Particle physics

Geiger–Marsden α-particle scattering

Alpha particles α粒子 fired at a thin gold foil were seen to:

• mostly pass straight through, with very little deflection 偏转,
• sometimes deflect through small angles,
• rarely (about $1$ in $8000$) deflect through angles greater than $90°$.

From this Rutherford worked out:

• the atom is mostly empty space (most α-particles pass straight through),
• there is a tiny, dense, positively charged nucleus 原子核 at the centre (the rare large deflections need a concentrated charge to push the α away),
• almost all of the atom's mass is in this nucleus.

Order of magnitude: atom diameter $\sim 10^{-10}\ \text{m}$, nucleus diameter $\sim 10^{-15}\ \text{m}$ — the nucleus is about $10^{5}$ times smaller than the atom.

The $\alpha$-scattering experiment — $\alpha$-particles strike a thin gold foil in a vacuum

Most $\alpha$-particles pass nearly straight through; a few are deflected sharply by the tiny nucleus

Simple nuclear model

An atom has:

• a central nucleus of protons 质子 (positive, charge $+e$) and neutrons 中子 (no charge),
• electrons 电子 (charge $-e$) around the nucleus.

The proton and neutron have almost the same mass ($\approx 1\ \text{u}$); the electron is about $\tfrac{1}{1836}$ of the proton's mass.

Simple models of a helium atom and a lithium atom (not to scale)

Notation and key numbers

For a nuclide 核素 written $^{A}_{Z}\text{X}$:

Nuclide notation: nucleon number on top, proton number below

• proton number 质子数 $Z$ (also the atomic number): the number of protons. It fixes the element.
• nucleon number 核子数 $A$ (also the mass number): the total number of nucleons 核子 (protons + neutrons).
• number of neutrons $N = A - Z$.

A neutral atom has the same number of electrons as protons.

Isotopes

Isotopes 同位素 are atoms of the same element (same $Z$) with different numbers of neutrons (different $A$). They behave the same chemically but differently in the nucleus. Example: $^{12}_{6}\text{C}$ and $^{14}_{6}\text{C}$ are isotopes of carbon.

Conservation laws in nuclear processes

In any nuclear process:

• nucleon number $A$ is conserved (total $A$ before $=$ total $A$ after),
• charge is conserved (this is conservation of charge 电荷守恒).

These two rules let you balance decay and reaction equations.

Unified atomic mass unit

The unified atomic mass unit 统一原子质量单位, symbol $\text{u}$, is set so that an atom of $^{12}_{6}\text{C}$ has mass exactly $12\ \text{u}$. Numerically,

A proton has mass $\approx 1.007\ \text{u}$; a neutron $\approx 1.009\ \text{u}$; an electron $\approx 5.5 \times 10^{-4}\ \text{u}$.

An unstable nucleus rearranges itself and gives out one of three kinds of radiation 辐射. This is radioactive 放射性 decay. Each kind has its own properties.

α-radiation

• Made of: a helium-4 nucleus, $^{4}_{2}\alpha$ (two protons + two neutrons).
• Mass: $\approx 4\ \text{u}$.
• Charge: $+2e$.
• Range in air: a few cm. Stopped by a sheet of paper.
• Ionising power: strong — it is good at ionising 电离.
• Energy spectrum: discrete 分立 (one decay gives α-particles at one or a few sharp energies).

A cloud chamber 云室 makes the tracks visible: each α-particle leaves a short, straight, thick trail of tiny droplets as it ionises the air. The short equal lengths show the α-particles all carry about the same energy.

Alpha-particle tracks in a cloud chamber, fanning out from an americium-241 source

β-radiation

Two types of beta particle β粒子:

• $\beta^{-}$: a fast electron, given out when a neutron turns into a proton.
• $\beta^{+}$: a positron 正电子 (the electron's antiparticle), given out when a proton in a proton-rich nucleus turns into a neutron.

Properties (both types):

• Mass: $\approx 1/1836\ \text{u}$ (much less than α).
• Charge: $-e$ for $\beta^{-}$, $+e$ for $\beta^{+}$.
• Range in air: about $1\ \text{m}$. Stopped by a few mm of aluminium.
• Energy spectrum: continuous 连续 up to a maximum (see below).

γ-radiation

• Made of: a high-energy photon 光子 — part of the electromagnetic spectrum 电磁波谱.
• Mass: zero (rest mass).
• Charge: zero.
• Range in air: large (follows the inverse-square law). Strongly attenuated 衰减 by several cm of lead or about a metre of concrete.
• Ionising power: weakest.
• Energy spectrum: discrete (a gamma ray γ射线 is given out as the nucleus drops between two nuclear energy levels).

A nucleus often gives out a γ-photon as a "tidy-up" step after an α or β decay leaves the daughter nucleus 子核 in an excited state 激发态.

Penetrating power: $\alpha$ is stopped by paper, $\beta$ by aluminium, $\gamma$ only attenuated by lead

Antiparticles, neutrinos and antineutrinos

Every particle has an antiparticle 反粒子 with the same mass but opposite charge. The positron is the antiparticle of the electron.

In β-decay, a third particle is always given out as well:

• $\beta^{-}$ decay: an antineutrino 反中微子 $\bar{\nu}_{\text{e}}$.
• $\beta^{+}$ decay: a neutrino 中微子 $\nu_{\text{e}}$.

Neutrinos and antineutrinos have zero charge, very small mass, and barely interact — they are very hard to detect, but they must be there to balance energy, momentum 动量 and other conserved quantities in β-decay.

Why β has a continuous spectrum (and α does not)

In α-decay the energy 能量 released is shared between just two particles (the daughter nucleus and the α). Conservation of momentum and energy then fixes the α's energy to one value (discrete).

In β-decay the energy is shared between three particles (the daughter nucleus, the β, and the (anti)neutrino). The β can take any share from zero up to a maximum, so its energy spectrum is continuous.

Writing decay equations

A general α-decay:

(check: $A = (A-4) + 4$, $Z = (Z-2) + 2$.)

A general $\beta^{-}$ decay:

A general $\beta^{+}$ decay:

Worked example. Uranium-238, $^{238}_{92}\text{U}$, decays by α-emission; carbon-14, $^{14}_{6}\text{C}$, decays by $\beta^{-}$-emission. Find each daughter nuclide.

α-decay lowers $A$ by 4 and $Z$ by 2; $\beta^{-}$-decay leaves $A$ unchanged and raises $Z$ by 1:

A bubble chamber reveals the curved tracks of charged particles.

Some particles are fundamental 基本粒子 (point-like, with no smaller parts as far as we know); others are built from fundamental ones.

Quarks

A quark 夸克 is a fundamental particle. There are six flavours 味:

• up (u), charge $+\tfrac{2}{3}e$,
• down (d), charge $-\tfrac{1}{3}e$,
• charm (c), charge $+\tfrac{2}{3}e$,
• strange (s), charge $-\tfrac{1}{3}e$,
• top (t), charge $+\tfrac{2}{3}e$,
• bottom (b), charge $-\tfrac{1}{3}e$.

Each quark has an antiquark 反夸克 with the same size of charge but the opposite sign: $\bar{u}$ (charge $-\tfrac{2}{3}e$), $\bar{d}$ (charge $+\tfrac{1}{3}e$). No other quark property is tested.

The six quarks: up/charm/top carry $+\tfrac23 e$, down/strange/bottom carry $-\tfrac13 e$

Hadrons: baryons and mesons

Particles built from quarks are hadrons 强子. Two types:

• baryons 重子 — three quarks. Examples: proton (u u d), neutron (u d d). Charge check: $\tfrac{2}{3} + \tfrac{2}{3} - \tfrac{1}{3} = +1$ for the proton; $\tfrac{2}{3} - \tfrac{1}{3} - \tfrac{1}{3} = 0$ for the neutron.
• mesons 介子 — one quark and one antiquark (for example $\pi^{+}$ is u$\bar{\text{d}}$).

Protons and neutrons are not fundamental — they are baryons made of quarks.

Quark changes in β-decay

In $\beta^{-}$ decay a neutron turns into a proton; in quark terms, one down quark turns into an up quark:

In $\beta^{+}$ decay a proton turns into a neutron; one up quark turns into a down quark:

Beta-minus decay: one down quark becomes an up quark, turning a neutron into a proton

Leptons

Leptons 轻子 are fundamental particles that are not made of quarks. Electrons and neutrinos are leptons. (Heavier leptons — the muon and tau — are not needed for this syllabus.)

Classifying particles

To answer "which are fundamental?": quarks and leptons (electrons, positrons, neutrinos, antineutrinos) are fundamental; protons, neutrons, baryons, mesons and hadrons are not — they are built from quarks.

Fundamental particles (quarks, leptons) versus hadrons (baryons, mesons)

• Describe the nuclear atom (a small, dense, positive nucleus) using the alpha-scattering evidence.
• Compare $\alpha$, $\beta$ and $\gamma$ by charge, mass, ionising power and penetration.
• Use quark composition (proton $uud$, neutron $udd$) and check that charge and nucleon number balance in an equation.
• In $\beta^-$ decay a neutron becomes a proton, an electron and an antineutrino.