FSc Part 1 Physics Chapter 12 Complete Guide Book — Nuclear and Particle Physics

Everything you can touch is built from atoms, and almost all of an atom's mass sits in a tiny ball at its centre — the nucleus. The book opens this chapter with a simple picture that is worth fixing in your mind: the nucleus holds only two kinds of particles. A proton carries a positive charge equal in size to the electron's charge (1.6 × 10⁻¹⁹ C) and has a mass of 1.67 × 10⁻²⁷ kg. The hydrogen nucleus, a single proton on its own, even gets its own name: protium. The neutron, whose existence James Chadwick pointed out in 1932, carries no charge at all — its name is the clue — and its mass is nearly the same as the proton's. Together, protons and neutrons are called nucleons.

Two numbers describe any nucleus, and examiners love both. The atomic number Z counts the protons. The mass number A counts all the nucleons, protons plus neutrons, so A = N + Z where N is the neutron number. A nucleus is written as ^A_ZX — X is the chemical symbol, A sits on top, Z below. Carbon always has 6 protons, but its nuclei do not always carry the same number of neutrons: ¹²₆C, ¹³₆C and ¹⁴₆C are all carbon, and nuclei like these — same protons, different neutrons — are called isotopes. The first two are stable; carbon-14 is unstable and decays into nitrogen, giving out a β-particle and a neutrino as it goes.

Because a single proton's mass in kilograms is an awkwardly small number, physicists weigh nuclei in a friendlier unit, the unified mass unit (u). By definition, 1 u is exactly one-twelfth of the mass of a carbon-12 atom: 1 u = 1.6608 × 10⁻²⁷ kg, which works out to 931 MeV of energy through E = mc². On this scale a proton is 1.007276 u, a neutron 1.008665 u and an electron only 0.00055 u. Keep that 931 MeV figure handy — you will need it for the Q-value numerical at the end of the chapter.

Before the book explains what glues the nucleus together, it steps back and asks a bigger question: how many different forces are there, really? The answer is only four, and every push, pull and explosion in the universe is one of them at work. They are gravity, the electromagnetic force, the weak nuclear force and the strong nuclear force — and the table the book prints (Table 12.1) is worth learning by heart, because it gives you each force's strength compared with the strong force, and how far it reaches.

Gravity is the weakest of the four — about 10⁻³⁸ times the strong force — but it never runs out of range, and it only ever attracts. That is why it rules planets and stars, whose masses are enormous, yet inside an atom it is so feeble you can ignore it. The electromagnetic force is much stronger (about 10⁻²), also reaches to infinity, and follows an inverse-square law like gravity. It runs everything from chemical bonds to light itself. In 1861 James Clerk Maxwell wrote four equations that showed electricity and magnetism were not two separate things at all, just two faces of this one force.

Then come the two nuclear forces, and this is where the nucleus stops being a mystery. Protons all carry positive charge, so they should blow each other apart — yet the nucleus holds together. It holds because the strong nuclear force between nucleons is stronger than their electrical repulsion, but only over a tiny distance, less than 10⁻¹⁵ m. It attracts every nucleon to every other: proton to proton, neutron to neutron, proton to neutron, all the same. The weak nuclear force (about 10⁻¹³, range under 10⁻¹⁸ m) is different in kind: it runs radioactive decay, especially beta decay, and it is the only force that can actually change one particle into another — a neutron into a proton, for instance. Without it, stars could not shine the way they do, because the fusion reactions inside them depend on such changes.

In 1928 Paul Dirac predicted something that sounded like science fiction: every fundamental particle should have an anti-particle — same rest mass as its partner, but opposite charge and magnetic moment. Four years later, in 1932, Anderson found the first one in a cloud-chamber experiment: the positron, written e⁺, the anti-particle of the electron. It weighs exactly what an electron weighs, but it carries a positive charge of the same size as the electron's negative one. Anti-particles are usually written with a bar over the letter — an anti-proton is p with a bar, an anti-neutrino is ν with a bar — and the book is careful to add that quarks and leptons, the particles we now call elementary, have anti-particles too.

Where do you actually meet anti-particles? The book gives three honest answers. Cosmic rays — high-energy particles raining down from outer space, mostly protons, neutrons and heavier nuclei — smash into the gases of our atmosphere and shower us with secondary particles all the time. Unstable nuclei in reactors throw out neutrons, neutrinos, α-particles, photons, electrons and positrons when they fission. And when accelerators hurl charged particles at targets, the debris of head-on collisions contains pions, kaons, muons and even anti-protons. That is what the big machines are for: a particle accelerator, the book says plainly, is a huge machine that pushes charged particles to speeds approaching light, and the Large Hadron Collider at CERN has shown that some of a colliding particle's mass turns into electromagnetic radiation while the leftover mass appears as brand-new sub-atomic particles.

📌 For your information (book's side box): a particle accelerator is a huge machine that accelerates charged particles, such as electrons, protons or ions, to extremely high energies and speeds approaching the speed of light. Linear accelerators, cyclotrons and betatrons are important types of particle accelerators.

📌 Interesting information (book's side box): for their work on this discovery, Dirac and Anderson received the Nobel Prize in Physics — Dirac in 1933 and Anderson in 1936. In 1955, Segrè and Chamberlain discovered the anti-proton using a particle accelerator and were awarded the Nobel Prize in Physics in 1959 for their discovery of the anti-proton.

📌 Do you know? (book's side box): (i) Cosmic rays are high-energy particles coming from outer space with unknown sources, like the Sun or other stars; they consist mostly of protons, neutrons and heavier nuclei, and when they interact with the atoms of the Earth's atmosphere they produce showers of secondary particles which rain down on us all the time. (ii) When nuclei of unstable radioactive elements, say ²³⁵U, undergo fission reactions in nuclear reactors, they emit a variety of particles such as neutrons, neutrinos, α-particles, photons, electrons and positrons. (iii) When charged particles such as electrons and protons are accelerated by an accelerator and then bombarded on the target material, which is hydrogen, these accelerated charged particles may also collide head-on with each other; as a result, the debris from these reactions contains particles like pions, kaons, muons and even anti-protons.

Here is one of the strangest, and most beautiful, facts in the chapter: pure energy can turn into matter, and matter can turn back into pure energy. Pair production happens when a γ-ray — a very high-energy photon — passes close to an atomic nucleus. Out of that photon comes an electron–positron pair. The nucleus itself has to be there, and the book explains why: a third particle must be present to conserve linear momentum. A photon on its own in empty space cannot do this trick.

There is also a strict minimum price. By mass–energy equivalence, the photon must carry at least the rest-mass energy of the two particles it creates: 2m_ec² = 1.02 MeV, a value confirmed by experiment. A photon with less than 1.02 MeV simply cannot make the pair; a photon with more gives the extra energy to the two particles as kinetic energy. Charge, momentum and energy are all conserved in the process, and the same idea works for any particle and its anti-particle.

Annihilation is the film run backwards. When an electron meets a positron, they destroy each other and become two γ-ray photons: e⁻ + e⁺ → γ + γ. Each photon carries 0.51 MeV, exactly the rest-mass energy of one electron (E = m_ec²). Two photons, not one, fly off in opposite directions — that detail matters, and it comes back as an exercise question, because a single photon could never balance both energy and momentum at once. The same annihilation can happen for other pairs too: proton and anti-proton, lepton and anti-lepton, quark and anti-quark.

📌 Do you know? (book's side box): pair production cannot take place in vacuum or space. Pair production can happen only in the presence of an external object like an atomic nucleus which can experience some recoil during the collision process, to conserve the energy and the momentum at the same time.

Some nuclei simply cannot sit still. The book's rule of thumb is that nuclei with atomic numbers greater than 82 are naturally unstable: left alone, they spontaneously throw out radiation. Such nuclei are called radioactive, and the emission itself is natural radioactivity. Unstable isotopes can also be made on purpose in a laboratory by bombarding a stable element with high-energy neutrons, protons, α-particles or γ-rays; that is artificial radioactivity, and the isotopes it produces are called radioisotopes or radionuclides.

The radiation comes in three kinds, and the book's electric-field experiment tells them apart in one glance. Send the beam between charged plates: α-particles bend towards the negative terminal, so they carry positive charge; they are fast — a few percent of the speed of light — but heavy, so they travel only a few centimetres in air. β-particles bend towards the positive terminal, so they are negative, and they bend more than the α-particles, which proves they are lighter; they are fast-moving electrons reaching up to 0.9995 of the speed of light. γ-radiations sail straight through the field untouched — no charge at all. They are electromagnetic waves made of photons, they travel at the speed of light, they penetrate the most and they ionize the least. The book's summary table (Table 12.2) puts numbers on all this: ionization in air roughly 10⁴ ion pairs per mm for α, 10² for β and about 1 for γ; range several centimetres for α and several metres for β; stopped by a sheet of paper (α), 1–5 mm of aluminium (β) and 1–10 cm of lead (γ). One small honesty note: the book's table skips a row number, jumping from row 4 to row 6 — a printing slip, not missing physics.

Alpha decay. When a nucleus has too many protons for its neutrons, electrical repulsion starts winning against the strong force, and the nucleus becomes unstable. Its way out is to throw out an α-particle — a helium nucleus, two protons and two neutrons together. The parent therefore loses two protons and two neutrons: its atomic number Z drops by 2 and its mass number A drops by 4, written generally as ^A_ZX → ^A−4_Z−2X′ + ⁴₂He. The book's example is radium-226: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He. Notice that the daughter is a different element — radium has become radon. That change of one element into another is called transmutation. In every α-decay, the number of nucleons and the total charge are conserved, exactly as the equation shows. There is one more quantity to notice: the parent nucleus is experimentally heavier than its daughter plus the α-particle put together, so the decay products carry less mass-energy than the parent did. That difference is the disintegration energy Q, the energy released by the decay.

Beta-minus decay. Some nuclides have a neutron-to-proton ratio (N/P) that is too large, and they fix it from the inside: a neutron in the nucleus turns into a proton, an electron and an anti-neutrino, written ¹₀n → ¹₁p + ⁰₋₁e + ν̄. The electron that flies out is the β-particle — and here is the point students usually get wrong: it is not one of the atom's orbital electrons. It is created inside the nucleus at the very moment of emission. No nucleons are lost, so A stays the same while Z rises by one: the parent of atomic number Z becomes a different element of atomic number Z+1. The book's example is thorium decaying to protactinium: ²³⁴₉₀Th → ²³⁴₉₁Pa + ⁰₋₁e + ν̄. Neutrinos and anti-neutrinos have zero charge and very small mass, which is why they slip through matter almost unnoticed and are so hard to observe.

Beta-plus decay. Other nuclides have the opposite problem, an N/P ratio too small for stability, and they decay by emitting a positron instead of an electron. A proton in the nucleus turns into a neutron and a positron, plus a neutrino: ^A_ZX → ^A_Z−1X′ + ⁰₊₁e + ν. The positron has the electron's mass but a positive charge. The book's example is neon turning into fluorine: ¹⁹₁₀Ne → ¹⁹₉F + ⁰₊₁e + ν. Again A does not change; Z falls by one.

Gamma radiation. After an α- or β-decay, the daughter nucleus is often left in an excited state, like an atom with its energy still raised. It settles down by throwing off the extra energy as a γ-ray photon, with no change to A or Z at all: ^A_ZX* → ^A_ZX + γ, where the star marks the excited nucleus and the unstarred symbol is the same nucleus in its ground state.

📌 For your information (book's side box): the neutrino was first proposed by Wolfgang Pauli in 1930 to obey the energy conservation in the beta-minus and beta-plus decays. Later, in 1953, the neutrino was detected by F. Reines and C. L. Cowan in a high-power nuclear reactor. On this discovery, F. Reines received the Nobel Prize in 1995.

Here is a difference that examiners return to again and again, and it is really a detective story. For one particular radionuclide, every α-particle comes out with the same sharply defined kinetic energy. Plot the number of α-particles against kinetic energy and you get distinct spikes — the book's Fig. 12.5. That is a discrete spectrum, and it tells you that α-decay is a two-body break-up: the energy is split in a fixed way between the α-particle and the recoiling daughter, so the α-particle always gets the same share.

β-particles behave completely differently. Their energies range all the way from zero up to a maximum value, and the plot is a smooth curve — the book's Fig. 12.6, a continuous spectrum. For years this looked like energy conservation was failing, until Pauli's neutrino solved it: the decay energy is shared between the β-particle and the (anti-)neutrino in varying proportions. Sometimes the electron takes nearly everything, sometimes the neutrino does, but the sum of the two energies is the same every time. So the total energy is conserved after all — it is just divided differently in each decay. Momentum and energy conservation apply to both α- and β-emission; the difference is only in how many particles share the energy.

A fundamental particle means a particle with no internal structure — nothing smaller inside it, nothing to take apart. Right now the fundamental building blocks of matter are taken to be quarks and leptons. That was not always obvious. Smash a nucleus in an ultra-high-energy accelerator, or collide two high-energy particles, and entirely new kinds of particles appear that do not exist inside ordinary atoms. More than a hundred were found and sorted into families by their properties; some fitted a theoretical scheme, and the rest were nicknamed "strange particles". They are always created in pairs — when a pion (π) hits a proton, for example, a kaon (K°) and a lambda (Λ°) appear together: π + p → K° + Λ°.

All particles spin on their axes, and the spin of a charged particle makes it a tiny magnet. Electrons, protons and neutrons have spin ½, the photon has spin 1 and pions are taken to have spin zero. That half-or-whole difference splits the particle world in two. Fermions have half-integer spin (½, 3⁄2, …) and obey Pauli's exclusion principle: only one particle of a kind can occupy a given quantum state. Bosons have zero or whole-number spin and do not obey that principle; they follow Bose–Einstein statistics instead. The older classification still used in the book runs alongside this: the nucleons and heavier particles that decay into nucleons, such as Λ° and K°, are called baryons (heavy), while particles that do not interact strongly with nucleons, along with electrons, tau and neutrinos, are called leptons (small).

Then the book sorts everything again, this time by whether a particle feels the strong force. Particles that experience the strong force are hadrons; those that do not are leptons. Hadrons are composite — they have quark structure inside — and they divide into mesons, which are bosons such as the pion, and baryons, which are fermions, protons and neutrons being the key examples. Baryons are made of an odd number of quarks, usually three; mesons are made of an even number, usually two — one quark and one anti-quark. Leptons, by contrast, interact only through the weak or electromagnetic interactions, and no experiment has yet revealed any internal structure in them: they appear to be truly fundamental. All known leptons have spin ½, so they are all fermions. There are six known leptons in three pairs (Table 12.3): the electron with its electron neutrino, the muon with its muon neutrino, and the tau with its tau neutrino, each pair with its anti-particles. Charged leptons can join other particles to form composite things like atoms and positronium, while neutrinos hardly interact with anything and are therefore rarely observed. The best-known lepton of all is the electron.

📌 For your information (book's side box): Hadrons — Mesons, e.g. pions, kaons; baryons, e.g. protons, neutrons, omega, sigma and lambda particles. Non-hadrons — Leptons, including electrons, muon, neutrinos; photons, gravitons.

The discovery that protons and neutrons are not fundamental at all led, in 1964, to Gell-Mann and Zweig's proposal: hadrons are built from combinations of three even more fundamental entities called quarks, or quark flavours. The three first proposed were up (u), down (d) and strange (s). Today we know six quarks, just as there are six leptons, on what the book calls a presumed symmetry in nature. The other three are charm (c), bottom (b) and top (t). Every quark has spin ½ and an electric charge that is a fraction of the electron's charge — something nobody had imagined before: up, charm and top carry +2⁄3, while down, strange and bottom carry −1⁄3 (Table 12.4). And quarks are invisible in a deeper sense than "small": they never appear on their own.

Now watch how beautifully the charges add up. A proton is uud, so its charge quantum number is q(uud) = 2⁄3 + 2⁄3 + (−1⁄3) = +1 — exactly the proton's charge. A neutron is udd, so q(udd) = 2⁄3 + (−1⁄3) + (−1⁄3) = 0 — exactly neutral. Mesons are quark–anti-quark pairs, and the same arithmetic works there: a π⁺ meson is an up quark plus an anti-down quark, and the anti-down carries +1⁄3, so q = 2⁄3 + 1⁄3 = +1. If you can add thirds, you can work out any hadron's charge in this chapter.

Then comes a second property with a deliberately silly name. Not long after quark theory, it was suggested that quarks carry another kind of charge called colour, or "colour charge", analogous to electric charge. Each flavour of quark can come in one of three colours — red, green and blue — and the names have nothing to do with what your eyes see; they are whimsical labels, like "charm" itself. Anti-quarks carry anti-colours: anti-red, anti-green and anti-blue. Baryons are made of three quarks, one of each colour, and mesons are a quark–anti-quark pair of a colour and its anti-colour. In both cases the colours cancel out, so baryons and mesons are colourless, or white — blue + red + green = white, just as in the book's Fig. 12.7.

Once you know the quark make-up of nucleons, beta decay stops looking like magic and starts looking like bookkeeping. A neutron is udd and a proton is uud. So when a neutron decays into a proton, what really happens at the deepest level is that one of its down quarks changes into an up quark: d → u + ⁰₋₁e + ν̄. The down quark's charge (−1⁄3) becomes the up quark's charge (+2⁄3), a jump of exactly +1 — and that +1 is carried away by the electron's −1 plus the rest of the bookkeeping, with the anti-neutrino balancing the lepton number. The book's point is larger than one equation: the quark model does not just list what particles are made of, it explains how they interact.

The force between quarks has its own name and theory. Each quark carries a colour charge, analogous to electric charge, and the strong force between quarks is called the colour force. The theory of that force is quantum chromodynamics (QCD) — "chromo" because it acts between colour charges, not electric ones. The strong force between whole hadrons, the one that holds nuclei together, is then understood as a leftover effect of the force between the quarks inside them. And the carriers of the colour force, the particles exchanged between quarks, are the gluons — the name is a hint, because they quite literally glue quarks together.

📌 Do you know? (book's side box): a neutron is stable only inside a nucleus. Free neutrons decay with a half-life of 900 s. Small honesty note on this box: the book prints 900 s; modern measurements put the neutron's mean lifetime near 880 s, which corresponds to a half-life of about 610 s (roughly 10 minutes) — so the book's 900 s is close to the mean lifetime rather than the half-life, but the point stands: a free neutron does not last long.

Fundamental particles, the book says, are the six quarks, the six leptons and the gauge bosons — the book's text here also names the Higgs boson among them, though strictly the Higgs is a scalar boson rather than a gauge boson, a distinction your level does not need to worry about. Leptons and quarks interact by sending and receiving bosons, and those exchanged bosons are what "carry" the forces. Two positively charged particles, for instance, push each other apart by exchanging photons; quarks inside a nucleus attract each other by exchanging gluons; the W⁺, W⁻ and Z bosons carry the weak nuclear force; and gravitons are the proposed carriers of gravity.

The Higgs boson is special, and it has its own section because it answers a question the rest of the chapter leaves hanging: why do particles have mass at all? Discovered in 2012 at the Large Hadron Collider at CERN, it is associated with the Higgs field, which the book pictures as permeating all of space. Particles get their mass by interacting with this field: particles that interact strongly with it, like the W and Z bosons, end up heavy, while particles like photons, which do not interact with it, keep zero rest mass. The Higgs boson itself has a mass of around 125 GeV/c² and decays rapidly into other particles. The book adds two key facts: the Higgs boson gets its own mass from its interactions with its associated Higgs field, and it can be a unique portal to the conditions of the universe shortly after the Big Bang and to signs of dark matter, because of its distinctive characteristics and properties.

Whatever the process — a reaction or a decay — section 12.8 says the same laws always hold, and they are your checking tool for every equation in the exercise: (1) conservation of energy, momentum and charge, including the nucleon number A and the charge number Z; (2) conservation of baryon number; (3) conservation of lepton number. If a proposed decay breaks any of these, it cannot happen. That is exactly how Pauli knew a neutrino had to exist: without it, beta decay would not balance.

12.9 — Why is there anything at all? Observations show an asymmetry between matter and anti-matter that the book calls the most remarkable feature of our universe. A number of hypotheses exist which show that the universe consists almost entirely of matter rather than anti-matter. The book's figures need reading carefully: about 5% of the universe is ordinary matter — electrons, protons and neutrons — and within that ordinary matter, roughly 71% is hydrogen atoms and 24% helium atoms; there is no contribution of anti-hydrogen or anti-helium atoms in the composition of the universe. Experiments explain the asymmetry as a violation of the conservation of baryon number — an imbalance in the number of baryons and anti-baryons. If particle–anti-particle symmetry is also violated, then there is a mechanism for making more quarks than anti-quarks, more leptons than anti-leptons, and eventually more matter than anti-matter. Even so, the book is blunt: the problem of the asymmetry of matter and anti-matter is still a mystery.

12.10 — Most of the matter in the observable universe is plasma. Our universe is more vast than our thinking, the book says, because we still know about only its 5% part and we still do not know about its remaining 95% part: about 27% is unknown matter called dark matter and about 68% is a mysterious anti-gravity material known as dark energy; 27 + 68 = 95, so 95% of the universe is out of our thinking. On the other hand, the 5% we do know about is ordinary matter, where hydrogen and helium are almost in the plasma state. Therefore, the book concludes, most of the matter in the observable universe is in the form of plasma.

12.11 — Two theories about where mass and force come from. To explain how particles interact through different mediators, the book gives two theories. In quantum field theory, each particle is represented by a field called a quantum field, which transmits a force from one particle to another: a positively charged particle makes an electric field in the space around it, and through that field it pulls a nearby negatively charged particle. The field can also carry energy and momentum, and where that energy and momentum are quantized, the quanta that exchange them are called field particles — all of them bosons. The electromagnetic force is mediated by photons (quanta of the electromagnetic field), the strong nuclear force by gluons, the electro-weak force by W and Z bosons, and gravity by gravitons. In string theory, an advanced concept in theoretical physics, the fundamental particles of the universe are not point-like at all but tiny vibrating strings, open or closed loops, whose vibrations determine the properties of particles, including mass and force. The string-theory framework, offering a potential theory of everything, still remains unproved experimentally.

12.12 — The Standard Model. The Standard Model is the collection of theories that describe the smallest experimentally observed particles of matter and the interactions between energy and matter. Three categories of particles form it (Fig. 12.8 in the book): matter, which makes up only 5% of the universe, is composed of quarks and leptons, and the fundamental bosons provide three forces — electromagnetism, the strong nuclear force and the weak nuclear force. The Higgs boson explains how the other particles get mass. But the model is still considered incomplete: it cannot currently explain gravity, dark matter (27% of the universe) or dark energy (68% of the universe). That incompleteness is not a failure to hide — it is the next chapter of physics, waiting to be written.