Nuclear physics

Learning objectives

• Describe isotopes using proton and nucleon numbers.
• Compare radiation types, detection and exposure precautions.
• Correct count rates for background and calculate whole half-lives.

The big idea

An atom has a small nucleus containing protons and neutrons, with electrons outside it. Isotopes have the same proton number but different neutron numbers, so they are forms of the same element.

Radioactive decay is random for an individual nucleus. A large sample has a predictable statistical pattern: activity halves in each half-life. Radiation can ionise matter, so exposure requires controlled professional procedures.

Topics to connect

• Atomic structure
• Isotopes
• Alpha, beta and gamma radiation
• Radioactive decay and half-life
• Detection, background and corrected count rates
• Nuclear energy and radiation safety

1. Atoms and isotopes

An atom contains a small positively charged nucleus and surrounding electrons. Proton number identifies the element; nucleon number counts protons plus neutrons. Isotopes share proton number but differ in neutrons. A neutral atom has equal proton and electron numbers; removing an electron makes an ion, not a new isotope. Alpha-particle scattering supports a small concentrated nucleus rather than a uniform distribution of positive charge.

2. Radiation and nuclear change

Alpha radiation consists of helium nuclei, beta-minus radiation of electrons from nuclear change, and gamma radiation of high-energy photons. Alpha emission reduces nucleon number by four and proton number by two; beta-minus leaves nucleon number unchanged and raises proton number by one. Gamma emission changes nuclear energy without changing these counts. Penetration and ionising ability differ, so shielding and exposure considerations depend on radiation type.

3. Detection, background and counting

A detector records some radiation interactions, not necessarily every decay in a source. Background comes from environmental and cosmic sources and varies statistically. Measure it for a suitable interval and subtract its count rate from the total to obtain a corrected count rate. A total of 150 counts/min with background 30 counts/min gives 120 counts/min corrected. Converting that result to activity requires information about detection efficiency and geometry.

4. Random decay and half-life

One nucleus has an unpredictable decay time, but many similar nuclei show a regular statistical trend. After each half-life, the expected number undecayed and the activity each halve. Corrected count rate can track that trend when detection conditions stay unchanged. Three half-lives leave one eighth, not one third. Small samples and short count intervals show fluctuations, so a single reading rarely gives an exact half-life.

5. Nuclear energy and protection

Fission splits a heavy nucleus and can produce neutrons capable of triggering further fissions. Fusion joins light nuclei under suitable conditions. Energy release corresponds to a reduction in total rest mass; it does not mean all matter disappears. Exposure should be minimised through suitable time, distance, shielding and controlled procedures. Contamination means radioactive material has spread; irradiation means radiation reaches something and does not necessarily make it radioactive. Never handle sources independently.

A method you can reuse

1. Write proton and nucleon numbers before and after a decay.
2. Convert detector counts to rates using the measured interval.
3. Subtract background before estimating a source’s decay trend.
4. Count elapsed half-lives or read a corrected graph.
5. Separate source activity from what the detector registers.

Equations and relationships

Investigate and explain

Model random decay by repeatedly removing coins that land heads; graph the remaining number. Use no radioactive materials.

Compare atomic identity with nuclear change, then view statistical decay. Simulations are educational representations, not instructions for sourcing, shielding or handling radioactive materials.

Open the interactive investigation

Check your understanding