Particles

Welcome to the Quantum World: An Introduction to Particles

Welcome! In this chapter, we are going to dive deep into the very building blocks of the universe. Have you ever wondered what you get if you keep cutting a piece of matter into smaller and smaller pieces? We’re moving beyond the simple "protons, neutrons, and electrons" model you learned at GCSE and discovering a busy world of antimatter, quarks, and fundamental forces.

Why is this important? Understanding particles helps us explain everything from how the Sun shines to how medical PET scanners work. Don't worry if it feels a bit "sci-fi" at first—we'll break it down step-by-step!

1. The Constituents of the Atom

Before we find new particles, let’s make sure we are 100% happy with the ones we already know. Every atom is made of a nucleus (containing protons and neutrons) and electrons orbiting around it.

Key Properties

You need to know the charge and mass of these particles in two ways: SI units (Coulombs and Kilograms) and relative units (comparing them to each other).

• Proton: Relative charge +1 | Relative mass 1
• Neutron: Relative charge 0 | Relative mass 1
• Electron: Relative charge -1 | Relative mass 0.0005 (essentially negligible)

Specific Charge

This is a favorite exam topic! Specific charge is simply the ratio of a particle's charge to its mass. It tells you how much "electrical punch" a particle has for its weight.

\( \text{Specific Charge} = \frac{\text{Charge}}{\text{Mass}} \)

The units are \(C \ kg^{-1}\).
Example: To find the specific charge of a nucleus, you take the total charge (number of protons \(\times\) \(1.60 \times 10^{-19} \ C\)) and divide it by the total mass (number of nucleons \(\times\) \(1.67 \times 10^{-27} \ kg\)).

Atomic Notation

We use the standard notation \(_{Z}^{A}X\):

• A (Nucleon Number): Total number of Protons + Neutrons.
• Z (Proton Number): Number of Protons (this defines the element).
• Isotopes: Atoms of the same element with the same number of protons but a different number of neutrons. They behave the same chemically but have different stabilities.

Quick Review: Specific charge is just Charge \(\div\) Mass. Electrons have a huge specific charge because they are so tiny!

2. Stable and Unstable Nuclei

Protons are all positive, so they should repel each other and fly out of the nucleus. Why don't they? Meet the Strong Nuclear Force (SNF).

The Strong Nuclear Force

Think of the SNF as the "nuclear glue." It is incredibly strong, but it has a very short range.

• Repulsive: Below \(0.5 \ fm\) (\(1 \ fm = 10^{-15} \ m\)). This stops the nucleons from collapsing into a single point.
• Attractive: Between \(0.5 \ fm\) and \(3.0 \ fm\). This holds the nucleus together.
• Zero Force: Beyond \(3.0 \ fm\). It has no effect at all outside the nucleus.

Decay: When the nucleus isn't happy

If a nucleus is too big or has the wrong balance of particles, it will decay to become more stable.

• Alpha (\(\alpha\)) decay: Occurs in very heavy nuclei. The nucleus spits out a "chunk" consisting of 2 protons and 2 neutrons.
• Beta-minus (\(\beta^{-}\)) decay: Occurs in "neutron-rich" nuclei. A neutron turns into a proton, emitting an electron and an electron antineutrino.

Did you know? Scientists originally thought only an electron was emitted in beta decay. However, they noticed energy was "missing." They hypothesized the neutrino to account for this missing energy!

Key Takeaway: The SNF keeps nuclei stable but only works over tiny distances (up to \(3 \ fm\)).

3. Particles, Antiparticles, and Photons

For every type of "normal" particle, there is a corresponding antiparticle. It's like a mirror image: it has the same mass but opposite charge.

The "Anti" List

• Positron: The antiparticle of the electron (\(e^{+}\)).
• Antiproton: The antiparticle of the proton (\(\bar{p}\)).
• Antineutron: The antiparticle of the neutron (\(\bar{n}\)).
• Antineutrino: The antiparticle of the neutrino (\(\bar{\nu}\)).

Energy and Photons

In particle physics, we often measure energy in MeV (Mega-electronvolts). We also treat electromagnetic radiation as packets of energy called photons.

The energy of a photon is: \(E = hf = \frac{hc}{\lambda}\)

Where \(h\) is the Planck constant, \(f\) is frequency, and \(\lambda\) is wavelength.

Annihilation and Pair Production

When matter meets antimatter, things get exciting!

• Annihilation: A particle and its antiparticle meet and vanish, turning all their mass into two photons of energy. Real-world use: PET scanners in hospitals!
• Pair Production: A single high-energy photon vanishes and creates a particle-antiparticle pair (usually an electron and a positron).

Don't forget: In pair production, the photon must have a minimum energy equal to the rest energy of the two particles it is creating.

4. Particle Interactions

How do particles "talk" to each other? They use exchange particles (also called gauge bosons). Imagine two people on ice skates throwing a heavy ball back and forth; the act of throwing and catching pushes them apart. The ball is the exchange particle.

The Four Fundamental Interactions

1. Gravity: Affects everything with mass. (Exchange particle: Graviton - not tested).
2. Electromagnetic: Affects charged particles. Exchange particle: Virtual Photon (\(\gamma\)).
3. Strong: Holds quarks together. Exchange particle: Gluon (between quarks) or Pion (between nucleons).
4. Weak: Responsible for decay (like beta decay). Exchange particles: \(W^{+}\) and \(W^{-}\) bosons.

Feynman Diagrams

These are simple sketches to show particle interactions.
- Incoming particles are at the bottom.
- Outgoing particles are at the top.
- The exchange particle is a wiggly line in the middle.

Example: In Electron Capture, a proton in a nucleus captures an inner-shell electron. A \(W^{+}\) boson is exchanged, turning the proton into a neutron and the electron into a neutrino.

Quick Review: If you see a change in "flavor" (like a neutron turning into a proton), it's almost always the Weak interaction involving a W boson.

5. Classification of Particles

We categorize particles based on which forces they feel. Use this hierarchy to keep them straight:

Hadrons (The "Strong" Ones)

Hadrons are particles made of quarks. They feel the Strong Nuclear Force.

• Baryons: Made of 3 quarks. The most famous are protons and neutrons. The proton is the only stable baryon—all others eventually decay into it.
• Mesons: Made of a quark and an antiquark. Examples: Pions (\(\pi\)) and Kaons (\(K\)).

Leptons (The "Weak" Ones)

Leptons are fundamental particles (not made of anything smaller). They do not feel the Strong Nuclear Force.

• Examples: Electrons, Muons (\(\mu\)), and Neutrinos (\(\nu\)).
• Muons are like heavy electrons that eventually decay into electrons.

Strange Particles

Kaons are "strange." They are produced by the Strong interaction (in pairs) but decay via the Weak interaction. They have a quantum property called Strangeness.

Mnemonic: Hadrons feel the Hard (Strong) force. Leptons feel the Less (Weak) force.

6. Quarks and Antiquarks

Quarks are the tiny building blocks of Hadrons. For A Level, you only need to know three: Up (u), Down (d), and Strange (s).

Quark Properties

• Up (u): Charge \(+\frac{2}{3}e\), Baryon number \(+\frac{1}{3}\), Strangeness \(0\).
• Down (d): Charge \(-\frac{1}{3}e\), Baryon number \(+\frac{1}{3}\), Strangeness \(0\).
• Strange (s): Charge \(-\frac{1}{3}e\), Baryon number \(+\frac{1}{3}\), Strangeness \(-1\).

Antiquarks have the exact opposite signs for everything!

Building Particles

• Proton: \(uud\) (Total charge: \(2/3 + 2/3 - 1/3 = +1\)).
• Neutron: \(udd\) (Total charge: \(2/3 - 1/3 - 1/3 = 0\)).
• Mesons: Always one quark and one antiquark (e.g., \(\pi^{+}\) is \(u\bar{d}\)).

Beta Decay Recap: In \(\beta^{-}\) decay, a neutron (\(udd\)) becomes a proton (\(uud\)). This means a down quark turned into an up quark.

7. Conservation Laws

In any particle interaction, certain properties must stay the same before and after. This is how you predict if a reaction is possible.

Always Conserved:

• Charge
• Baryon Number (B): (Baryons = +1, Antibaryons = -1, everything else = 0).
• Lepton Number (L): (Leptons = +1, Antileptons = -1, everything else = 0). Note: You must conserve Electron-lepton number (\(L_e\)) and Muon-lepton number (\(L_\mu\)) separately!
• Energy and Momentum

The "Strangeness" Exception:

• Strangeness (S) is conserved in Strong interactions.
• In Weak interactions, Strangeness can change by \(0, +1, \text{or} -1\).

Common Mistake: Don't forget that an anti-lepton (like a positron) has a lepton number of -1. Students often accidentally give them a +1 because they are particles!

Final Key Takeaway: If a question asks why a reaction cannot happen, check these conservation laws. Usually, one of them (like Lepton number) is being broken!