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

This guide follows the OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards. It covers 3.7.2 h to j (half-life, contamination and irradiation, the range of half-lives), 3.7.3 (nuclear fission) and 3.7.4 (nuclear fusion). The types of radiation and decay equations (3.7.2 a to g) are taught elsewhere, so here you only need to know that alpha, beta and gamma are emitted by unstable nuclei.

Links: revision notes, practice questions, course hub, printable checklist and the 10-minute diagnostics.

What this unit covers

Spec	What you must be able to do
3.7.2 h	Define half-life in terms of nuclei and in terms of count rate; use it in calculations
3.7.2 i	Define contamination and irradiation; compare their hazards
3.7.2 j	Link half-life to how much radiation is emitted and for how long; evaluate hazards and uses
3.7.3 a to c	Describe fission, name U-235 and Pu-239, explain neutron absorption and the energy released
3.7.3 d	Explain a chain reaction and control rods; sketch or complete a labelled diagram
3.7.3 e	Explain why nuclear waste is hazardous and why it must be managed
3.7.4 a to d	Describe fusion, mass to energy, the conditions needed, and fusion in stars

3.7.2 h: Half-life

Radioactive decay is random. You cannot say when one particular nucleus will decay. In a sample with a huge number of nuclei, though, the proportion that decays in a set time can be predicted. Half-life uses this.

The half-life of a radioactive isotope is:

• the average time it takes for the number of nuclei of the isotope in a sample to halve, or
• the time it takes for the count rate from a sample containing the isotope to fall to half its initial level.

“Average” matters: the half-life describes the sample, not one nucleus.

Using half-life

1. Find the number of half-lives: time elapsed divided by half-life.
2. Halve the starting value once for each half-life.

After n half-lives the amount left is the start value divided by 2ⁿ. The fraction left after 1, 2, 3, 4 half-lives is 1/2, 1/4, 1/8, 1/16.

Worked example 1 (nuclei). A sample holds 6.4 × 10¹² nuclei of an isotope with a half-life of 12 days. How many undecayed nuclei remain after 36 days, and what fraction has decayed?

• Number of half-lives = 36 ÷ 12 = 3.
• Nuclei left = 6.4 × 10¹² ÷ 2³ = 6.4 × 10¹² ÷ 8 = 8.0 × 10¹¹.
• Fraction left = 1/8, so the fraction decayed = 1 − 1/8 = 7/8.

Count rate and background

A detector counts the radiation reaching it. Count rate is the number of counts per unit time. The detector also picks up background radiation (3.7.2 d), so you must remove it before halving.

1. Corrected count rate = measured count rate − background count rate.
2. Halve the corrected value once per half-life.
3. Add the background back if the question asks for what the detector would read.

Worked example 2. A source gives a reading of 340 counts per minute at the start. Background is 20 counts per minute. The half-life is 25 minutes. What will the detector read after 75 minutes?

• Corrected start = 340 − 20 = 320 counts per minute.
• Half-lives = 75 ÷ 25 = 3, so the corrected rate = 320 ÷ 8 = 40 counts per minute.
• Detector reading = 40 + 20 = 60 counts per minute.

Finding half-life from data

Read the time for the corrected count rate to halve. Check with a second pair.

Worked example 3. The table gives the corrected count rate from a source.

Time / min	0	5	10	15	20	25
Count rate / counts per minute	560	396	280	198	140	99

• 560 falls to 280 between 0 and 10 minutes: 10 minutes.
• Check: 280 falls to 140 between 10 and 20 minutes: 10 minutes again.
• Half-life = 10 minutes.

On a graph, draw a horizontal line at half the initial value, read across to the curve and then down to the time axis.

3.7.2 i: Contamination and irradiation

Radioactive contamination is the unwanted presence of radioactive atoms on other materials. The hazard comes from the decay of the contaminating atoms. The type of radiation emitted affects how hazardous it is.

Irradiation is the process of exposing an object to ionizing radiation. The irradiated object does not become radioactive.

	Contamination	Irradiation
What happens	Radioactive atoms get onto or into a material or person	An object is exposed to radiation from a source outside it
Does the object become radioactive?	It carries radioactive atoms, so it is a source itself	No
When does exposure stop?	Only when the atoms are removed or have decayed	When the object moves away, the source is shielded or the source is removed
Main hazard	Atoms can be taken into the body, so the radiation acts on tissue for as long as they stay	Damage while the object or person is being exposed

Because contaminating atoms can enter the body, the type of radiation matters. Alpha is strongly ionising and is absorbed within a short distance, so alpha-emitting atoms inside the body put all their energy into nearby cells. Alpha from a source outside the body is far less of a problem, as it travels only a short distance in air. Gamma is weakly ionising but penetrates, so it can reach the body from outside.

Precautions for irradiation sources include keeping the exposure time short, staying as far away as practical, using shielding, and handling the source with tongs or remotely. These all lower the dose received.

3.7.2 j: The range of half-lives

Isotopes have a very wide range of half-lives, from a tiny fraction of a second to billions of years. The values below illustrate the range.

Isotope	Approximate half-life	Radiation
Technetium-99m	6 hours	gamma
Iodine-131	8 days	beta and gamma
Cobalt-60	5 years	beta and gamma
Caesium-137	30 years	beta and gamma
Americium-241	430 years	alpha
Carbon-14	5700 years	beta
Plutonium-239	24 000 years	alpha
Uranium-235	700 million years	alpha

The link between instability and half-life is this:

• The most unstable nuclei have the shortest half-lives. Decay is rapid and a lot of radiation is emitted in a short time.
• The least unstable nuclei have the longest half-lives. They emit little radiation each second, but they go on emitting for a very long time.

Evaluating uses and dangers

To choose an isotope or weigh up a hazard, ask these questions.

1. Which radiation is emitted, and can it reach the detector or the target?
2. Is the source inside the body, or outside it?
3. Is the half-life long enough for the job but short enough that the source is not a problem afterwards?

Worked example 4. A hospital wants a source to inject for a scan. The detector is outside the body. Isotope A emits alpha with a half-life of 430 years. Isotope B emits gamma with a half-life of 6 hours. Which is better?

• Gamma can leave the body and reach the detector; alpha would be absorbed in the tissue.
• B’s half-life is long enough to complete the scan, but the activity soon falls, so the patient is exposed for less time.
• A would stay active in the body for a very long time and damage nearby cells.
• B is the better choice.

Uses follow from the radiation type. Gamma passes through materials, so it suits tracers detected outside the body and sterilising equipment. Beta is stopped by thin metal, so it suits checking the thickness of sheet material. Alpha has a very short range, so it suits sealed sources where nothing must pass through. A long half-life suits a source that must keep working for years. A short half-life suits a tracer, where you want the activity gone soon afterwards.

3.7.3: Nuclear fission

Nuclear fission is the splitting of a large and unstable nucleus and the release of energy.

Two fissionable substances are in common use in nuclear reactors: uranium-235 and plutonium-239. The majority of nuclear reactors use uranium-235.

How fission happens

1. A U-235 (or Pu-239) nucleus absorbs a neutron. This makes the nucleus unstable.
2. The nucleus splits into two smaller nuclei.
3. Two or three neutrons are released, along with energy.

One possible outcome is shown below; mass number and proton number balance.

n + U-235 → Ba-141 + Kr-92 + 3 n. Mass numbers: 1 + 235 = 236 and 141 + 92 + 3 = 236. Proton numbers: 92 = 56 + 36.

The energy released is much greater than in a chemical reaction involving a similar mass of material.

Chain reactions and control rods

The neutrons released can be absorbed by other nuclei, which then split, releasing more neutrons. This is a chain reaction.

neutron --> U-235 nucleus --> two smaller nuclei + 2 or 3 neutrons + energy
                                     |
            each released neutron can hit another U-235 nucleus
                                     |
                      more fissions --> more neutrons --> more fissions

If on average more than one neutron per fission causes another fission, the number of fissions grows rapidly.

Worked example 5. Each fission releases 2 neutrons and every neutron causes a new fission. One fission starts the process. How many fissions are in the fifth generation?

• Generations: 1, 2, 4, 8, 16.
• The fifth generation has 2⁴ = 16 fissions.

In a reactor, control rods absorb fission neutrons so that on average only one neutron per fission goes on to cause another fission. Then the rate of fission, and the rate of energy transfer, stays steady. Lowering the rods further into the core absorbs more neutrons and slows the reaction; raising them absorbs fewer and speeds it up. Materials such as boron are used for rods because they absorb neutrons well.

For your own labelled diagram, label the neutron, the U-235 nucleus, the daughter nuclei, the released neutrons and the energy, and show at least two neutrons hitting further nuclei. For a reactor, add a control rod absorbing some neutrons.

Waste

Nuclear reactions produce waste that may be dangerous because it is radioactive, and it may stay so for a long time, depending on its half-life and products. Its disposal needs careful management, and this is a factor that may influence whether nuclear power is used to generate electricity.

3.7.4: Nuclear fusion

Nuclear fusion happens when two light nuclei join to form a heavier nucleus. In the process, some of the mass of the smaller nuclei is converted into energy.

An example is hydrogen-2 and hydrogen-3 joining to form helium-4 and a neutron. The mass numbers balance (2 + 3 = 4 + 1) and so do the proton numbers (1 + 1 = 2).

Why it needs extreme conditions

Both nuclei are positive, so they repel each other. This force of repulsion must be overcome for the nuclei to get close enough to fuse.

• Very high temperature: the nuclei move very fast, so they have enough kinetic energy to get close despite the repulsion.
• Very high pressure: the nuclei are packed closely together, so close approaches are frequent.

Fusion in stars

Nuclear fusion is the process by which energy is released in stars. In the core of a star the temperature and pressure are high enough for fusion to take place.

	Fission	Fusion
What happens	One large unstable nucleus splits	Two light nuclei join
Starting condition	Nucleus must absorb a neutron	Very high temperature and pressure
Used in	Nuclear reactors	Stars

Common errors

• Using half the elapsed time as the number of half-lives.
• Forgetting to subtract background before halving the count rate.
• Saying the irradiated object becomes radioactive.
• Saying a long half-life means a high count rate. It means a slow decay and little radiation each second.
• Saying control rods “stop” the reaction. In normal running they hold it at one neutron per fission.

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.