neutrons.
2. Isotopic data: the relative amounts of different isotopes of an element present in a substance.
   Carbon dating: the proportion of radioactive carbon-14 decreases over time in dead things that can be used to determine age.
   Isotopic ratios in drinking water are different around the world, so hair samples can be used to determine where a person has recently been.
3. Specific charge is the ratio of the total charge of a particle to its mass, measured in coulombs per kilogram.
   Specific charge = charge / mass = Q / m

Question 3

P1-7
1. Explain the strong nuclear force
2. What are the properties for the strong nuclear force?
3. Compare the electrostatic and strong forces

Answer 3

1. The strong nuclear force is an attractive force acting between all nucleons.
   The strong nuclear force acts between quarks, which protons and neutrons are made from. It prevents the nucleus being pulled apart by repulsive electrostatic forces between protons due to their positive charge.
2. The key features of the graph are:
   The strong force is highly repulsive at separations below 0.5 fm
   The strong force is very attractive up to a nuclear separation of 3.0 fm
   The maximum attractive value occurs at around 1.0 fm, which is a typical value for nucleon separation
   The equilibrium position, where the resultant force is zero, occurs at a separation of about 0.5 fm
   In comparison to other fundamental forces, the strong nuclear force has a very small range (from 0.5 to 3.0 fm)
3. The electrostatic force is influenced by charge, whereas the strong nuclear force is not. This means the strength of the strong nuclear force is roughly the same between all types of nucleon (i.e. proton-proton, neutron-neutron and proton-neutron). However, this only applies for separations between 0.5 and 3.0 fm (where the electrostatic force between protons is insignificant).
   The equilibrium position for protons, where the electrostatic repulsive and strong attractive forces are equal, occurs at a separation of around 0.7 fm; beyond which the electrostatic repulsion line on a graph plateaus, while the strong nuclear force goes downwards, forming an upsidown hill, with a minimum at 1 fm.

Question 4

P1-7
1. Explain alpha decay
2. Explain beta-minus decay

Answer 4

1. In alpha decay, a nucleus emits an alpha particle and decays into a different nucleus. The alpha particle contains 2 protons and 2 neutrons (a helium nucleus). When an alpha particle is emitted from a nucleus, the proton number decreases by 2, and the nucleon number decreases by 4.
2. A beta-minus particle is a high energy electron emitted from the nucleus. Beta-minus decay is when a neutron turns into a proton, emitting an electron and an anti-electron neutrino. When a beta-minus particle is emitted from a nucleus, the proton number increases by one, and the nucleon number remains the same.

Question 5

P1-7
1. Explain beta-plus decay
2. Explain neutrino emission
3. What does a graph for the number of alpha and beta particles look like when plotted against kinetic energy?

Answer 5

1. A beta-plus particle is a high energy positron emitted from the nucleus. Beta-plus decay is when a proton turns into a neutron emitting a positron (anti-electron) and an electron neutrino. When a beta-plus particle is emitted from a nucleus: the proton number decreases by one, and the nucleon number remains the same.
2. An electron neutrino is a type of subatomic particle with no charge and negligible mass which is emitted from the nucleus. The anti-neutrino is the antiparticle of a neutrino. Electron anti-neutrinos are produced during β– decay. Electron neutrinos are produced during β+ decay.
3. When the number of β particles is plotted against kinetic energy, the graph shows a curve, therefore beta particles (electrons or positrons) have a continuous range of energies.
   This is because the energy released in beta decay is shared between the beta particles (electrons or positrons) and neutrinos (or anti-neutrinos). On the other hand, when the number of α particles is plotted against kinetic energy, there are clear spikes that appear on the graph. This demonstrates that α-particles have discrete energies (only certain values)

Question 6

1. What are the properties of antimatter?
2. Define photon
3. How do you calculate photon energy?

Answer 6

1. Corresponding matter and antimatter particles have: opposite charges, the same mass, the same rest mass-energy. The rest mass-energy of a particle is the energy equivalent to the mass of the particle when it is at rest.
2. Photon: A massless “packet” or a “quantum” of electromagnetic energy.
3. E = hf, or using the wave equation E = he / λ
   Where:
   E = energy of the photon (J)
   h = Planck’s constant (J s)
   c = the speed of light (m s-1)
   f = frequency (Hz)
   λ = wavelength (m)

Question 7

1. Define annihilation
2. What is the formula for the minimum energy after annihilation?
3. How is momentum conserved?

Answer 7

1. Annihilation: The destruction of a particle-antiparticle pair when they collide and convert their mass into two gamma-ray photons.
2. E min = h f min = E
   Where:
   E min = minimum energy of one of the photons produced (J)
   h = Planck’s Constant (J s)
   F min = minimum frequency of one of the photons produced (Hz)
   E = rest mass energy of one of the particles (J)
3. To conserve momentum, the two photons will move apart in opposite directions.
   As with all collisions, the mass and energy is still conserved.

Question 8

1. What is the formula for the minimum energy of one photon to undergo pair production?
2. Define pair production
3. What is the formula for the minimum energy required for a photon to undergo pair production?

Answer 8

1. The minimum energy required for a photon to undergo pair production is equal to the total rest mass energy of the particles produced.
   E min = h f min = 2 E
   Where:
   E min = minimum energy of the incident photon (J)
   h = Planck’s Constant (J s)
   f min = minimum frequency of the photon (Hz)
   E = rest mass energy of one of the particles (J)
2. Pair production is the opposite of annihilation, it is defined as:
   The creation of a particle-antiparticle pair when a high-energy photon spontaneously converts its energy into mass.
3. To achieve pair production, a single photon must have enough energy to create both particles. The minimum energy required for a photon to undergo pair production is equal to the total rest mass energy of the particles produced:

Question 9

1. What are hadrons?
2. What are the classes of hadrons?

Answer 9

1. Hadrons are the group of subatomic particles that are made up of quarks
   Therefore, hadrons can feel the strong nuclear force.
2. There are two classes of hadrons:
   Baryons (3 quarks)
   Mesons (quark and anti–quark pair)
   The most common baryons are protons and neutrons
   The most common mesons are pions and kaons
   There are two classes of anti–hadrons:
   Anti–baryons (3 anti-quarks)
   Anti–mesons (quark and anti–quark pair)

Question 10

Explain how the notation works for particles

Question 11

1. What is baryon number?
2. Explain the most stable baryon

Answer 11

1. The baryon number of a particle shows whether it is a baryon (+1), antibaryon (-1) or neither (0). Baryon number is always conserved in particle interactions.
   The up (u), down (d) and strange (s) quark have a baryon number of 1/3 each
   This means that the anti–up, anti–down and anti–strange quarks have a baryon number of –1/3 each
   The implication of this is that baryons are made up of all quarks and anti-baryons are made up of all anti-quarks
   There are no baryons (yet) that have a combination of quarks and anti-quarks eg. up, anti-down, down
   The reason being that this would equate to a baryon number that is not a whole number (integer)
2. The proton is the most stable baryon: it has the longest half life (as other baryons eventually decay into it), and it is the lightest baryon (heavier particles decay into lighter particles, so a proton decay would violate the conservation of baryon number),

Question 12

1. Explain pions
2. Explain a pion’s role as an exchange particle

Answer 12

1. Pions (π–mesons) can be positive (π^+), negative (π^-) or neutral (π^0). They contain up and down quarks only, so they have zero strangeness.
   The antiparticle of the positive pion is the negative pion (and vice versa). The neutral pion is its own antiparticle.
   Pions are the lightest mesons, making them more stable than other types of mesons.
2. The strong nuclear force, one of the four fundamental interactions, keeps the protons and neutrons bound together in a nucleus. Fundamental interactions are mediated by exchange particles.
   The pion is the exchange particle of the strong nuclear force between baryons. In a nucleus, protons and neutrons exhibit the strong force by exchanging pions. Pions are said to mediate (bring about) the strong nuclear force. The pion created is a temporary violation of energy and mass conservation, but since it is a virtual particle, it is not directly observed.

Question 13

1. Explain kaons
2. Explain kaon production and decay

Answer 13

1. Kaons (K-mesons) can be positive (K^+), negative (K^-) or neutral (K^0).
   Kaons have a property known as strangeness
   This is because they contain a strange quark, which can be paired with either an up or down quark
   The antiparticle of the positive kaon is the negative kaon (and vice versa)
   Unlike the neutral pion, the neutral kaon is not its own antiparticle
   Kaons are heavy and unstable and normally decay into pions
   They are known to have unusually long lifetimes (compared to other mesons)
   This is characteristic of particles containing strange quarks
2. Kaons can be produced in pairs (pair production) via the strong interaction, where strangeness is always conserved
   An example of kaon pair production is through a high-energy proton-proton collision:
   p + p —> p + p + K^+ + K^-
   The strangeness on both sides is zero, so strangeness is conserved.

Question 14

1. Explain leptons
2. Explain leptons number

Answer 14

1. Leptons are a group of fundamental (elementary) particles
   This means they are not made up of any other particles (no quarks)
   Leptons interact with other particles via the weak, gravitational or electromagnetic interactions
   They do not interact via the strong nuclear force
   The most common leptons are:
   The electron, e^–
   The electron neutrino, ve (subscript e)
   The muon, μ^–
   The muon neutrino, vμ
   Neutrinos are the most abundant leptons in the universe and have no charge and negligible mass (almost 0)
   Although quarks are fundamental particles too, they are not classed as leptons
   Leptons do not interact with the strong force, whilst quarks do
2. The lepton number, L is the number of leptons in an interaction
   L depends on whether the particle is a lepton, anti-lepton or neither
   Leptons have a lepton number L = +1
   Anti-leptons have a lepton number L = –1
   Particles that are not leptons have a lepton number L = 0
   Lepton number is a quantum number and is conserved in all interactions
   This is helpful for knowing whether an interaction is able to happen

Question 15

Explain Muon Decay

Answer 15

Muons are leptons that are slightly heavier than the electron
The mass of an electron is about 0.0005u, whereas the mass of a muon is about 0.1u
Electrons and muons both have a charge of -1e
Muons (μ–) typically decay into an electron
Anti-muons (μ+) typically decay into positrons
Muon decay occurs through the weak interaction
This can be recognised by the exchange of the W– boson on a Feynman diagram

Question 16

What are the quark combinations for baryons?

Answer 16

Protons are made up of two up quarks and a down quark.
Neutrons are made up of two down quarks and an up quark.

Question 17

What are the quark combinations for mesons?

Answer 17

Pions and kaons are made up of a quark and anti-quark pair
Pions are either:
π+ made up of an up quark and an anti-down quark
π– made up on an anti-up quark and a down quark
π0 made up of an up quark and anti-up quark or down quark and anti-down quark

Kaons are either:
K+ made up of an up quark and an anti-strange quark
K– made up on an anti-up quark and a strange quark
K0 made up of an down quark and anti-strange quark or anti-down quark and strange quark

Question 18

1. Explain strange particles
2. Explain strangeness

Answer 18

1. Strange particles are particles that include a strange or anti-strange quark
   An example of these are kaons
   Strange particles always:
   Are produced through the strong interaction
   Decay through the weak interaction
   Are produced in quark-antiquark pairs
2. Strangeness, S, like baryon and lepton number, is a quantum number
   Strangeness is conserved in every interaction except the weak interaction
   This means that strange particles are always produced in pairs (e.g. K+ and K–)
   S depends on whether the particle contains a strange quark, anti-strange quark, or no strange quarks
   Particles with an anti-strange quark have S = +1
   Particle with a strange quark have S = –1
   Particles with no strange quark have S = 0
   Strangeness can change by 0, +1 or –1 in weak interactions

Question 19

1. What are the four fundamental interactions?
2. What are the ranges of the four fundamental interactions?

Answer 19

1. There are four fundamental interactions, or fundamental forces, that exist. These are:
   Gravity
   Electromagnetism
   Strong Nuclear (or Strong Interaction)
   Weak Nuclear
2. They also have different ranges:
   The electromagnetic and gravitational interactions have an infinite range
   The weak force has a range of up to 10–18 m
   The strong force has a range of ~ 10–15 m

Question 20

1. What are the weakest and strongest fundamental forces?
2. What particles do the fundamental interactions affect?
3. What are the exchange particles for the different fundamental interactions?

Answer 20

1. Gravity is the weakest of these forces, whilst the strong interaction is the strongest (hence the name).
2. The gravitational interaction only affects particles with mass
   The electromagnetic interaction only affects particles with charge
   The weak interaction affects all particles
   The strong interaction only affects hadrons.
3. For strong forces: pions (pi symbol).
   For weak forces: W-bosons or Z-bosons.
   For electromagnetic forces: photons (gamma symbol)

Question 21

Explain exchange particles

Answer 21

When two particles interact, there cannot be instantaneous action at a distance
This means one particle needs to “know” that the other is there
This is the idea behind exchange (or virtual) particles
When two particles exert a force on each other, a virtual particle is created
Virtual particles only exist for a short amount of time and carry the fundamental force between each particle
A force can be attractive or repulsive. An analogy of exchange particles would be:
Two people are on skateboards and a ball is passed between them. Due to this, they start to move away from each other. The ball represents an exchange particle creating repulsion
However, if one person throws a boomerang to the other, they will start to move closer together. The boomerang represents an exchange particle creating attraction
Each fundamental interaction is transmitted by its own exchange particle
These are also called gauge bosons

Question 22

1. Explain the exchange particle of the electromagnetic force
2. Explain the exchange particles of the strong interaction.

Answer 22

1. The electromagnetic force is only between charged particles
   The exchange particle that carries this force is the virtual photon, γ
   Properties of the photon are:
   It has no mass
   It has no charge
   It is its own antiparticle
   Electromagnetic interactions occur whenever two charged particles interact with each other
   For example, when two charged particles, such as electrons, are repelled by each other, a virtual photon is exchanged between them to produce this repulsion

The electromagnetic force is also responsible for binding electrons to atoms
This is due to the attractive force between the negative electrons and positive nucleus

2. Hadrons are particles that are made up of quarks
   Hence they are subject to the strong interaction
   The exchange particle of the strong interaction is either:
   The pion (between nucleons)
   The gluon (between quarks)
   This means that leptons cannot interact with the strong force, since they are not made up of quarks

Question 23

Explain the weak interaction

Answer 23

The weak interaction is responsible for the radioactive decay of atoms

The exchange particle that carries this force is the W–, W+ or Z0 boson

The type of exchange particle depends on the type of interaction

β– and β+ decay are examples of the weak interaction in action

In β– decay, a neutron turns into a proton emitting an electron and an anti-electron neutrino
The W– boson is the exchange particle in this interaction.

In β+ decay, a proton turns into a neutron emitting a positron and an electron neutrino. The W+ boson is the exchange particle in this interaction.

Question 24

Explain electron capture and electron-proton collisions

Answer 24

Electrons and protons are attracted to each other via the electromagnetic interaction. However, when they interact with each other, it is the weak interaction that facilitates the collision.
Both electron capture and electron-proton collisions have the same decay equation
p + e^- -> n + ve

Electron capture is when an atomic electron is absorbed by a proton in the nucleus resulting in the release of a neutron and an electron neutrino.
This decay is mediated by the W+ boson.
Electron-proton collisions are similar; when an electron collides with a proton, a neutron and an electron neutrino are emitted.
This decay is mediated by the W– boson.

Question 25

What are the rules for Feynman diagrams?

Answer 25

The y-axis represents time and the x-axis represents space. A vertex is where particles and exchange particles meet - these represent points of interaction (e.g. electromagnetic, weak or strong). Incoming particles come in at the bottom, and outgoing particles leave at the top. Particles are represented by straight lines which have arrows. Each straight line must have an arrow with its direction forward in time. Exchange particles are represented by wavy lines which have no arrows. The transfer of exchange particles is from left to right unless indicated by an arrow above the wavy line. Hadrons/quarks are present on the left and leptons on the right, they must never meet at a vertex. Charge, baryon number and lepton number must be conserved at each vertex. Lines must not cross over

Question 26

Explain exchange particles in Feynman diagrams

Answer 26

Exchange particles act as a force carrier between particles in an interaction In electromagnetic interactions, the exchange particle is a virtual photon In weak interactions, the exchange particle is the W boson Exchange particles are represented as wavy lines Charged exchange particles, such as W+ and W–, sometimes have an arrow above the wavy line to indicate their direction

Question 27

Explain beta-minus decay on Feynman diagram

Answer 27

Beta-minus decay is an example of the weak interaction The exchange particle is a W− boson This is because the β− particle (electron) has a negative charge During beta-minus decay: A neutron decays into a proton and a W− boson. Then, the W− boson decays into an electron and anti-electron neutrino.