Particle physics
Contents: 8 sections
Alpha-particle scattering
Alpha particles were fired at a thin gold foil. Three observations, each with its own conclusion, and the marks are for pairing them correctly:
| Observation | Conclusion |
|---|---|
| Most passed straight through | The atom is mostly empty space |
| A small number were deflected through large angles | There is a concentrated positive charge |
| A very few, about 1 in 8000, were deflected through more than 90° | That charge is in a very small, massive nucleus |
The last row is the one to state carefully. It is the rarity of the large-angle deflections that shows the nucleus is small, and the fact that a heavy alpha particle can be turned back at all that shows it is massive.
Nuclide notation
A nuclide is written with the nucleon number A above and the proton number Z below the symbol.
- Proton number Z: the number of protons. It defines the element.
- Nucleon number A: protons plus neutrons.
- Neutrons = A − Z.
Isotopes are nuclei of the same element with different numbers of neutrons: same Z, different A. They have identical chemical behaviour, because that is set by the electrons, and different nuclear behaviour.
In any nuclear equation both A and Z must balance. That single rule solves most equation questions without any other knowledge.
The three radiations
| Alpha | Beta-minus | Gamma | |
|---|---|---|---|
| Nature | Helium nucleus, 2p + 2n | Fast electron | Electromagnetic wave |
| Charge | +2e | −e | 0 |
| Mass | 4u | ~1/1836 u | 0 |
| Stopped by | Paper, few cm of air | Few mm of aluminium | Several cm of lead |
| Ionising power | Strongest | Moderate | Weakest |
Ionising power and penetration run in opposite directions, and the reason is one idea: a strongly ionising particle loses its energy quickly in a short distance, so it does not get far.
In a magnetic field, alpha and beta deflect in opposite directions because their charges are opposite, and gamma is undeflected. Beta deflects far more than alpha for the same field, because it has a much smaller mass. A question showing three paths is answered by noting which way each bends and how sharply.
The decays
- Alpha decay: A decreases by 4, Z decreases by 2.
- Beta-minus decay: a neutron becomes a proton, so A is unchanged and Z increases by 1. An electron and an antineutrino are emitted.
- Beta-plus decay: a proton becomes a neutron, so A is unchanged and Z decreases by 1. A positron and a neutrino are emitted.
- Gamma emission: neither A nor Z changes; the nucleus loses energy.
Beta-minus increases the proton number even though a negative particle leaves. Following the nucleon bookkeeping rather than intuition is what gets this right: carbon-14 decaying by beta-minus becomes nitrogen-14, with A unchanged at 14 and Z rising from 6 to 7.
The antineutrino was proposed because the emitted electrons have a range of energies rather than the single value conservation of energy would require. It carries away the balance.
Fundamental particles
A fundamental particle has no internal structure. Electrons are fundamental; protons and neutrons are not.
Quarks
Three quarks are on the syllabus, with their charges as fractions of e:
| Quark | Charge |
|---|---|
| up (u) | +2/3 |
| down (d) | −1/3 |
| strange (s) | −1/3 |
Antiquarks have the opposite sign.
- Proton = uud, charge +2/3 + 2/3 − 1/3 = +1
- Neutron = udd, charge +2/3 − 1/3 − 1/3 = 0
Being able to reconstruct these two from the charges, rather than recalling them, is what makes the less familiar combinations answerable.
Hadrons are particles made of quarks, and split into two families:
- Baryons: three quarks. Protons and neutrons are baryons.
- Mesons: a quark and an antiquark.
Leptons are fundamental and are not made of quarks: the electron, the muon and their neutrinos, plus the antiparticles.
Beta decay in quark terms
Beta-minus decay is a down quark changing into an up quark:
d → u + e⁻ + antineutrino
which turns udd into uud, a neutron into a proton. Beta-plus is the reverse, u → d.
Being asked to express beta decay at the quark level is now standard, and the answer is that single transformation.
Conservation laws
In any particle reaction the following are conserved, and questions ask which of four proposed reactions is possible:
- Charge
- Baryon number (each baryon +1, each antibaryon −1, mesons and leptons 0)
- Lepton number (each lepton +1, each antilepton −1)
- Energy and momentum
Check charge first, since it is fastest, and a reaction failing any one of them cannot occur.
Antiparticles
Every particle has an antiparticle of the same mass and opposite charge. The positron is the antiparticle of the electron. When a particle meets its antiparticle they annihilate, and their mass is converted into energy as two gamma photons.
Common mistakes
- Saying the large-angle deflections show the nucleus is large; it is their rarity that shows it is small.
- Saying beta-minus decay decreases the proton number.
- Giving the ionising power and penetration in the same order.
- Saying alpha and beta deflect the same way in a magnetic field.
- Calling the electron a hadron, or the proton fundamental.
- Getting the quark charges the wrong way round, so a proton comes out neutral.
- Forgetting the antineutrino in beta-minus decay, and with it the explanation for the energy spectrum.
- Failing to check baryon and lepton number when only charge balances.
Check you have it
Question 1
A π+ meson has a charge of +e, where e is the elementary charge. It consists of an up quark and one other quark.
What could be the other quark in the π+ meson?
Answer: A.
The up quark carries +2/3, so the other constituent must carry
+1 − 2/3 = +1/3
A down quark carries −1/3, so its antiquark carries +1/3. So the other particle is the anti-down, which is A. The π⁺ meson is therefore u and anti-d.
B, anti-up, carries −2/3, giving a total of 0. That combination is a neutral meson.
C, bottom, carries −1/3, giving +1/3, which is not a whole number and so cannot be a real particle. Free particles always carry a whole number of elementary charges.
D, charm, carries +2/3, giving +4/3, which is likewise impossible.
That two of the options give fractional totals is a useful shortcut: they can be eliminated without knowing anything about pions. The only way to build +1 from a quark and an antiquark is 2/3 plus 1/3, so the pair must be an up-type quark with an anti-down-type.
Question 2
A top quark has a charge of + ² e , where e is the elementary charge. 3
What is the charge of an anti top quark?
Answer: A.
The top quark has charge +⅔e, so the anti top quark has charge –⅔e. Nothing else needs calculating.
D, +⅔e, is the charge of the top quark itself, unchanged, which is the answer if "anti" is read as meaning only a different mass or a different name.
B and C, ±⅓e, are the charges belonging to the other family of quarks: down, strange and bottom carry –⅓e, and their antiquarks carry +⅓e. Switching to the wrong quark family is the other way this mark goes.
The same rule runs through the rest of the topic. The positron has the same mass as the electron and a charge of +e. The antiproton is negative. A neutral particle such as the neutron still has an antiparticle, because the quarks inside it are all replaced by antiquarks even though the total charge stays zero.
Baryon number and lepton number flip sign too, which is what makes them useful for checking whether a proposed nuclear reaction can happen.
Question 3
Some particles are a combination of three quarks.
Which combination of quarks does not result in a particle with a charge of either +1.6 × 10⁻¹⁹ C or zero?
Answer: D.
A, up, down, down: +2/3 − 1/3 − 1/3 = 0 ✓ allowed
B, up, strange, strange: +2/3 − 1/3 − 1/3 = 0 ✓ allowed
C, up, up, down: +2/3 + 2/3 − 1/3 = +1 ✓ allowed
D, up, up, up: +2/3 + 2/3 + 2/3 = +2 ✗
So D.
Notice that A and B give the same charge, because strange behaves exactly like down for charge purposes. A is the ordinary neutron, and B is a heavier neutral baryon with two strange quarks in place of the downs. The strange quark is much more massive, so the particle is far heavier and very short-lived, but its charge is identical.
The value 1.6 × 10⁻¹⁹ C in the question is the elementary charge, so the question is asking which combination gives neither +e nor 0. Three up quarks is the only way to reach +2e from this list, and it is the maximum a three-quark particle can carry.
What the syllabus asks for on this topicSyllabus points
Syllabus points
- Describe the evidence from the alpha-particle scattering experiment for a small, massive, positively charged nucleus.
- Describe the composition of the nucleus in terms of protons and neutrons, and use nuclide notation.
- Understand isotopes and represent nuclear reactions with balanced equations.
- Describe the nature, penetration and deflection of alpha, beta and gamma radiation.
- Understand that protons and neutrons are not fundamental, and describe the quark model.
- Recall that leptons are fundamental, and apply conservation laws to particle reactions.
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