Physics · Lesson 26

Atomic & nuclear physics: radioactivity, half-life, fission/fusion

JAMBWAECNECO

What the syllabus asks

JAMB: Atomic and nuclear physics

WAEC: Structure of the atom (models of the atom, nucleus, isotopes); radioactivity (alpha, beta, gamma; properties; detection; decay equations; half-life and decay constant); nuclear reactions (fission, fusion, mass defect, binding energy, E = mc²); uses and hazards of radioactivity

NECO: Structure of the atom (models of the atom, nucleus, isotopes); radioactivity (alpha, beta, gamma; properties; detection; decay equations; half-life and decay constant); nuclear reactions (fission, fusion, mass defect, binding energy, E = mc²); uses and hazards of radioactivity

What you will learn

Describe the nuclear model of the atom and the evidence for it.
Use A, Z and N notation and identify isotopes.
Compare the properties of alpha, beta and gamma radiation.
Write and balance nuclear decay equations.
Solve half-life problems from data, tables and graphs.
Calculate mass defect and binding energy; explain fission, fusion, uses and hazards.

Key points

Rutherford: atom mostly empty; tiny dense positive nucleus.
ᴬ_Z X: Z protons, A − Z neutrons; isotopes have equal Z, different A.
α = ⁴₂He (most ionising, least penetrating); β⁻ = electron; γ = EM wave (most penetrating, uncharged).
α decay: A − 4, Z − 2; β⁻ decay: Z + 1; γ: no change in A or Z.
Half-life: N = N₀(½)^(t/T); λ = 0.693/T; activity A = λN; subtract background.
Mass defect × 931 MeV = binding energy; E = mc².
Fission: heavy nucleus splits (reactor: fuel, moderator, control rods, coolant); fusion: light nuclei join at very high temperature.
Uses: radiotherapy, tracers, gauges, carbon dating, smoke detectors; follow safety rules (tongs, lead, distance, short time).

Start here: Models of the atom

Our picture of the atom developed through experiments.

Dalton (1803): atoms are tiny indivisible spheres.
Thomson (1897): discovered the electron; proposed the "plum pudding" model, a sphere of positive charge with electrons embedded.
Rutherford (1911): the alpha-scattering experiment showed that the atom is mostly empty space with a tiny, dense, positive nucleus.
Bohr (1913): electrons move in fixed orbits (energy levels) and emit or absorb light only when they jump between levels (the lesson “Quantum physics: photoelectric effect & X-rays”).

Rutherford’s gold-foil experiment

Geiger and Marsden fired alpha particles at very thin gold foil. Results and conclusions:

Observation	Conclusion
Most alpha particles passed straight through	The atom is mostly empty space
A few were deflected through large angles	There is a concentrated positive charge
Very few (about 1 in 8,000) bounced back	The positive charge and most of the mass are in a very tiny nucleus

The nucleus is about 10⁻¹⁵ m across, while the atom is about 10⁻¹⁰ m: if the atom were the size of a football stadium, the nucleus would be a small bead on the centre spot.

Worked example 26.1

Why could the plum pudding model not explain the alpha particles that bounced back?

In that model the positive charge is spread thinly, so its field is weak everywhere.
A weak, spread-out charge cannot turn back a fast, heavy alpha particle. Only a concentrated charge can.

Because a large deflection needs a concentrated nucleus

Try it yourself. State two conclusions of the Rutherford scattering experiment.

Show solution

The atom is mostly empty space; it has a small, dense, positively charged nucleus containing most of the mass.

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Practice questions

1. How many neutrons are in ²²⁶₈₈Ra?

Show worked answer

138.

2. ²²²₈₆Rn emits an alpha particle. Give the product.

Show worked answer

²¹⁸₈₄Po.

3. ⁹⁰₃₈Sr emits a beta particle. Give the product’s A and Z.

Show worked answer

A = 90, Z = 39 (yttrium).

4. A 120 g sample has half-life 3 h. How much remains after 9 h?

Show worked answer

15 g.

5. An activity falls from 1,600 to 200 counts/min in 6 days. Find T.

Show worked answer

3 half-lives: T = 2 days.

Key words

Nucleus: The small central part of an atom containing protons and neutrons.
Nucleon: A proton or a neutron.
Atomic number (Z): Number of protons in the nucleus.
Mass number (A): Number of nucleons in the nucleus.
Isotopes: Atoms of the same element with different numbers of neutrons.
Nuclide: A particular nucleus with specified A and Z.
Radioactivity: Spontaneous disintegration of unstable nuclei with emission of radiation.
Activity: Number of disintegrations per second; unit becquerel (Bq).
Half-life: Time taken for half the radioactive nuclei in a sample to decay.
Decay constant (λ): Probability per unit time that a nucleus decays; λ = 0.693/T.
Ionisation: Removing electrons from atoms, producing ions.
Mass defect: Difference between the total mass of separate nucleons and the mass of the nucleus.

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