Atom, emission spectra & radioactivity

Learning goals

What students should be able to explain, calculate and investigate after completing The Atom, Emission Spectra and Radioactivity.

Goals marked Higher Level are required only for Higher Level students; the remaining goals are for all students.

• Describe how atomic models developed from Thomson through Rutherford to Bohr, and why each was revised.
• Explain emission spectra in terms of electron energy levels.
• Define isotope, mass defect and binding energy, and calculate binding energy using E = mc².
• Classify alpha, beta and gamma radiation by penetrating power, ionising effect, charge and mass.
• Higher Level: Use the radioactive decay law and half-life to solve problems.
• Describe methods of detecting ionising radiation.

Key definitions

Precise terms, symbols and SI units used in The Atom, Emission Spectra and Radioactivity.

Development of Atomic Models

Successive experiments replaced the indivisible-atom model with evidence for electrons, a tiny nucleus and quantised electron energy levels.

J. Thomson's 'plum pudding' model pictured the atom as a sphere of positive charge with electrons embedded throughout, based on his discovery of the electron. Rutherford's gold-foil scattering experiment (firing alpha particles at thin gold foil) found that most alpha particles passed straight through, but a small number deflected sharply, some almost straight back — evidence Thomson's model could not explain. Rutherford concluded that an atom's positive charge and almost all its mass must be concentrated in a tiny, dense central nucleus, with electrons orbiting at a relatively large distance — but classical physics predicted such orbiting electrons should continuously radiate energy and spiral into the nucleus almost instantly, which does not happen. Bohr resolved this by proposing that electrons can only exist in specific, fixed energy levels (not spiralling continuously), successfully explaining the discrete emission spectrum of hydrogen — though the Bohr model itself was later refined further by full quantum mechanics for more complex atoms.

Energy Levels and Emission Spectra

Electrons in an atom can only occupy specific, discrete energy levels.

When an atom absorbs energy (e.g. from a photon, or a collision), an electron can jump to a higher energy level; when it falls back down to a lower level, it emits a photon whose energy exactly matches the difference between the two levels: E₂ − E₁ = hf. Since each element has its own unique set of energy levels, each element produces its own unique emission spectrum (a distinctive pattern of specific wavelengths), which can be used to identify elements — including identifying the elements present in distant stars from the light they emit.

Isotopes, Mass Defect and Binding Energy

Isotopes of an element share the same number of protons (and so the same chemical properties) but differ in the number of neutrons, giving different mass numbers.

A bound nucleus has a lower total mass-energy than the same nucleons separated. The difference in mass is the mass defect. Through E = Δmc², it corresponds to the binding energy: this energy is released when the nucleus forms and must be supplied to separate it completely. Binding energy per nucleon helps compare how tightly nuclei are bound, but nuclear stability also depends on factors such as the neutron–proton balance.

• In nuclide notation, A is the nucleon number, Z is the proton number, and neutrons = A − Z.

Types of Ionising Radiation

Alpha particles (helium nuclei, 2 protons + 2 neutrons) are heavy and highly ionising, but have very low penetrating power — stopped by paper or a few centimetres of air.

Beta radiation is most commonly a fast electron (β⁻, emitted when a neutron converts to a proton in the nucleus), though a minority of unstable nuclei instead emit a positron (β⁺, emitted when a proton converts to a neutron) — school examples are almost always β⁻ unless stated otherwise. Beta particles are lighter than alpha, less ionising, and more penetrating — stopped by a few millimetres of aluminium. Gamma rays (high-energy electromagnetic photons) are the most penetrating and least ionising per interaction — reduced in intensity by thick lead or concrete, but never completely stopped. Summary comparison:

Radioactive Decay and Half-Life

Radioactive decay is random for an individual nucleus, but a large sample follows a predictable exponential pattern: both the number of undecayed nuclei and the activity halve during each half-life.

Each unstable nucleus has a constant probability of decaying per unit time, but the time at which one particular nucleus decays is unpredictable. A large sample therefore shows exponential decay. After every half-life the same fraction—one half—remains, so the absolute decrease becomes smaller in successive intervals.

Detecting Radiation

Ionising radiation cannot be seen directly, but can be detected because it ionises the material it passes through.

Ionising radiation entering the thin window creates ion pairs in the low-pressure gas. Electrons accelerate towards the positive central wire and trigger further ionisation, producing a short current pulse that can be counted. The count rate includes background radiation, which must be measured separately and subtracted when finding the source count rate.

Diagrams and formulae

Key diagrams and equations for reviewing The Atom, Emission Spectra and Radioactivity.

• Bohr model energy levels: an electron absorbs a photon to jump to a higher level, and emits a photon (E₂ − E₁ = hf) when it falls back down.
• Penetrating power: alpha is stopped by paper; beta is stopped by a few millimetres of aluminium; gamma is only reduced (never fully stopped) by thick lead or concrete.
• Radioactive decay curve: the number of undecayed nuclei halves during every successive half-life.

Bohr model energy levels: an electron absorbs a photon to jump to a higher level, and emits a photon (E₂ − E₁ = hf) when it falls back down.

Penetrating power: alpha is stopped by paper; beta is stopped by a few millimetres of aluminium; gamma is only reduced (never fully stopped) by thick lead or concrete.

Radioactive decay curve: the number of undecayed nuclei halves during every successive half-life.

Worked Example

A step-by-step calculation applying the central relationships in The Atom, Emission Spectra and Radioactivity.

A radioactive isotope has a half-life of 8 days. A sample starts with an activity of 800 Bq. Calculate the activity after 24 days.

• 24 days ÷ 8 days per half-life = 3 half-lives
• Activity after 3 half-lives = 800 × (½)³ = 800 × ⅛ = 100 Bq

Practical / Investigation

Experimental planning, measurement and evaluation for The Atom, Emission Spectra and Radioactivity.

Investigation: Half-life simulation or secondary data analysis

• Method (simulation): using a large number of dice (or coins) as a model for radioactive nuclei, remove ('decay') all dice showing a chosen number (e.g. a six) after each round; plot the number remaining against the round number.
• Data-analysis skill: the resulting graph should show an approximately exponential decay curve, similar in shape to a real radioactive decay curve, with a roughly constant 'half-life' in terms of number of rounds.
• Alternatively, analyse provided secondary data (e.g. a table of activity vs time for a real isotope) to determine its half-life from a graph, and compare with the accepted value.
• Evaluate limitations: the dice/coin model represents random decay well, but does not capture the actual physical mechanism of nuclear decay, nor the vast range of real half-lives (fractions of a second to billions of years).

• Record the number remaining after every round, including the initial value at round 0; repeat the full simulation and average corresponding rounds.
• Plot number remaining (or activity for isotope data) against round number or time. Read successive halving intervals from the curve rather than forcing a straight-line fit.
• Keep the initial number of dice, decay rule and throwing method consistent. The model demonstrates random decay and statistical fluctuation, not the nuclear mechanism.

Quick-Check Questions

Short retrieval questions covering the essential ideas in The Atom, Emission Spectra and Radioactivity.

1. What evidence from Rutherford's scattering experiment could not be explained by Thomson's model?

2. Why does each element produce a unique emission spectrum?

3. Define mass defect and state how it relates to binding energy.

4. Rank alpha, beta and gamma radiation by penetrating power, from least to most penetrating.

5. What happens to the activity of a radioactive sample after two half-lives have passed?

Common mistakes and exam tips

Common misconceptions and exam-technique checks for The Atom, Emission Spectra and Radioactivity.

• Avoid: Treating ionising ability and penetrating power as the same property. Correct idea: Keep them separate: alpha is strongly ionising but weakly penetrating; gamma is weakly ionising per interaction but highly penetrating.
• Avoid: Saying thick lead completely stops gamma radiation. Correct idea: Shielding reduces gamma intensity; it does not guarantee that every photon is stopped.
• Avoid: Thinking radioactive decay ends after one half-life. Correct idea: After each half-life, half of the nuclei then present remain undecayed; the process continues.

• For a half-life calculation, count the elapsed half-lives before halving the remaining amount.
• In a mass-defect calculation, subtract the nucleus mass from the total mass of its separated nucleons before using E = mc².
• When comparing alpha, beta and gamma, state the property being compared.

Exam-style questions

Five exam-style questions with worked answers on The Atom, Emission Spectra and Radioactivity.

Higher Level — Required Content

Required Higher Level content for this topic.

For a large sample, the rate of radioactive decay is proportional to the number of undecayed nuclei present.

• Use consistent time units for λ and t.
• Whole-number half-lives can also be handled by repeated halving.

• The strong nuclear interaction binds protons and neutrons in the nucleus over very short distances.
• The weak interaction is involved in beta decay.

End-of-unit revision

Formulae, definitions, experiments and mixed revision questions for The Atom, Emission Spectra and Radioactivity.

• E₂ − E₁ = hf (emission spectra)
• E = mc² (mass-energy equivalence / binding energy)
• A = −ΔN/Δt = λN (activity; the minus sign keeps A positive, since N decreases)
• T½ = ln2/λ (half-life)

• Isotope
• Energy level and emission spectrum
• Mass defect and binding energy
• Activity and half-life

• Bohr energy-level diagram with photon absorption/emission
• Alpha/beta/gamma penetrating power through paper, aluminium and lead
• Exponential radioactive decay curve

• Half-life simulation (dice/coins) or secondary-data half-life analysis

• Thinking gamma can be fully stopped by any material
• Confusing ionising ability with penetrating power
• Thinking decay 'stops' after one half-life
• Treating the Bohr model as the complete final picture

1. A sample has an initial activity of 640 Bq and a half-life of 3 hours. Calculate its activity after 12 hours.

2. Explain why Rutherford concluded the nucleus must be small and dense, based on his scattering results.

3. State one similarity and one difference between beta particles and electrons produced by thermionic emission .

4. Explain, in terms of energy levels, why an atom can only emit light at specific wavelengths rather than a continuous range.

1. 12 ÷ 3 = 4 half-lives. Activity = 640 × (½)⁴ = 640 ÷ 16 = 40 Bq.

2. Since most alpha particles passed straight through the foil, most of the atom must be empty space; since a small number deflected sharply (some almost straight back), a small, dense, positively charged region (the nucleus) must occasionally repel an alpha particle strongly at close range.

3. Similarity: both are streams of electrons. Difference: beta particles come from inside an unstable nucleus during radioactive decay, while thermionic emission releases electrons that were already free within the metal, using heat energy rather than nuclear decay.

4. Electrons can only occupy specific, discrete energy levels; light is only emitted when an electron falls from one specific level to another, so only photons with energy exactly equal to the difference between two allowed levels (E₂−E₁ = hf) can be emitted, giving specific wavelengths rather than a continuous spread.

The table below shows which equations from this unit appear in the official State Examinations Commission Formulae and Tables book, and where.

The current specification includes atomic models, spectra, isotopes, mass defect, binding energy and ionising-radiation classification for all students; radioactive-decay calculations and strong/weak nuclear-force treatment are Higher Level.