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Chapter 32: Particle Physics Please remember to photocopy 4 pages onto one sheet by going A3→A4 and using back to back on the photocopier.
Cockroft and Walton shared the Nobel Prize for their work on splitting the atom.*
Operation
- Protons are produced and released at the top.
- The protons get accelerated across a potential difference of 800 kVolt.
- The protons collide with a lithium nucleus, and as a result two alpha particles are produced.
- The alpha particles move off in opposite directions at high speed.
- They then collide with a zinc sulphide screen, where they cause a flash and get detected by microscopes.
1
H 1 +
7
Li 3 →
4 2
4
He 2 + He + K.E.
1 MeV 17.3 MeV 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 = mc^2 , 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.
Why was this experiment significant?
- First artificial splitting of the nucleus.
- First transmutation using artificially accelerated particles.
- First verification of Einstein’s E = mc^2.
- First Particle Accelerator
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 These particles make up what is known as ‘the particle zoo’.
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.
Pair Production* A gamma ray photon gets absorbed by a neutron, and an electron and a positron are emitted.
gamma ray photon (γ) → e-^ + e+^ + K.E. Note:
1. Conservation of Charge Net charge before and after is zero. 2. Conservation of Momentum * The gamma ray photon does have momentum! So for momentum to be conserved, there must be momentum afterward, therefore the two new particles cannot move off in opposite directions.
- 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. The same applies for the generation of other higher energy leptons such as the muon and tau. Why do we need the neutron?*
Pair Annihilation An electron and a positron collide to produce two gamma ray photons
e-^ + e+^ → 2γ
Note:
1. Conservation of Charge Net charge before and after is zero. 2. 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.
You must use the phrase ‘gamma-ray photons’, and not just ‘photons’; the logic being that ‘gamma-ray’ implies a very high level of energy!
The neutrino* 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 was neutrino was itself coined by the Italian physicist Enrico Fermi. The neutrino is extremely small, has almost no mass, and has zero charge (the term itself means ‘little neutral one’).
Fundamental forces of nature Happily (hah!) we can categorise all particles on the basis of the quark composition and the forces which they are subject to. It turns out that there are actually only four fundamental forces in nature; Strong, weak, electro-magnetic and weak.
Force Role Range
Strong Binds nucleus together Short Weak Responsible for Beta decay Short Electro- Magnetic
Force between charged particles Inverse square law
Gravitational Force between planets Inverse square law
All fundamental particles can now be categorised as follows: Leptons* : Indivisible point objects not subject to the Strong Force, e.g. positron, electron, muon, tao, neutrino. Hadrons : Feel all four forces. Hadrons can be further sub-divided into Mesons and Baryons. 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.
Because a quark is composed of a quark and an anti-quark (matter and anti-matter) it annihilates almost immediately.
Leaving Cert Physics Syllabus
Content Depth of Treatment Activities STS
- Conservation of energy and momentum in nuclear reactions
Radioactive decay resulting in two particles. If momentum is not conserved, a third particle (neutrino) must be present.
Appropriate calculations to convey sizes and magnitudes and relations between units.
- Acceleration of protons
Cockcroft and Walton – Proton energy approximately 1 MeV: Outline of experiment.
Appropriate calculations. First artificial splitting of nucleus. First transmutation using artificially accelerated particles. Irish Nobel laureate for physics, Professor E. T. S. Walton (1951).
- Converting mass into other forms of energy
“Splitting the nucleus” H + Li → He + He + Q 1 MeV 17.3 MeV Note energy gain. Consistent with E = mc^2
- Converting other forms of energy into mass
Reference to circular accelerators progressively increasing energy available: proton-proton collisions p + p + energy → p + p + additional particles.
Audiovisual resource material. History of search for basic building blocks of nature:
- Greeks: earth, fire, air, water
- 1936: p, n, e. Particle accelerators, e.g. CERN.
- Fundamental forces of nature
Strong nuclear force: Force binding nucleus, short range. Weak nuclear force: Force between particles that are not subject to the strong force, short range. Electromagnetic force: Force between charged particles, inverse square law. Gravitational force: inverse square law.
- Families of particles
Mass of particles comes from energy of the reactions – m = E/c^2 The larger the energy the greater the variety of particles. These particles are called “particle zoo”. Leptons: indivisible point objects, not subject to strong force, e.g. electron, positron, and neutrino. Baryons: subject to all forces, e.g. protons, neutrons, and heavier particles. Mesons: subject to all forces, mass between electron and proton.
Appropriate calculations. Pioneering work to investigate the structure of matter and origin of universe. International collaboration, e.g. CERN.
- Anti-matter e+^ positron, e–^ electron. Each particle has its own anti-particle. Pair production: two particles produced from energy. γ rays → e+^ + e–^ conserve charge, momentum. Annihilation: Two γ rays from annihilation of particles. e+^ + e–^ → 2 hf (γ rays) conserve charge, momentum.
Paul Dirac predicted anti-matter mathematically.
- Quark model Quark: fundamental building block of baryons and mesons. Six quarks – called up, down, strange, charmed, top, and bottom. Charges: u+2/3^ , d-1/3^ , s-1/ Anti-quark has opposite charge to quark and same mass. Baryons composed of three quarks: p = uud, n = udd, other baryons any three quarks. Mesons composed of any quark and an anti- quark.
Identify the nature and charge of a particle given a combination of quarks.
James Joyce: “Three quarks for Muster Mark”.
Where p = momentum, and M 0 represents the mass of the particle at rest. This gets reduced to E = mc^2 for most applications. However for a photon, its mass is zero, and therefore the equation in this case reduces to E = pc Therefore for a photon which does have energy hf but no mass and therefore no rest energy, its momentum is given by p=E/c. This means that the 'push' that photons give on e.g. a solar sail is due to their momentum which is not mv but E/c. Still confusing? Okay, but do I not at least get some points for acknowledging that this is a source of confusion – many of the textbooks mention this in a blasé manner which suggests this is most obvious thing in the world. What is this thing called ‘rest mass’? Why do objects get more ‘massive’ when they travel at very fast speeds? From the formula E = mc^2 If you try to accelerate a proton, at first its velocity increases, but as its velocity increases so does its mass (from special relativity), and as a result it gets harder to accelerate it. At a speed of 99.997 the speed of light the mass of the proton is 430 times its ‘rest mass’. This is why running particle accelerators is usually done at night; the amount of electricity would actually be enough to power a small town.
*Why do we need the neutron? The disappearance of a photon followed by the appearance of an electron and positron (without any neutron) cannot conserve both total energy and momentum. To ensure that momentum as well as energy is conserved, you need something nearby to participate and absorb the recoil. So there you go.
*The Lepton The name lepton derives from Greek word leptos meaning “light, not heavy”. It was originally assigned to electron and neutrino.
*Murray Gell-Mann He wrote that Physics at high school was “the dullest course I had ever taken”, and he only applied to study physics at university “to please my father”. Taken from; When we were kids: how a child becomes a scientist. I wonder how his physics teacher felt when he read that?
- The Neutrino We have seen that in Beta Decay, a neutron breaks up in to a proton and an electron. The equation is n^0 → p+^ + e-
However when scientists investigated the momentum before and after, they noticed something strange. The momentum after was a little less than the momentum beforehand, and no matter how many times they repeated the experiment they got the same result. It was as if there was something missing on the right hand side, but they couldn’t find anything. It was all very confusing. Picture the situation: A certain amount of energy and momentum go into the equation, but not enough comes out. Up steps a well-known Italian scientist called Wolfgang Pauli to suggest that there actually is more momentum coming out, but the reason that it is not detected is because it comes in the form of particles which have no charge, and whose mass is too small to be detected. It’s kinda hard to be proved wrong in that one! Pauli coined the name ‘neutrino’ for the particle because it means ‘little neutral one’ in Italian. By the way, this is indeed the same Pauli of ‘Pauli’s Exclusion Principle’ fame, which those of you sad enough to be doing Chemistry will recognise.
To give an idea of how radical a prediction this is, remember that all good science is supposed to be built upon the cornerstone of experiments. If you predict something to exist but that it can never be verified by experiment then you may as well be talking about the existence of God; It’s not to say that God doesn’t exist, it’s just that in science we have to stick to what we can verify by experiment. Then along comes Pauli and breaks this golden rule. In fairness, Pauli realised this himself. He admitted, “ I have done a terrible thing – I have predicted the existence of a particle which cannot be detected”!
But these were strange times in physics; Ernest Rutherford was probably the foremost physicist alive at this stage (he had, after all, split the atom. Cockroft and Walton were working under Rutherford when they carried out their groundbreaking experiment). Rutherford’s advice was to assume that the Conservation of Energy law probably didn’t apply at this level.
As it turned out, the neutrino was detected experimentally in 1956, although there is still much that remains unknown about this particle. For instance did you know that somewhere between 90% and 99% of all matter in this universe is unaccounted for? One possible explanation is that the neutrino is carrying this mass. While it is obviously very, very, very light, the small mass it does have, multiplied by the sheer (literally?) weight of numbers, may make it the culprit.
Did you know there are 10 x 10^14 neutrinos pass through you every second, coming from the sun? The fact that at night-time the Earth is between you and the Sun doesn’t matter – these little critters pass straight through the Earth!
Cosmic Gall Neutrinos, they are very small. They have no charge and have no mass And do not interact at all. The earth is just a silly ball To them, through which they simply pass, Like dustmaids down a draughty hall Or photons through a sheet of glass. They snub the most exquisite gas, Ignore the most substantial wall, Cold shoulder steel and sounding brass, Insult the stallion in his stall, And scorning barriers of class, Infiltrate you and me! Like tall And painless guillotines, they fall Down through our heads into the grass. At night they inter at Nepal And pierce the lover and his lass From underneath the bed – you call It wonderful; I call it crass.
Telephone Poles and Other Poems , John Updike, Knopf, 1960
