Welcome to the Subatomic World!
Welcome to the start of your journey into Particle Physics! Don't worry if this seems a bit "sci-fi" at first. In this chapter, we are going to zoom in past the cells, past the atoms, and look at the very building blocks of the universe. We’ll discover that the world is much more interesting (and a bit stranger) than it looks on the surface. By the end of these notes, you’ll understand what you are made of and the hidden forces that keep you from falling apart!
3.2.1.1 Constituents of the Atom
At GCSE, you learned about protons, neutrons, and electrons. At A-Level, we need to be much more precise about their properties.
The Basics
- Proton: Found in the nucleus. Mass = \(1.67 \times 10^{-27}\) kg, Charge = \(+1.60 \times 10^{-19}\) C.
- Neutron: Found in the nucleus. Mass = \(1.67 \times 10^{-27}\) kg, Charge = \(0\).
- Electron: Orbits the nucleus. Mass = \(9.11 \times 10^{-31}\) kg, Charge = \(-1.60 \times 10^{-19}\) C.
Specific Charge
This is a favorite exam question! Specific charge is simply the charge-to-mass ratio of a particle.
\(Specific Charge = \frac{Charge}{Mass}\)
Example: To find the specific charge of a magnesium ion, you take the total charge of the ion and divide it by the total mass of all its protons and neutrons.
Nuclide Notation
We represent atoms (nuclides) like this: \(_{Z}^{A}X\)
A (Nucleon Number): Total number of protons + neutrons.
Z (Proton Number/Atomic Number): Number of protons.
Isotopes: Atoms with the same number of protons but different numbers of neutrons. They behave the same chemically but have different masses.
Quick Review:
- Protons and neutrons are nucleons.
- Specific charge units are \(C kg^{-1}\).
- Electrons have the highest specific charge because their mass is so tiny!
3.2.1.2 Stable and Unstable Nuclei
Have you ever wondered why the nucleus stays together? Protons are all positive, so they should repel each other and fly apart!
The Strong Nuclear Force (SNF)
The Strong Nuclear Force is the "glue" that holds the nucleus together. It is very powerful but has a very short range.
- Repulsive: Below \(0.5\) fm (femtometres), it pushes nucleons apart so they don't collapse into each other.
- Attractive: Between \(0.5\) fm and \(3\) fm, it pulls nucleons together.
- Zero Range: Beyond \(3\) fm, it has no effect at all.
Analogy: Think of the SNF like a piece of Velcro. It's incredibly strong when the two sides are touching, but once you pull them a few centimeters apart, they don't feel each other at all.
Alpha and Beta Decay
When a nucleus is too big or has the wrong balance of protons and neutrons, it becomes unstable and decays.
- Alpha (\(\alpha\)) Decay: A big nucleus spits out an alpha particle (2 protons, 2 neutrons). The nucleon number \(A\) drops by 4, and the proton number \(Z\) drops by 2.
- Beta Minus (\(\beta^{-}\)) Decay: A neutron turns into a proton, emitting an electron and an antineutrino.
The Neutrino
Did you know? Scientists originally thought energy was being lost in beta decay. To save the law of conservation of energy, they hypothesized a tiny, invisible particle was carrying the "missing" energy away. We now call this the neutrino.
Key Takeaway:
The Strong Nuclear Force is only attractive between 0.5 and 3 fm. If a nucleus gets too large, the SNF can't reach across it, making it unstable!
3.2.1.3 Particles, Antiparticles and Photons
For every particle, there is an antiparticle. It's like a mirror image with the opposite charge but the same mass.
The "Anti" List
- Electron \(\leftrightarrow\) Positron
- Proton \(\leftrightarrow\) Antiproton
- Neutron \(\leftrightarrow\) Antineutron
- Neutrino \(\leftrightarrow\) Antineutrino
Photons
Light isn't just a wave; it travels in little packets of energy called photons.
The energy of a photon is: \(E = hf\) or \(E = \frac{hc}{\lambda}\)
(Where \(h\) is Planck’s constant and \(c\) is the speed of light).
Annihilation and Pair Production
Annihilation: When a particle meets its antiparticle, they vanish and turn into two photons of energy.
Pair Production: The opposite! A single high-energy photon vanishes and creates a particle-antiparticle pair.
Common Mistake:
In annihilation, you must produce two photons to conserve momentum. Don't forget that!
3.2.1.4 Particle Interactions
Forces aren't just "magic" acting at a distance. They are caused by the exchange of exchange particles (also called gauge bosons).
Analogy: Imagine two people on ice skates throwing a heavy ball back and forth. Every time they catch or throw the ball, they move apart. The ball is the "exchange particle" creating a force between them.
The Four Fundamental Interactions
- Gravity: Affects everything with mass (very weak).
- Electromagnetic: Affects charged particles. Exchange particle = Virtual Photon.
- Strong Nuclear: Holds the nucleus together. Exchange particle = Pion (between nucleons).
- Weak Nuclear: Responsible for decay (like beta decay). Exchange particle = W bosons (\(W^{+}\) and \(W^{-}\)).
Quick Review:
- Electron Capture: A proton in the nucleus "captures" an inner-shell electron, turning into a neutron and a neutrino. This is a weak interaction.
3.2.1.5 Classification of Particles
We can group particles into two main families:
1. Hadrons
These feel the Strong Nuclear Force. They are made of quarks.
- Baryons: Made of 3 quarks (e.g., Protons, Neutrons). The Proton is the only stable baryon.
- Mesons: Made of 1 quark and 1 antiquark (e.g., Pions, Kaons).
2. Leptons
These are fundamental (not made of anything smaller) and do not feel the Strong Nuclear Force.
Examples: Electrons, Muons, Neutrinos.
Note: Muons are like "heavy electrons" that eventually decay into electrons.
Strange Particles
Kaons are "strange" because they are produced via the Strong interaction but decay via the Weak interaction. They have a property called Strangeness.
Memory Aid:
Baryons = Big (3 quarks).
Mesons = Middle-weight (2 quarks).
Leptons = Lightweight (fundamental).
3.2.1.6 Quarks and Antiquarks
Quarks are the tiny bits that make up Hadrons. For your exam, you only need to know three:
- Up (u): Charge = \(+\frac{2}{3}\)
- Down (d): Charge = \(-\frac{1}{3}\)
- Strange (s): Charge = \(-\frac{1}{3}\), Strangeness = \(-1\)
How to Build a Particle
- Proton: \(uud\) (Total charge: \(2/3 + 2/3 - 1/3 = +1\))
- Neutron: \(udd\) (Total charge: \(2/3 - 1/3 - 1/3 = 0\))
Antiquarks have the exact opposite properties (e.g., an anti-up quark has a charge of \(-\frac{2}{3}\)).
3.2.1.7 Applications of Conservation Laws
In every particle interaction, certain things must be conserved (the total before must equal the total after):
- Charge
- Baryon Number (B): Protons/Neutrons have \(B=1\), quarks have \(B=1/3\).
- Lepton Number (L): Electrons/Neutrinos have \(L=1\). There are separate totals for electron-leptons and muon-leptons!
- Energy and Momentum
- Strangeness (S): This is conserved in Strong interactions but can change by \(+1, 0, or -1\) in Weak interactions.
Beta Decay at the Quark Level
In \(\beta^{-}\) decay, a neutron (\(udd\)) turns into a proton (\(uud\)). This means a down quark changed into an up quark. This is only possible through the Weak Interaction!
Final Check - Can it happen?
If you are asked if an interaction is possible, check Charge, Baryon Number, and Lepton Number. If any of those aren't equal on both sides, the answer is "No!"
Good luck with your revision!
Don't worry if you don't memorize the quark compositions immediately—keep practicing building them based on their charges, and it will become second nature!