CDS Physics · Modern Physics

Atoms and Nuclei

The particles inside and beyond the atom, the three kinds of radioactive decay and the fallout isotopes, and how fission and fusion release energy in reactors, bombs and the Sun.

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Why this matters

Eight CDS questions from 2016 (II) to 2024 (I). Three ask about particles (the neutron, the muon and the Higgs boson), two about radioactive decay and fallout, and three about fission and fusion. The Higgs boson question of 2024 (I) is the chapter's one HARD question.

Concept 1 of 3: Subatomic particles

An atom has a tiny heavy nucleus of protons and neutrons, with electrons moving round it. Any particle smaller than an atom is called subatomic: the three that build atoms, and others such as the muon from cosmic rays and the Higgs boson found in a giant collider.

Definition

What to know:

The nucleus holds protons and neutrons (together called nucleons). Electrons move round the nucleus.
Atomic number $Z$ = number of protons. Mass number $A$ = protons + neutrons. Neutrons = $A - Z$ .
The neutron is slightly heavier than the proton; the electron is about 1836 times lighter than the proton.
Protons and neutrons are themselves made of quarks.
Mass is often given as energy: 1 u is about 931.5 MeV, and 1 GeV = 1000 MeV.

Particle	Charge	Mass and where it is found
Electron	Negative (−1)	About 1/1836 of a proton; moves round the nucleus
Proton	Positive (+1)	About 1 u (938 MeV); in the nucleus
Neutron	None	Slightly more than a proton; in the nucleusQ CDS 2020 (II): neutrons are inside the nucleus; it is electrons that move round it.
Muon	Negative (−1)	About 207 times an electron; made by cosmic rays, lives about 2 millionths of a secondQ CDS 2024 (I): the electron, proton, neutron and muon are all subatomic particles.
Photon	None	No rest mass; carries light and all electromagnetic radiation
Higgs boson	None	About 125 GeV; found at CERN's Large Hadron Collider in 2012Q CDS 2024 (I): of 0.5 MeV, 900 MeV, 100 GeV and 1000 GeV, the closest to its mass is 100 GeV.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2020 · CDS (II) 2020 — General Knowledge · Q88Easy

Example 1 · Modern Physics · Atoms and Nuclei

Which one of the following statements about the properties of neutrons is not correct?

Neutrons stay in the nucleus

Only electrons move round the nucleus. Neutrons and protons are packed inside it.

The Higgs boson is about 125 GeV, not MeV

Its mass is about 125 GeV, more than 100 times a proton's (about 0.94 GeV). Do not pick an MeV value because the number looks familiar.

Drill 2 more on subatomic particles

Concept 2 of 3: Radioactive decay and fallout

An unstable nucleus settles down by throwing something out. If it throws out an alpha particle, it loses two protons and two neutrons. If it throws out a beta particle, a neutron has turned into a proton. If it gives out a gamma ray, it only sheds extra energy: nothing in it is counted differently. Radioactive dust from a nuclear blast or accident gets into plants and animals, and from them into us.

Definition

What to know:

Alpha stops in a sheet of paper; beta in a few millimetres of aluminium; gamma needs thick lead or concrete. Alpha ionises the most, gamma the least.
Half-life: the time for half the nuclei of a sample to decay.
Fallout isotopes enter the body through the food chain: strontium-90 settles in bones (it behaves like calcium), iodine-131 in the thyroid (often through milk), caesium-137 in soft tissue (it behaves like potassium).
Useful isotopes: cobalt-60 for cancer treatment, iodine-131 for thyroid disease, carbon-14 for dating old wood and bones (half-life about 5730 years).

Decay	What leaves the nucleus	Change in Z and A
Alpha	A helium nucleus (2 protons and 2 neutrons)	Z falls by 2, A falls by 4
Beta (minus)	An electron, made when a neutron turns into a proton	Z rises by 1, A unchanged
Gamma	A high-energy photon	No change in Z or AQ CDS 2016 (II): in gamma decay neither the mass number nor the atomic number changes.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2016 · CDS (II) 2016 — General Knowledge · Q17Moderate

Example 2 · Modern Physics · Atoms and Nuclei

In the gamma decay of a nucleus

Gamma changes no count

A gamma ray is a photon: no charge, no mass. The nucleus only loses energy, so Z and A stay the same.

Beta decay raises the atomic number

In beta decay a neutron becomes a proton and an electron leaves. So Z goes up by 1 while A is unchanged. It does not go down.

All three fallout isotopes travel through food

Strontium-90, iodine-131 and caesium-137 all enter the body through the food chain, each settling where a similar element normally goes.

Drill 1 more on radioactive decay and fallout

Concept 3 of 3: Fission, fusion and nuclear energy

Splitting a very heavy nucleus (fission) and joining two very light ones (fusion) both release energy, because in each case the pieces at the end weigh a little less than what you started with. That missing mass becomes energy by Einstein's

E = mc^{2}

, and because

c^{2}

is huge, a tiny loss of mass gives a vast amount of energy.

Definition

The rules:

Fission: a heavy nucleus such as uranium-235, hit by a slow neutron, splits into two middle-sized nuclei and 2 or 3 neutrons, giving about 200 MeV. Those neutrons split more nuclei: a chain reaction.
Nuclear reactor: the chain reaction is controlled. A moderator (heavy water or graphite) slows the neutrons; control rods (cadmium or boron) absorb spare neutrons; a coolant carries the heat away.
Atom bomb (uranium or plutonium): the fission chain reaction is uncontrolled.
Fusion: light nuclei (isotopes of hydrogen) join to make helium. It needs millions of degrees, so it is called thermonuclear. It powers the Sun and the hydrogen bomb.
Energy from lost mass: $E = \Delta m\,c^{2}$ ; a loss of 1 u gives about 931.5 MeV.
In biology, fission also means an organism such as amoeba splitting into two (binary fission).

Mass and energy

E = \Delta m\,c^{2} \qquad 1\ \text{u} \equiv 931.5\ \text{MeV}

Δmmass lost in the reaction (mass defect)
cspeed of light, 3 × 10⁸ m/s

Worked example

When a deuterium nucleus and a tritium nucleus fuse into helium-4 and a neutron, the mass lost is 0.0189 u. How much energy is released? How much energy would 1 g of mass give if it were turned completely into energy?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2023 · CDS (I) 2023 — General Knowledge · Q46Easy

Example 3 · Modern Physics · Atoms and Nuclei

The hydrogen bomb and the uranium bomb are based, respectively on

Fission splits, fusion joins

Fission breaks a heavy nucleus into lighter ones. Fusion joins light nuclei into a heavier one. Joining two nuclei is never fission.

A reactor has a chain reaction too, kept under control

Both a reactor and an atom bomb run a fission chain reaction. The reactor keeps it controlled with a moderator and control rods; the bomb lets it run away.

Moderator slows, control rods absorb

The moderator (heavy water, graphite) slows neutrons so they can split uranium-235. The control rods (cadmium, boron) absorb neutrons to keep the rate steady. Do not swap them.

Drill 2 more on fission, fusion and nuclear energy

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Fission, fusion and nuclear energy
Mass and energy
$E = \Delta m\,c^{2} \qquad 1\ \text{u} \equiv 931.5\ \text{MeV}$

Reference tables (2)

Subatomic particles6 rows

Particle	Charge	Mass and where it is found
Electron	Negative (−1)	About 1/1836 of a proton; moves round the nucleus
Proton	Positive (+1)	About 1 u (938 MeV); in the nucleus
Neutron	None	Slightly more than a proton; in the nucleusQ CDS 2020 (II): neutrons are inside the nucleus; it is electrons that move round it.
Muon	Negative (−1)	About 207 times an electron; made by cosmic rays, lives about 2 millionths of a secondQ CDS 2024 (I): the electron, proton, neutron and muon are all subatomic particles.
Photon	None	No rest mass; carries light and all electromagnetic radiation
Higgs boson	None	About 125 GeV; found at CERN's Large Hadron Collider in 2012Q CDS 2024 (I): of 0.5 MeV, 900 MeV, 100 GeV and 1000 GeV, the closest to its mass is 100 GeV.

Radioactive decay and fallout3 rows

Decay	What leaves the nucleus	Change in Z and A
Alpha	A helium nucleus (2 protons and 2 neutrons)	Z falls by 2, A falls by 4
Beta (minus)	An electron, made when a neutron turns into a proton	Z rises by 1, A unchanged
Gamma	A high-energy photon	No change in Z or AQ CDS 2016 (II): in gamma decay neither the mass number nor the atomic number changes.

Watch out for (8)

Neutrons stay in the nucleus
→ Subatomic particles
The Higgs boson is about 125 GeV, not MeV
→ Subatomic particles
Gamma changes no count
→ Radioactive decay and fallout
Beta decay raises the atomic number
→ Radioactive decay and fallout
All three fallout isotopes travel through food
→ Radioactive decay and fallout
Fission splits, fusion joins
→ Fission, fusion and nuclear energy
A reactor has a chain reaction too, kept under control
→ Fission, fusion and nuclear energy
Moderator slows, control rods absorb
→ Fission, fusion and nuclear energy

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