Ch 1 · 11 Particle Physics · A Level Physics 9702
Topic 1 of 1 in Particle Physics — A Level Physics 9702 — 126 lessons.
Introduction
What is matter made of? The answer has gone from atoms, to nuclei and electrons, to protons and neutrons, to quarks. This topic follows that story, from Rutherford's gold foil to the quark changes inside β decay. (Syllabus topic 11: sections 11.1–11.2.)
Key ideas — 11.1 (a) Alpha-particle scattering and the nucleus
Alpha particles were fired at a thin gold foil in a vacuum.
🧑🏫 Teacher's explanation
Imagine you are throwing a handful of sand at a large, dark room. If most of the sand grains pass through without hitting anything, you would assume the room is mostly empty space. However, if a few grains suddenly bounce back sharply towards you, you would conclude that there is something very small, very dense, and very hard sitting in the middle of that room.
📖 Definitions
🔍 Worked example — Easy
An atom of Carbon-14 is represented by the notation ^14_6C. State the number of protons, neutrons, and electrons in a neutral atom of this nuclide.
🔍 Worked example — Standard
A nucleus undergoes β^- decay and transforms from ^238_92U to ^238_93Np. Determine the number of protons and neutrons in the parent and daughter nuclei.
🔍 Worked example — Exam-style
A particle is composed of one 'up' quark (charge +2/3e) and two 'down' quarks (charge -1/3e each). Calculate the total charge of this particle in units of elementary charge e.
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🎯 Exam question
(a) State the change in the nucleon number and the proton number of the nucleus. [2] (b) Explain why the kinetic energy of the emitted β^+ particle is not a single discrete value. [2] [4 marks]
Key ideas — 11.1 (b) The nuclear atom
A nucleus of protons (charge +e) and neutrons (no charge), together called nucleons, is surrounded by orbital electrons (charge -e).
🧑🏫 Teacher's explanation
Imagine a massive, heavy bowling ball sitting in the middle of a vast football stadium, with tiny gnats buzzing around the perimeter. If you fired high-speed marbles (alpha particles) at the stadium, most would fly straight through the empty space, but a few would bounce off at wild angles if they hit that tiny, dense bowling ball. This is how we know the nucleus is incredibly small and dense compared to the rest of the atom.
📖 Definitions
🔍 Worked example — Easy
A nucleus is represented by the notation ^14_6 extC. Determine the number of protons and neutrons in this nucleus.
🔍 Worked example — Standard
An isotope of an element has 26 protons and 30 neutrons. Write its nuclide notation ^A_Z extX.
🔍 Worked example — Exam-style
A nucleus undergoes β^- decay and transforms from ^14_6 extC to ^14_7 extN. Verify that the nucleon number is conserved.
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🎯 Exam question
Key ideas — 11.1 (c) Conservation laws in nuclear processes
In every nuclear process, nucleon number is conserved and charge is conserved (top and bottom numbers balance in a decay equation).
🧑🏫 Teacher's explanation
Think of a nuclear decay like a chemical reaction, but instead of atoms rearranging, the very building blocks of the nucleus are changing. In any such process, there are strict 'accounting rules' that must be followed. The first rule is that the total number of particles in the nucleus (protons and neutrons combined) must stay the same. The second rule is that the total electric charge must remain constant.
📖 Definitions
🔍 Worked example — Easy
A nucleus of Carbon-14 (^14_6C) undergoes β^- decay. Write the balanced decay equation for the resulting nucleus, ensuring nucleon number and charge are conserved.
🔍 Worked example — Standard
A proton undergoes β^+ decay. Write the complete decay equation including the resulting nucleon, the positron, and the neutrino.
🔍 Worked example — Exam-style
In a specific nuclear reaction, a parent nucleus X decays into a daughter nucleus Y, an α-particle, and a β^- particle. If the parent nucleus has A=238 and Z=92, determine the A and Z values for the daughter nucleus Y.
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🎯 Exam question
Key ideas — 11.1 (d) The three radiations
🧑🏫 Teacher's explanation
When an unstable nucleus wants to become stable, it releases energy in different forms. Think of it like a person trying to lose weight: they might drop heavy objects (alpha particles), shed small bits of debris (beta particles), or simply emit heat/light (gamma radiation). Each type of radiation has a very different 'personality' in terms of mass and charge.
📖 Definitions
🔍 Worked example — Easy
Identify the composition and charge of an α particle.
🔍 Worked example — Standard
A nucleus undergoes β^- decay. Complete the following decay equation: ^14_6C arrow ^14_7N + X. Identify X and its charge.
🔍 Worked example — Exam-style
Calculate the mass of 5.0 × 10^-24 α particles in unified atomic mass units (u), given that 1 u = 1.66 × 10^-27 kg and the mass of one α particle is 4.00 u.
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🎯 Exam question
Key ideas — 11.1 (e) Antiparticles and neutrinos
An antiparticle has the same mass as its particle but the opposite charge. The positron (e^+) is the antiparticle of the electron.
🧑🏫 Teacher's explanation
Think of particles and antiparticles like a coin and its mirror image. If a particle is a 'positive' entity, its antiparticle is its 'negative' twin. They look identical in terms of mass—they weigh exactly the same—but their electrical charges are perfect opposites. If you bring them together, they annihilate each other in a flash of energy.
📖 Definitions
🔍 Worked example — Easy
A particle has a mass of 9.11 × 10^-31 kg and a charge of -1.60 × 10^-19 C. State the mass and charge of its antiparticle.
🔍 Worked example — Standard
Complete the following β^- decay equation: _0^1n arrow _1^1p + e^- + ?
🔍 Worked example — Exam-style
In β^+ decay, a proton transforms into a neutron. Write the complete decay equation including the emitted positron and the neutrino, and state the conservation laws used.
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🎯 Exam question
Key ideas — 11.1 (f) Discrete α energies, continuous β energies
In α decay only two products share the energy released: the α-particle and the daughter nucleus. Momentum and energy conservation fix how it is shared, so all α-particles from a given decay have the same (discrete) energy.
🧑🏫 Teacher's explanation
Imagine you are throwing a heavy medicine ball (the α-particle) to a friend (the daughter nucleus). Because there are only two of you, the laws of conservation of momentum and energy dictate exactly how much energy the ball carries. If you know the total energy released, the ball must always take a specific, predictable portion of it. This results in a 'discrete' or fixed energy level.
📖 Definitions
🔍 Worked example — Easy
In a hypothetical α decay, the total energy released (the Q-value) is 5.0 MeV. If the α-particle carries 4.7 MeV, what is the energy of the daughter nucleus?
🔍 Worked example — Standard
A β^- particle is emitted with a kinetic energy of 2.2 MeV. If the maximum possible kinetic energy for this decay is 2.5 MeV, how much energy was carried away by the antineutrino?
🔍 Worked example — Exam-style
An isotope undergoes β^- decay. The total energy released is Q. If the β particle is measured to have an energy E_β, express the energy of the antineutrino E_barnu in terms of Q and E_β, assuming the recoil of the nucleus is negligible.
⚠️ Common errors
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🎯 Exam question
(a) State the type of particle emitted alongside the β particle. [1] (b) Calculate the kinetic energy of the emitted particle. [2] [3 marks]
Key ideas — 11.1 (g) Decay equations
^238_\ 92U arrow\ ^234_\ 90Th +\ ^4_2α
🧑🏫 Teacher's explanation
Think of a nuclear decay equation like a balanced accounting ledger. In a bank transaction, the total amount of money before and after must be the same, and the types of currency must match. In a nucleus, we have two strict rules: the total number of protons and neutrons (the nucleon number, A) must stay the same, and the total electric charge must stay the same.
📖 Definitions
🔍 Worked example — Easy
Complete the following β^- decay equation: ^13_6C arrow\ ^A_ZN + ^0_-1β^- + barnu
🔍 Worked example — Standard
A nucleus undergoes β^+ decay to become ^14_7N. Write the full decay equation including the neutrino.
🔍 Worked example — Exam-style
In a β^- decay process, a neutron transforms into a proton. Describe the change in quark composition and state the resulting particles.
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🎯 Exam question
Key ideas — 11.1 (h) The unified atomic mass unit
The unified atomic mass unit (u) is 1/12 of the mass of an atom of carbon-12:
🧑🏫 Teacher's explanation
In particle physics, the masses of subatomic particles are incredibly tiny. If we used kilograms (kg) for everything, we would be constantly writing numbers like 0.00000000000000000000000000166 kg. This is impractical for calculations and prone to error. To make life easier, physicists use a 'standard' unit, much like how we use 'dozen' for eggs or 'centimeters' for small objects, but instead of a count, we use a specific mass.
📖 Definitions
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🎯 Exam question
Key ideas — 11.2 (a) Quarks
A quark is a fundamental particle (it is not made of anything smaller). There are six flavours:
🧑🏫 Teacher's explanation
Imagine you are looking at a Lego castle. From a distance, it looks like a single solid object (a hadron). But as you get closer, you realize the castle is actually built from individual, smaller bricks (quarks). In particle physics, protons and neutrons are not the 'end of the line'; they are composite structures made of even smaller, fundamental building blocks called quarks.
📖 Definitions
🔍 Worked example — Easy
A proton is composed of two 'up' quarks and one 'down' quark. Calculate the total charge of the proton in units of elementary charge e.
🔍 Worked example — Standard
A neutron is composed of one 'up' quark and two 'down' quarks. Calculate the total charge of the neutron in units of elementary charge e.
🔍 Worked example — Exam-style
During β^- decay, a neutron (composition udd) transforms into a proton (composition uud). Describe the change in quark composition and determine the charge of the emitted particle (the electron) based on charge conservation.
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🎯 Exam question
(a) Determine the total charge of this particle in units of e. (b) State whether this particle is a baryon or a meson. [2 marks]
Key ideas — 11.2 (b) Protons, neutrons and hadrons
Protons and neutrons are not fundamental: they are made of quarks.
🧑🏫 Teacher's explanation
Think of fundamental particles like quarks as the 'LEGO bricks' of the universe. You cannot break a single LEGO brick into smaller pieces, but you can snap them together to build much larger, more complex structures. In particle physics, these 'bricks' are called fundamental particles because they have no internal structure.
📖 Definitions
🔍 Worked example — Easy
Calculate the total electric charge of a proton in units of elementary charge e, given its quark composition is uud and the charges of the quarks are u = +2/3 and d = -1/3.
🔍 Worked example — Standard
A meson is composed of an up quark (u) and an anti-down quark (bard). Determine the total charge of this meson.
🔍 Worked example — Exam-style
During β^- decay, a neutron (udd) transforms into a proton (uud). Describe the change in quark composition and identify the emitted particle (excluding the neutrino).
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🎯 Exam question
Key ideas — 11.2 (c) Quark changes in β decay
d arrow u + e^- + barnu
🧑🏫 Teacher's explanation
Think of quarks as the fundamental 'building blocks' of matter. While protons and neutrons seem solid, they are actually composite particles made of even smaller entities called quarks. In the world of subatomic physics, particles aren't always permanent; they can transform into other particles if the 'ingredients' change.
📖 Definitions
🔍 Worked example — Easy
A neutron has a quark composition of udd. In β^- decay, the neutron transforms into a proton. Identify the quark change and the resulting quark composition of the proton.
🔍 Worked example — Standard
A proton has a quark composition of uud. During β^+ decay, the proton transforms into a neutron. Write the quark change equation and the resulting quark composition.
🔍 Worked example — Exam-style
In a β^- decay process, a neutron (udd) decays into a proton (uud), an electron (e^-), and an antineutrino (barnu_e). Verify that the total electric charge is conserved using the charges of the quarks: u = +2/3 and d = -1/3.
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🎯 Exam question
Key ideas — 11.2 (d) Leptons
Electrons and neutrinos are fundamental particles called leptons. They are not made of quarks.
🧑🏫 Teacher's explanation
Think of the universe as being built from two different types of 'Lego' bricks. The first type are 'Hadrons' (like protons and neutrons), which are complex structures made by snapping smaller 'Quark' bricks together. The second type are 'Leptons'. Leptons are the 'indivisible' pieces; they cannot be broken down into anything smaller. They are the simplest, most fundamental building blocks of matter.
📖 Definitions
🔍 Worked example — Easy
Identify whether the following particles are leptons or hadrons based on their quark composition: (i) Proton (uud), (ii) Electron.
🔍 Worked example — Standard
A particle is composed of one quark and one antiquark. Classify this particle as a baryon or a meson, and state if it is a lepton or a hadron.
🔍 Worked example — Exam-style
In a β^- decay process, a neutron turns into a proton. The quark composition changes from udd to uud. Identify the emitted lepton and state its charge.
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🎯 Exam question
Worked example
Example 1. Find the charge of the meson ubars. Charge = +tfrac23 + tfrac13 = +1e (the anti-strange quark has charge +tfrac13 e).
🔍 Worked example — Easy
Calculate the total charge of a meson composed of an up quark (u) and an anti-strange quark (bars). Use the charges: u = +2/3e and s = -1/3e.
🔍 Worked example — Standard
A nucleus of Polonium-218 (^218_84Po) undergoes α decay followed by β^- decay. Determine the final nuclide notation (^A_ZX) of the resulting nucleus.
🔍 Worked example — Exam-style
A neutron decays via the process: n arrow p + e^- + barnu_e. Show that charge is conserved, given the charges: n = 0, p = +1e, e^- = -1e, and barnu_e = 0.
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Practice
Answers: (1) The atom is mostly empty space; the nucleus is very small, dense and positively charged. (2) Proton uud: tfrac23 + tfrac23 - tfrac13 = +1; neutron udd: tfrac23 - tfrac13 - tfrac13 = 0. (3) The energy is shared between the β-particle, the (anti)neutrino and the nucleus in varying proportions. (4) An up quark changes into a down quark, emitting a positron and a neutrino. (5) ^40_19K arrow\ ^40_20Ca +\ ^\ 0_-1β + barnu. (6) A baryon has three quarks; a meson has a quark and an antiquark.