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Particle Physics
http://homepage.eircom.net/~louiseboylan/index.html
1. Nuclear reactions 2. Cockcroft and Walton
3. Energy to mass and mass to energy 4. Fundamental forces of nature 5. Families of particles
6. The quark model
1. Nuclear Reactions
Conservation Laws - In nuclear reactions the following are observed
Conservation of mass – energy: The more traditional laws of conservation of energy and conservation of mass are found to be false in nuclear reactions. Using Einstein’s idea of the
equivalence of mass and energy (E=mc2) you will find that if mass is lost in a nuclear reaction it will be converted to energy and energy may be converted to mass. The mass-energy total will remain the same.
Conservation of momentum – For momentum to be conserved you must note that the electron and positron are either moving directly towards each other beforehand or are at rest and so have no (net) momentum.Therefore, in order for there to be no (net) momentum after, the two photons produced must fly off in opposite directions. If momentum is not conserved a neutrino must be present.
Conservation of Charge – In a nuclear reaction the total amount of electric charge before the reaction equals the total amount of electric charge after the reaction.Net charge before and after is zero.
The neutrino
When the energy of the beta particles was measured experimentally, the values varied a lot and were usually out by 0.1559MeV. This would suggest that the laws of conservation of momentum and conservation of mass – energy was not correct.
The neutrino was first postulated by the Austrian physicist Wolfgang Pauli (of Pauli’s Exclusion Principle), to account for the apparent discrepancy between the momentum before and after beta decay (remember this happens when a neutron splits into a proton and an electron). The term neutrino was itself coined by the Italian physicist Enrico Fermi.
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2. Cockroft and Walton -
shared the Nobel Prize for their work on splitting the atom.They bombarded Lithium with protons as outlined below. Their experiment was the first experimental verification of Einstein’s famous equation E=mc2.
Operation
1. Protons are produced and released at the top.
2. The protons get accelerated across a potential difference of 400 kVolt.
3. The protons collide with a lithium nucleus, and as a result two alpha particles are produced. 4. The alpha particles move off in opposite directions at high speed.
5. They then collide with a zinc sulphide screen, where they cause a flash and get detected by microscopes.
1 1
H + Li37
4 2 4
2 He
He + K.E.
Note:
The energy of the emitted alpha particles was far greater than the energy of the incoming protons which meant that energy had been obtained from mass i.e a verification of Einstein’s equation E=mc2
This was the first transmutation (changing of one element to another) using artificially accelerated particles.
In 1919 Rutherford performed the first transmutation but he used naturally occurring alpha particles to bombard nitrogen.
Question: Calculate the disintegration energy Q in the Cockcroft and Walton reaction.
1 1
H + Li37
4 2 4
2 He
3 Left Hand Side:
The total mass/energy in consists of the proton plus lithium (plus kinetic energy of the proton of 1 MeV). Right Hand Side:
The total energy out consists of the two alpha particles, (plus kinetic energy of the alpha particles of 17.3 MeV).
Using E = mc2, the scientists could explain the fact that there was more kinetic energy after than there was before: some of the mass had disappeared! The scientists were able to establish both the masses and the kinetic energies of all the particles and so could verify Einstein’s equation.
The significance of the experiment
1. First artificial splitting of the nucleus.
2. First transmutation using artificially accelerated particles. 3. First verification of Einstein’s E = mc2.
4. First Particle Accelerator
Accelerators
After the success of Cockcroft and Walton the race was on to build bigger and better particle accelerators.
When particles such as protons are accelerated to very high speeds and allowed to collide with each other new particles are produced.
The higher the kinetic energy of the colliding particles the greater the number of different particles produced and indeed the greater the mass of the particles produced.
The particles produced in these reactions tend to be very unstable and only last for a very short time
Several hundred such particles have been observed and initially there was no connection between the particles, no pattern. The collection became known as the particle zoo.
Converting other forms of energy into mass
Nowadays the particle accelerators are much more powerful, and one of the more common experiments is to whack two protons off of each other.
To do this they are sent in opposite directions around a circular particle accelerator (e.g. in CERN).
The kinetic energy gets transformed into new and exotic particles.
𝒑+ + 𝒑+ + kinetic energy = 𝒑+ + 𝒑+ + additional particles
The larger the kinetic energy of the protons before collision, the greater will be the variety of new particles produced
4 Cyclotron (Circular accelerator)
The length of an accelerator does not have to be so long if the particles are allowed to follow a circular path.
A magnetic field is applied perpendicularly to the ‘D’ shaped cavities in which the charged particles will move.
When the charged particle from the source enters the magnetic field it follows a circular path. An alternating voltage is applied across and the charged particles accelerate each time.
As the charged particle gets to the edge of the cyclotron it leaves and is fired at its target.
Anti-matter
Each particle has its own anti-particle, which is identical in mass, but opposite in charge. The English physicist Paul Dirac predicted anti-matter mathematically before it was detected experimentally.
3. Energy to Mass and Mass to Energy
Pair Production - The simultaneous creation of a particle and its antiparticle from electromagnetic energy.
When high energy x-rays are fired at a sheet of lead an electron and a positron are produced. The energy of the photon is converted into the mass of the two particles. Any energy of the photon
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The above diagram indicates what would be observed if the reactions take place in a cloud chamber. A magnetic field will cause the two particles to be deflected in the opposite directions. (One charged positively and one negatively)
Charged is conserved in this reaction i.e the incoming photon has no charge and since the electron and positron have equal and opposite charge there is no net charge after the reaction.
Momentum is conserved in this reaction also.
K.E. represents the kinetic energy of the electron and positron as they move off.
Pair production can only occur if the photon has an energy exceeding twice the rest mass of the electron.
Pair Annihilation
An electron and a positron collide to produce two gamma ray photons
𝑒++ 𝑒− → 2𝛾
Used in PET scans. Radioactive materials that decay by positron emission are used. The positrons annihilate the electrons from damaged body tissue and the emitted photons are picked up by the detectors and give an outline of the damaged tissue.
Fundamental forces of nature
All matter and energy in the universe have to abide by one or more of the following fundamental forces.
Gravity
Electromagnetic force
Weak nuclear force
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4. Families of particles
With the improvement in particle accelerators it became possible to obtain high energy particles for collisions with other particles. During collisions some of this energy was converted to mass (new particles) and the greater the initial energy the greater the mass of these new particles and the greater the variety of particles produced.
Eventually physicists noticed an order to the ‘particle zoo’. The criterion for the order was whether or not a particle felt the strong nuclear force.
The result was that two groups of families became evident
Leptons – are affected by the weak nuclear force but not the strong nuclear force
They are affected by the gravitational force and if charged they also feel the electromagnetic force. All the evidence suggests that leptons are elementary particles
The family is made up of the electron the muon and the tau. It includes the neutrino of these three and also the corresponding six antiparticles.
Hadrons – are affected by both the strong force and the weak force. They are affected by the strong nuclear force and the weak nuclear force.
Hadrons are also affected by the gravitational force and the electromagnetic force.
There are very many different hadrons but we usually divide them into two groups called baryons and mesons.
Mesons: Subject to all forces; mass between electron and proton; composed of a quark and an anti-quark, e.g. the pion
Baryons: Subject to all forces; composed of 3 quarks or 3 anti-quarks, e.g. the proton and the neutron.
5. Quarks
Gell-Man and Zweig proposed independently that baryons and mesons are made up of smaller
particles which are called ‘quarks’. The name was taken from a book called Finnegan’s Wake by James Joyce.
At first only three different types of quarks were suggested and they were called up (u), down (d) and strange (s). Later it was realised that three more were needed and they were called charm ©, top (t) and bottom (b).
It is believed that quarks cannot be subdivided and so are elementary particles that make up the baryons and mesons.
Quarks have a charge and it is either 1/3 or 2/3 unit charge
There are also six antiquarks and they have the same mass as their corresponding quarks but of course they have the opposite charge.
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Where e is the charge of one electron, e.g. the Up quark has a charge of two thirds the charge of an electron.
Only the charges of the first three need to be known (and these are available in the log-tables).
So what’s different about the Up, Charmed and Top particles if they all have the same charge?
Answer: Mass. The Up has the smallest mass and the Top the greatest (which is why it took the longest time to detect). Same goes for Down, Strange and Bottom.
Anti-quarks
An anti-quark has the same mass as its quark counterpart, but opposite charge. e.g. an anti-up has a charge of – 2/3 e.
If a particle is composed of three quarks it is called a baryon and if it is composed of two quarks it is called a meson (actually the quark will be composed of a quark and an antiquark).
Particles made from quarks/antiquarks Classification Example Composition Charge
Proton uud +1 (+2/3, +2/3, -1/3) Baryon
Neutron udd 0 (+2/3, -1/3, -1/3) Baryon
Pion ud +1 (+2/3, +1/3) Meson
Name of Quark Symbol Charge
Up u + 2/3 e
Down d - 1/3 e
Strange s - 1/3 e
Charmed c + 2/3 e
Bottom b - 1/3 e
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All fundamental particles can now be categorised as follows:
9 Example Questions
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2. Calculate the energy released in the alpha decay of to as indicated by the following equation. Mass of the uranium atom = 238.050784u
Mass of thorium atom = 234.043593u Mass of helium atom = 4.00260.
3. In the following reaction calculate the energy of the beta particle, which is the emitted electron.
4. In the Large Hadron Collider, two beams of protons are accelerated to high energies in a circular accelerator. The two beams of protons then collide producing new particles.
Each proton in the beams has a kinetic energy of 2.0 GeV.
What is the maximum net mass of the new particles created per collision?
5. In a circular accelerator, two protons, each with a kinetic energy of 1 GeV, travelling in opposite directions, collide. After the collision two protons and three pions are emitted.
What is the net charge of the three pions? Justify your answer.
(i) Calculate the combined kinetic energy of the particles after the collision.
(ii) Calculate the maximum number of pions that could have been created during the collision.
11 Key Definitions:
Antimatter
Leptons
Mesons
Baryons
Pair production
Pair annihilation
Quark
Exam Questions
mass of proton = 1.6730 × 10-27kg; mass of electron = 9.1 × 10–31 kg;
mass of lithium nucleus = 1.1646 × 10-26kg; mass of α-particle = 6.6443 × 10-27kg;
mass of neutron = 1.6749 × 10–27 kg; charge on electron = 1.6022 × 10–19 C;
mass of pion = 2.4842 × 10–28 kg;
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Particle Accelerators, Cockroft and Walton Experiment and E = mc2
1. [2009]
In 1932 Cockcroft and Walton succeeded in splitting lithium nuclei by bombarding them with artificially accelerated protons using a linear accelerator.
Each time a lithium nucleus was split a pair of alpha particles was produced. (i) How were the protons accelerated?
(ii) How were the alpha particles detected?
2. [2005]High voltages can be used to accelerate alpha particles and protons but not neutrons. Explain why.
3. [2009]Most of the accelerated protons did not split a lithium nucleus. Explain why.
4. [2002]In 1932, Cockcroft and Walton carried out an experiment in which they used high-energy protons to split a lithium nucleus. Outline this experiment.
5. [2007]
(i) Draw a labelled diagram to show how Cockcroft and Walton accelerated the protons.
(ii) What is the velocity of a proton when it is accelerated from rest through a potential difference of 700 kV?
6. [2009] [2007] [2005][2002]
Write a nuclear equation to represent the splitting of a lithium nucleus by a proton.
7. [2009] [2007][2002]
Calculate the energy released in this reaction.
8. [2005][2009]Circular particle accelerators were later developed. Give an advantage of circular accelerators over linear accelerators.
9. [2004]In beta decay, a neutron decays into a proton with the emission of an electron. Write a nuclear equation for this decay.
10. [2004] Calculate the energy released during the decay of a neutron.
The neutrino
11. [2008]The existence of the neutrino was proposed in 1930 but it was not detected until 1956. Give two reasons why it is difficult to detect a neutrino.
12. [2007] In beta decay it appeared that momentum was not conserved. How did Fermi’s theory of radioactive decay resolve this?
13. [2004]Momentum and energy do not appear to be conserved in beta decay.
Explain how the existence of the neutrino, which was first named by Enrico Fermi, resolved this.
Antimatter
14. [2007]Compare the properties of an electron with that of a positron.
15. [2007]What happens when an electron meets a positron?
16. [2003] Give one contribution made to Physics by Paul Dirac.
17. [2005]In an accelerator, two high-speed protons collide and a series of new particles are produced, in addition to the two original protons. Explain why new particles are produced.
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Cockcroft and Walton’s apparatus is now displayed at CERN in Switzerland, where very high energy protons are used in the Large Hadron Collider.
In the Large Hadron Collider, two beams of protons are accelerated to high energies in a circular accelerator. The two beams of protons then collide producing new particles.
Each proton in the beams has a kinetic energy of 2.0 GeV.
(i) Explain why new particles are formed.
(ii) What is the maximum net mass of the new particles created per collision?
19. [2008]
(iii) In a circular accelerator, two protons, each with a kinetic energy of 1 GeV, travelling in opposite directions, collide. After the collision two protons and three pions are emitted.
What is the net charge of the three pions? Justify your answer.
(iv) Calculate the combined kinetic energy of the particles after the collision.
(v) Calculate the maximum number of pions that could have been created during the collision.
Pair Production
20. [2003]The following reaction represents pair production: γ → e+ + e–
Calculate the minimum frequency of the γ-ray photon required for this reaction to occur.
21. [2003]What is the effect on the products of a pair production reaction if the frequency of the γ-ray photon exceeds the minimum value?
Pair Annihilation
22. [2006] During a nuclear interaction an antiproton collides with a proton.
Pair annihilation takes place and two gamma ray photons of the same frequency are produced. (i) What is a photon?
(ii) Calculate the frequency of a photon produced during the interaction. (iii) Why are two photons produced?
(iv) Describe the motion of the photons after the interaction. (v) How is charge conserved during this interaction?
(vi) After the annihilation, pairs of negative and positive pions are produced. Explain why.
23. [2003]
(i) Write a reaction that represents pair annihilation.
(ii) Explain how the principle of conservation of charge and the principle of conservation of momentum apply in pair annihilation.
2014 Question 11(a)
Read the following passage and answer the accompanying questions. Cyclotrons and PET Scanners
Positron emission tomography (PET) scanners are designed to detect the pair of photons generated from the annihilation reaction between a positron and an electron.
A carbon–11 nucleus, which has a half-life of twenty minutes, decays with the emission of a positron. The positron travels only a short distance before colliding with an electron in the surrounding matter. Pair annihilation occurs. The emitted photons travel in opposite directions.
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magnetic field until they have sufficent velocity and are deflected into a target producing radioactive nuclei, including carbon–11.
(Adapted from “Essentials of Nuclear Medicine Physics”; Powsner & Powsner; 1998)
(i) Electrons are leptons.
List the three fundamental forces that electrons experience in increasing order of strength. (ii) Write an equation to represent the pair annihilation described in the text.
(iii)Calculate the frequency of each photon produced in this pair annihilation. (iv)Why do the photons produced in pair annihilation travel in opposite directions? (v) Write a nuclear equation to represent the decay of carbon–11.
(vi)What is the value of the decay constant of carbon–11?
(vii) Explain why the carbon–11 nuclei used in the PET scanner must be produced in a cyclotron in, or close to, the same hospital as the scanner.
(viii) Give an expression for the momentum of a particle in the cyclotron in terms of the magnetic flux density of the field, the charge on the particle and the radius of its circular path at any instant.
2013 Question 10(a)
In 1932 J.D. Cockroft and E.T.S. Walton accelerated protons to energies of up to 700 keV and used them to bombard a lithium target. They observed the production of alpha-particles from the collisions between the accelerated protons and the lithium nuclei.
(i) How did Cockroft and Walton accelerate the protons? (ii) How did they detect the alpha-particles?
(iii)Write the nuclear equation for the reaction that occurred and indicate the historical significance of their observation.
(iv)Calculate the speed of a proton that has a kinetic energy of 700 keV.
Many modern particle accelerators, such as the Large Hadron Collider (LHC) in CERN, have a circular design.
The diagram shows a simplified design of a circular accelerator. (v) Why is the tube evacuated?
(vi)What is the purpose of accelerating the particles to high velocities? (vii) What is the purpose of the magnets?
(viii) Give an advantage of a circular accelerator over a linear accelerator.
(ix)Can an accelerator of this design be used to accelerate neutrons? Explain your answer.
2012 Question 10(a) (i) What is a positron?
(ii) When a positron and an electron meet two photons are produced. Write an equation to represent this interaction.
(iii)Why are photons produced in this interaction? (iv)Explain why two photons are produced.
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(vi)Explain why the photons produced usually have a greater frequency than your calculated minimum frequency value.
(vii) Why must two positrons travel at high speeds so as to collide with each other? (viii) How are charged particles given high speeds?
(ix)Explain why two positrons cannot annihilate each other in a collision.
2011 Question 10(a)
(i) List three quantities that are conserved in nuclear reactions. (ii) Write an equation for a nucleus undergoing beta-decay.
(iii)In initial observations of beta-decay, not all three quantities appear to be conserved. What was the solution to this contradiction?
(iv)List the fundamental forces of nature in increasing order of their strength. (v) Which fundamental force of nature is involved in beta-decay?
(vi)In the Large Hadron Collider, two protons with the same energy and travelling in opposite directions collide. Two protons and two charged pi mesons are produced in the collision.
Why are new particles produced in the collision? (vii) Write an equation to represent the collision.
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Fundamental Forces
24. [2008] Baryons and mesons are made up of quarks and experience the four fundamental forces of nature. List the four fundamental forces and state the range of each one.
25. [2006] List the fundamental forces of nature that pions experience.
26. [2002][2005] Name the fundamental force of nature that holds the nucleus together.
27. [2004] Beta decay is associated with the weak nuclear force.
List two other fundamental forces of nature and give one property of each force.
28. [2002] Name the four fundamental forces of nature.
29. [2009] Arrange the fundamental forces of nature in increasing order of strength.
30. [2002] Give two properties of the strong force.
Quark Composition and Particle Classification
31. [2008] Name the three positively charged quarks.
32. [2008]What is the difference in the quark composition of a baryon and a meson?
33. [2008]What is the quark composition of the proton?
34. [2007] A kaon consists of a strange quark and an up anti-quark. What type of hadron is a kaon?
35. [2006] Pions are mesons that consist of up and down quarks and their antiquarks. Give the quark composition of (i) a positive pion, (ii) a negative pion.
36. [2006]Name the three negatively charged leptons.
37. [2004] Give the quark composition of the neutron.
38. [2005]A huge collection of new particles was produced using circular accelerators. The quark model was proposed to put order on the new particles. List the six flavours of quark.
39. [2005]Give the quark composition of the proton.
