Particle physics - Physics (9702) - Cambridge A-Level

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✨ AS Level Physics (9702) Study Notes: Particle Physics (Topic 11) ✨

Welcome to one of the most exciting areas of Physics—the world inside the atom! Particle Physics helps us answer the fundamental question: What is everything made of? This chapter links many concepts you've learned about charge, forces, and energy, giving you a deep understanding of matter itself. Don't worry if the names are new; we will break down the tiny components into easy, manageable concepts!

11.1 Atoms, Nuclei and Radiation

The Structure of the Atom

1. The Existence and Size of the Nucleus (Rutherford Scattering)

The structure of the atom we use today wasn't discovered overnight. It came primarily from the famous Alpha-particle Scattering Experiment (also known as the Geiger-Marsden experiment).

The Setup: Alpha particles (positively charged, heavy) were fired at a thin sheet of gold foil.
The Expected Result (based on the old "plum pudding" model): Since the positive charge was thought to be spread out, all alpha particles should pass straight through with only minor deflections.
The Actual Results:
1. Most $\alpha$-particles passed straight through (implying the atom is mostly empty space).
2. A small number were deflected through large angles (> 90°).
3. A tiny fraction (about 1 in 8000) were reflected straight back.
The Inference: The large deflections meant the alpha particles must have encountered a tiny, dense, positively charged region. This region is the nucleus.

Key Takeaway: The nucleus is extremely small compared to the atom, and it contains virtually all the mass and all the positive charge.

2. Simple Model for the Nuclear Atom

The nuclear atom consists of three key components:

Protons: Found in the nucleus. They carry a positive charge ($+e$).
Neutrons: Found in the nucleus. They carry zero charge (neutral).
Orbital Electrons: Orbit the nucleus. They carry a negative charge ($-e$). In a neutral atom, the number of electrons equals the number of protons.

Did you know? Protons and neutrons are collectively called nucleons because they reside in the nucleus.

3. Nucleon Number, Proton Number, and Nuclide Notation

We use specific numbers to define an atomic nucleus:

Proton Number (Z): The number of protons in the nucleus. This defines the element. (Also called Atomic Number).
Neutron Number (N): The number of neutrons in the nucleus.
Nucleon Number (A): The total number of particles in the nucleus (protons + neutrons).
Formula: $A = Z + N$ (Also called Mass Number).

The standard notation for representing a nuclide (a specific nucleus) is: $$\frac{A}{Z} X$$ where X is the chemical symbol, A is the Nucleon Number (top), and Z is the Proton Number (bottom).

Example: ${}^{12}_{6} C$ means Carbon with 6 protons and $12-6=6$ neutrons.

4. Isotopes

Isotopes are forms of the same element (meaning they have the same Proton Number, Z) but have different numbers of neutrons (and thus different Nucleon Numbers, A).

Analogy: Think of isotopes as siblings. They belong to the same family (element, defined by Z) but have different total weights (A, because of different numbers of neutrons).
Example: Carbon-12 (${}^{12}_{6} C$) and Carbon-14 (${}^{14}_{6} C$). Both have 6 protons, but C-14 has 8 neutrons while C-12 has 6.

5. Conservation in Nuclear Processes

When a nuclear reaction (like radioactive decay or collision) occurs, two crucial properties must be conserved:

Conservation of Nucleon Number (A): The total number of nucleons (A) before the reaction equals the total number of nucleons after.
Conservation of Charge (Proton Number, Z): The total charge (Z) before the reaction equals the total charge after.

Quick Review Box 1.1: Always check that the top numbers (A) balance and the bottom numbers (Z) balance across the arrow in a nuclear equation.

Types of Radiation ($\alpha, \beta, \gamma$)

Radioactive decay involves unstable nuclei emitting radiation to become more stable.

Composition and Properties

Alpha ($\alpha$) Radiation:
- Composition: Two protons and two neutrons (a Helium nucleus: ${}^4_2 He$).
- Charge: $\mathbf{+2e}$.
- Mass: 4 u (relatively heavy).
- Speed: Slowest (up to 10% of $c$).
Beta-Minus ($\beta^-$) Radiation:
- Composition: High-energy electron (emitted from the nucleus).
- Charge: $\mathbf{-e}$ ($-1$ on the Z line in equations: ${}^0_{-1} e$).
- Mass: Very small (negligible in nuclear equations).
- Speed: Fast (up to 99% of $c$).
Beta-Plus ($\beta^+$) Radiation:
- Composition: Positron (the antiparticle of the electron).
- Charge: $\mathbf{+e}$ ($+1$ on the Z line: ${}^0_{+1} e$).
- Mass: Very small (same as electron).
- Speed: Fast.
Gamma ($\gamma$) Radiation:
- Composition: Electromagnetic radiation (high-energy photon).
- Charge: 0.
- Mass: 0.
- Speed: Speed of light ($c$).

Important Note on $\beta^\pm$ decay: The $\beta$ particles do not pre-exist in the nucleus; they are created during the decay process when a proton converts to a neutron (or vice-versa).

Antiparticles and Neutrinos

Every particle has an antiparticle. An antiparticle has the same mass but opposite charge to its corresponding particle.

The antiparticle of an electron ($\beta^-$) is the positron ($\beta^+$).
Neutrinos ($\nu$) and Antineutrinos ($\bar{\nu}$) are tiny, neutral particles required for conservation of energy and momentum during beta decay.
- Beta-Minus ($\beta^-$) Decay: Produces an antineutrino ($\bar{\nu}$). (Neutron turns into Proton + Electron + Antineutrino)
- Beta-Plus ($\beta^+$) Decay: Produces a neutrino ($\nu$). (Proton turns into Neutron + Positron + Neutrino)

Energy Spectra of $\alpha$ and $\beta$ Particles

When a single type of nucleus decays, the energy released is always the same. This energy is distributed among the products.

Alpha ($\alpha$) Particles: Have discrete energies. Since only two products are typically emitted (the new nucleus and the $\alpha$ particle), the energy is shared uniquely between them, resulting in specific, fixed kinetic energies for the $\alpha$ particles.
Beta ($\beta^\pm$) Particles: Have a continuous range of energies. This is because there are three particles emitted (the new nucleus, the $\beta$ particle, and the (anti)neutrino). The kinetic energy of the decay is shared among these three particles, meaning the $\beta$ particle itself can have any energy up to a maximum value.

Nuclear Decay Equations

You must be able to represent $\alpha$ and $\beta$ decay using the notation ${}^A_Z X$.

1. Alpha ($\alpha$) Decay: The Nucleon Number (A) decreases by 4, and the Proton Number (Z) decreases by 2. $$ {}_{Z}^{A} X \rightarrow {}_{Z-2}^{A-4} Y + {}_{2}^{4} \alpha $$ Example: Uranium-238 decaying to Thorium-234. $$ {}_{92}^{238} U \rightarrow {}_{90}^{234} Th + {}_{2}^{4} \alpha $$

2. Beta-Minus ($\beta^-$) Decay: A neutron turns into a proton. Nucleon Number (A) stays the same; Proton Number (Z) increases by 1. $$ {}_{Z}^{A} X \rightarrow {}_{Z+1}^{A} Y + {}_{-1}^{0} e + \bar{\nu} $$

3. Beta-Plus ($\beta^+$) Decay: A proton turns into a neutron. Nucleon Number (A) stays the same; Proton Number (Z) decreases by 1. $$ {}_{Z}^{A} X \rightarrow {}_{Z-1}^{A} Y + {}_{+1}^{0} e + \nu $$

Unified Atomic Mass Unit (u)

The masses of nuclei are extremely small, so we use a special unit: the unified atomic mass unit (u).

Definition: 1 u is defined as exactly 1/12th the mass of a single neutral carbon-12 atom.
Purpose: It provides a convenient, standard unit for measuring atomic and nuclear masses.

Key Takeaway: Radioactive processes must conserve the total number of nucleons (A) and the total charge (Z). Beta decay always involves the emission of a neutrino or antineutrino, which explains the continuous energy spectrum.

11.2 Fundamental Particles

Don't worry if this section sounds like science fiction! It’s the standard model of particle physics simplified. We are going beyond protons and neutrons to look at the truly fundamental building blocks of matter.

1. Quarks: The Building Blocks of Hadrons

A quark is a fundamental particle—meaning it is not made up of any smaller components.

There are six "flavours" (or types) of quarks, but in AS Physics, we mainly focus on the constituents of everyday matter: the up and down quarks. The six flavours are:
up, down, strange, charm, top, bottom

Charge of Quarks: Quarks have fractional charges (fractions of the elementary charge, $e$).

Quark Flavour	Symbol	Charge (in units of $e$)
Up	u	+$\frac{2}{3}$
Down	d	-$\frac{1}{3}$

Antiquarks: For every quark, there is an antiquark (denoted by a bar, e.g., $\bar{u}$ for anti-up). Antiquarks have the opposite charge:

Anti-up ($\bar{u}$) has charge $-\frac{2}{3}e$.
Anti-down ($\bar{d}$) has charge $+\frac{1}{3}e$.

2. Hadrons (Particles made of Quarks)

Protons and neutrons are not fundamental; they are composite particles belonging to a group called hadrons (particles that interact via the strong nuclear force).

Hadrons are split into two categories based on their quark composition:

i) Baryons (Three Quarks)

Baryons consist of three quarks (qqq). The most important examples are the constituents of the nucleus:

Proton ($p$): Composed of two up quarks and one down quark (uud).
Check the charge: $+\frac{2}{3}e + +\frac{2}{3}e + (-\frac{1}{3})e = +\frac{3}{3}e = +e$. (Correct!)
Neutron ($n$): Composed of one up quark and two down quarks (udd).
Check the charge: $+\frac{2}{3}e + (-\frac{1}{3})e + (-\frac{1}{3})e = 0$. (Correct!)

Memory Aid: Protons are positive, so they need more 'ups' than 'downs'. Neutrons are neutral, so the 'ups' and 'downs' cancel out their fractional charges.

ii) Mesons (Quark-Antiquark Pair)

Mesons consist of one quark and one antiquark ($q\bar{q}$). These particles are highly unstable and are often involved in carrying forces (like the strong force).

3. Leptons (Truly Fundamental)

Leptons are fundamental particles that do not feel the strong nuclear force. They include the everyday particle, the electron, and the elusive neutrinos.

The key leptons you must recall are:

Electrons ($e^-$)
Neutrinos ($\nu$)

Note: Electrons and neutrinos are fundamental; they are not made of quarks.

4. Quark Changes in Beta Decay

We now know that beta decay involves changes inside the nucleon composition:

i) Beta-Minus ($\beta^-$) Decay:
A neutron decays into a proton, an electron ($\beta^-$), and an electron antineutrino ($\bar{\nu}$).

Quark Change: A down quark ($d$) inside the neutron changes into an up quark ($u$).
Nucleon Change: $(udd) \rightarrow (uud)$. Neutron changes to Proton.

This increases the charge of the nucleon by $\frac{1}{3}e - (-\frac{2}{3}e) = +e$. This charge is conserved by emitting the negatively charged electron.

ii) Beta-Plus ($\beta^+$) Decay:
A proton decays into a neutron, a positron ($\beta^+$), and an electron neutrino ($\nu$).

Quark Change: An up quark ($u$) inside the proton changes into a down quark ($d$).
Nucleon Change: $(uud) \rightarrow (udd)$. Proton changes to Neutron.

Common Mistake to Avoid: Confusing Hadrons (made of quarks) and Leptons (fundamental, like the electron). The electron is not a hadron and is not composed of quarks.

Final Summary of Key Particle Types:

Fundamental Particles: Quarks (u, d, s, c, t, b) and Leptons (e, $\nu$, etc.)
Composite Particles (Hadrons):

Baryons: 3 quarks (Proton, Neutron).
Mesons: Quark + Antiquark.