OxfordAQA International GCSE Physics: Half-life, contamination, nuclear fission and fusion (9203) – Revision Notes

These notes condense half-life, contamination and irradiation, fission and fusion for the OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards: sections 3.7.2 h to j, 3.7.3 and 3.7.4. For full explanations and worked examples read the study guide, then test yourself with the practice questions. See also the course hub, the printable checklist and the 10-minute diagnostics.

Key definitions

Term	Meaning
Radioactive decay	Random process in which an unstable nucleus emits radiation and changes to a more stable one
Half-life (nuclei)	The average time for the number of nuclei of the isotope in a sample to halve
Half-life (count rate)	The time for the count rate from a sample containing the isotope to fall to half its initial level
Contamination	The unwanted presence of radioactive atoms on other materials
Irradiation	Exposing an object to ionizing radiation; the object does not become radioactive
Nuclear fission	The splitting of a large and unstable nucleus, releasing energy
Chain reaction	Neutrons from fission go on to cause further fission
Control rods	Absorb fission neutrons so that on average only one neutron per fission causes another
Nuclear fusion	Two light nuclei join to make one heavier nucleus

3.7.2 h: Half-life

Decay is random for one nucleus, but the fraction of a big sample that decays is predictable.

Half-lives passed	0	1	2	3	4	5
Fraction left	1	1/2	1/4	1/8	1/16	1/32
Fraction decayed	0	1/2	3/4	7/8	15/16	31/32

Method for a half-life calculation

1. Number of half-lives = time ÷ half-life.
2. If a count rate is given, subtract background first.
3. Divide by 2 once for each half-life (divide by 2ⁿ).
4. Add background back only if the question asks what the detector reads.
5. Give the unit and check the answer is smaller than the start value.

Method for finding a half-life from data

1. Subtract background from every reading.
2. Pick a value and find the time at which it has halved.
3. Repeat from a second value. The two answers should agree.
4. On a graph, show your construction lines.

Worked reminders

• 3 200 nuclei, half-life 2 h, after 6 h: 3 half-lives, 3 200 ÷ 8 = 400 nuclei.
• Reading 150 counts per minute, background 18, half-life 4 min, after 8 min: corrected start 132, two half-lives, 132 ÷ 4 = 33, plus 18 gives 51 counts per minute.
• Corrected rates of 800, 400, 200 at 0, 6, 12 days: the rate halves every 6 days, so the half-life is 6 days.

Must-know distinctions

• A half-life is not half the time for everything to decay. After two half-lives a quarter is left, not nothing.
• Decay is random, but the half-life of a sample is predictable.
• Atoms that decay are not destroyed. They become a different nucleus.
• “Average” in the nuclei definition shows it describes a large sample, not one nucleus.

3.7.2 i: Contamination and irradiation

	Contamination	Irradiation
What it is	Radioactive atoms present on or in something	Exposure of an object to radiation
Object radioactive afterwards?	Yes, it carries radioactive atoms	No
Hazard comes from	Decay of the contaminating atoms	Radiation reaching the object while exposed
Stops when	Atoms are removed or have decayed	Source removed, shielded or the object moves away
Danger depends on	Type of radiation emitted	Type of radiation and the precautions used

Points to remember:

• The type of radiation affects the level of hazard. An alpha emitter inside the body is very damaging because alpha is strongly ionising and is absorbed close by. Alpha from outside the body is much less of a risk.
• Gamma penetrates well and is weakly ionising. It can reach the body from outside.
• Precautions for a radioactive source: short exposure time, large distance, shielding, handling tools.
• Contamination is hard to stop, because the atoms can spread and be taken in. Irradiation stops when the exposure stops.

3.7.2 j: Range of half-lives, uses and dangers

Half-lives range from a tiny fraction of a second to billions of years.

Half-life	Behaviour	Consequence
Very short	Most unstable. Decay is rapid; a lot of radiation in a short time	High activity at first, gone quickly
Very long	Least unstable. Little radiation each second	Low activity, but it lasts for a very long time

Illustrative values: technetium-99m about 6 hours, iodine-131 about 8 days, caesium-137 about 30 years, plutonium-239 about 24 000 years.

Method for choosing an isotope

1. Which radiation is emitted? Can it reach the target or detector?
2. Is the source inside or outside the body?
3. Is the half-life long enough for the job, but short enough to limit later exposure?

Short half-life suits a medical tracer. Long half-life suits a source that must keep working for years. A long-lived source needs safe storage for a long time.

3.7.3: Nuclear fission

Facts

• Fissionable substances in common use in reactors: uranium-235 and plutonium-239.
• The majority of nuclear reactors use uranium-235.
• A nucleus first absorbs a neutron, which makes it unstable.
• It splits into two smaller nuclei and releases two or three neutrons and energy.
• The energy released is much greater than in a chemical reaction with a similar mass of material.

Chain reaction

neutron --> U-235 --> 2 smaller nuclei + 2 or 3 neutrons + energy
                          each neutron may hit another U-235 nucleus

Average neutrons per fission that cause another fission	Result
More than 1	Number of fissions grows rapidly
Exactly 1	Steady rate of fission and energy transfer (normal reactor running)
Less than 1	Reaction dies away

Control rods absorb neutrons. Lowering them slows the reaction; raising them lets it speed up.

Waste

• Nuclear waste is dangerous because it is radioactive.
• It may stay radioactive for a long time, depending on its half-life and products.
• Its disposal must be managed with care. This can influence whether nuclear power is used to generate electricity.

3.7.4: Nuclear fusion

• Two light nuclei join to form a heavier nucleus.
• Some of the mass of the smaller nuclei is converted into energy.
• Both nuclei are positive, so there is a force of repulsion between them. It must be overcome for them to get close and fuse.
• That needs very high temperature (nuclei move fast) and very high pressure (nuclei close together).
• Fusion is the process by which energy is released in stars.

	Fission	Fusion
Change	Large nucleus splits	Light nuclei join
Before it happens	A neutron is absorbed	Repulsion is overcome
Used in	Reactors	Stars

Quick self-test

1. A sample has 5.0 × 10¹⁰ nuclei and a half-life of 3 hours. How many remain undecayed after 12 hours?
2. A source reads 2 000 counts per minute with negligible background. Its half-life is 3 days. What is the count rate after 9 days?
3. Reading 150 counts per minute, background 18 counts per minute, half-life 4 minutes. What will the detector read after 8 minutes?
4. What fraction of a sample has decayed after 3 half-lives?
5. State the difference between contamination and irradiation.
6. Why is an alpha-emitting contaminant inside the body especially hazardous?
7. Which two substances are in common use as fissionable material in reactors?
8. What must a nucleus do before it undergoes fission?
9. What do control rods do, and why?
10. Why must nuclei be at very high temperature and pressure to fuse?

Answers

1. 12 ÷ 3 = 4 half-lives. 5.0 × 10¹⁰ ÷ 16 = 3.1 × 10⁹ nuclei (3.125 × 10⁹ before rounding).
2. 9 ÷ 3 = 3 half-lives. 2 000 ÷ 8 = 250 counts per minute.
3. Corrected 132; two half-lives gives 33; add background: 51 counts per minute.
4. 1 − 1/8 = 7/8.
5. Contamination is radioactive atoms on or in a material, which then carries its own source. Irradiation is exposure to radiation from a source, and the object does not become radioactive.
6. Alpha is strongly ionising and is absorbed close to the atoms, so nearby cells receive all the energy. The atoms stay in the body until they are removed or have decayed.
7. Uranium-235 and plutonium-239.
8. Absorb a neutron, which makes it unstable.
9. They absorb fission neutrons so that on average only one neutron per fission goes on to cause another, keeping the rate steady.
10. The positive nuclei repel each other. High temperature gives them enough speed to get close; high pressure packs them close together.

Where marks are usually lost

• Using half the elapsed time as the number of half-lives.
• Not subtracting background before halving a count rate.
• Writing “half the time” in a definition. Say that it is the time for the number of nuclei, or the count rate, to halve.
• Saying an irradiated object becomes radioactive.
• Giving a long half-life as a “high count rate”. A long half-life means a slow decay.
• Saying alpha is dangerous without saying where the source is. Position and radiation type both matter.
• Saying control rods “stop” the reaction, when in running they hold it at one neutron per fission.
• Giving high temperature for fusion without explaining the repulsion between the nuclei.
• Saying waste is a problem without linking it to radioactivity and half-life.

Official syllabus

OxfordAQA International GCSE Physics (9203), published by OxfordAQA, for exams May/June 2018 onwards: sections 3.7.2 h to j, 3.7.3 and 3.7.4.