Radioactive decay, half-life and uses

What you'll learn

How the atomic model changed from “plum pudding” to the nuclear model.
What happens in alpha, beta, gamma and neutron emission.
How to balance nuclear equations using mass number and charge.
How half-life links to activity, uses of radioactivity, and radiation risks.

The atom: the starting point

An atom is the smallest part of an element that still behaves like that element. It has a tiny central nucleus, containing protons and neutrons, with electrons around the outside.

A proton has relative charge +1.
A neutron has relative charge 0.
An electron has relative charge -1.

The nucleus is very small compared with the whole atom, but it contains almost all the atom’s mass.

Definition

Atomic number and mass number

The atomic number, $Z$ , is the number of protons in the nucleus. It decides which element the atom is.
The mass number, $A$ , is the total number of protons and neutrons in the nucleus.
The number of neutrons is found using $A - Z$ .
An isotope is an atom of the same element with the same number of protons but a different number of neutrons.

Nuclear notation is written like this:

ZAX^{A}_{Z}\text{X}

where X is the chemical symbol of the element.

Example

Finding protons and neutrons

A nucleus is written as $614C^{14}_{6}\text{C}$ .

Use the bottom number for the number of protons: $Z = 6$ , so carbon has 6 protons.
Use the top number for total protons plus neutrons: $A = 14$ .
Subtract to find neutrons: $14 - 6 = 8$ , so this nucleus has 8 neutrons.

How the atomic model changed

Scientific models change when new evidence cannot be explained by the old model.

Early in the 1900s, the plum pudding model described the atom as a ball of positive charge with negative electrons embedded in it.

Rutherford’s team then fired alpha particles at very thin gold foil. Most alpha particles passed straight through, but a few were deflected through large angles or even reflected backwards. This showed that most of the atom is empty space, with a tiny, dense, positively charged nucleus.

Bohr later developed this into a model where electrons are arranged in shells around the nucleus.

Diagram showing the plum pudding model, Rutherford alpha scattering, and the Bohr nuclear model

Key Idea

Evidence changed the model

The alpha scattering experiment showed that atoms are mostly empty space and that positive charge and mass are concentrated in a tiny nucleus.

Example

Using scattering evidence

A student says: “If the plum pudding model were correct, alpha particles should mostly be strongly deflected.”

In the plum pudding model, positive charge is spread out through the atom, so no tiny region has a very large positive charge.
Alpha particles are positively charged, so they would only feel weak repulsion from a spread-out positive charge.
Large deflections need a concentrated positive charge, so the results support the nuclear model instead.

What radioactive decay means

Some nuclei are unstable. This means they can change into a more stable nucleus by emitting radiation.

Definition

Radioactive decay

Radioactive decay is the random process where an unstable nucleus emits radiation and changes into a more stable nucleus.

The decay of one particular nucleus is random: you cannot predict exactly when it will decay. However, with a very large number of nuclei, you can predict the overall pattern using half-life.

Types of radioactive decay

Alpha decay

An alpha particle is a helium nucleus: two protons and two neutrons.

It is written as:

24He^{4}_{2}\text{He}

In alpha decay:

mass number decreases by 4
atomic number decreases by 2

Beta-minus decay

In beta-minus decay, a neutron changes into a proton and an electron. The electron is emitted as beta-minus radiation.

neutron→proton+electron\text{neutron} \to \text{proton} + \text{electron}

In beta-minus decay:

mass number stays the same
atomic number increases by 1

The emitted electron can be written as $−10e^{0}_{-1}\text{e}$ .

Beta-plus decay

In beta-plus decay, a proton changes into a neutron and a positron. A positron is like an electron but has positive charge.

proton→neutron+positron\text{proton} \to \text{neutron} + \text{positron}

In beta-plus decay:

mass number stays the same
atomic number decreases by 1

The emitted positron can be written as $+10e^{0}_{+1}\text{e}$ .

Gamma radiation

Gamma radiation is electromagnetic radiation emitted from the nucleus. Nuclei that have already decayed often rearrange themselves and lose energy as gamma radiation.

In gamma emission:

mass number does not change
atomic number does not change

Neutron emission

In neutron emission, the nucleus emits a neutron, written as $01n^{1}_{0}\text{n}$ .

In neutron emission:

mass number decreases by 1
atomic number stays the same

Common Mistake

Gamma does not change the element

Gamma radiation is energy released from the nucleus. It does not change the number of protons or neutrons, so it does not change the element.

Balancing nuclear equations

In nuclear equations, the total mass number must be the same on both sides, and the total atomic number must be the same on both sides.

Key Idea

Balance mass and charge

For nuclear equations, balance the top numbers separately from the bottom numbers.

Example

Balancing an alpha decay equation

Complete this decay equation:

88226Ra→ZARn+24He^{226}_{88}\text{Ra} \to ^{A}_{Z}\text{Rn} + ^{4}_{2}\text{He}

Balance the mass numbers on the top: $226 = A + 4$ , so $A = 222$ .
Balance the atomic numbers on the bottom: $88 = Z + 2$ , so $Z = 86$ .
Write the completed equation: $88226Ra→86222Rn+24He^{226}_{88}\text{Ra} \to ^{222}_{86}\text{Rn} + ^{4}_{2}\text{He}$ .

Activity and the becquerel

The activity of a radioactive source is the rate at which unstable nuclei decay.

Definition

Activity

Activity is measured in becquerels, Bq. An activity of 1 Bq means 1 decay per second.

As time passes, there are fewer undecayed nuclei left, so fewer nuclei can decay each second. This means the activity decreases over time.

Half-life

Definition

Half-life

The half-life of a radioactive isotope is the time taken for half of the undecayed nuclei to decay, or for the activity of the source to fall by half.

Half-life does not tell you when one particular nucleus will decay. It lets you predict what happens to a large sample.

Graph showing radioactive activity halving every two days

On the graph, the activity halves from 80 Bq to 40 Bq in 2 days, then to 20 Bq after another 2 days. So the half-life is 2 days.

Example

Using half-life to calculate activity

A radioactive source has an activity of 320 Bq. Its half-life is 5 days. Find its activity after 15 days.

Work out how many half-lives have passed: $15 \div 5 = 3$ half-lives.
Halve the activity once for each half-life: 320 Bq becomes 160 Bq, then 80 Bq, then 40 Bq.
After 15 days, the activity is 40 Bq.

Common Mistake

Background count

If a question gives a background count rate, subtract it before using half-life. Half-life calculations should use the radiation from the source, not the background radiation already present.

Uses of radioactivity

In GCSE Physics 1PH0, you also need to describe important uses of radioactivity.

Smoke alarms

Some smoke alarms use alpha radiation to ionise air, allowing a small current to flow. Smoke absorbs the alpha radiation, the current drops, and the alarm sounds.

Irradiating food

Food can be exposed to gamma radiation to kill bacteria and reduce spoilage. The food does not become radioactive.

Sterilising equipment

Medical equipment can be sterilised using gamma radiation. This kills microorganisms without needing high temperatures.

Tracing and thickness gauging

A tracer is a radioactive substance used to follow the movement of a material, such as fluid in a pipe or a substance in the body.

In thickness gauging, radiation passes through a material to a detector. If the count rate is too high, the material is too thin. If the count rate is too low, the material is too thick.

Diagnosis and treatment of cancer

Radioactive tracers can help doctors diagnose disease by showing how substances move through the body. Radiation can also be used in treatment to kill cancer cells, although it must be carefully targeted to reduce damage to healthy tissue.

Example

Choosing radiation for a thickness gauge

A factory measures the thickness of aluminium foil using a source and detector. Which type of radiation is most suitable?

Alpha radiation would be stopped too easily, even by very thin material, so it would not give useful changes for foil thickness.
Gamma radiation is very penetrating, so most of it may pass through even when the foil is thicker.
Beta radiation is partly absorbed by thin aluminium, so changes in thickness produce clear changes in detector count rate.

Common Mistake

Irradiated does not mean radioactive

Food that has been irradiated has been exposed to radiation. It does not become a radioactive source.

Dangers and precautions

Definition

Ionising radiation

Ionising radiation can remove electrons from atoms, forming ions. In living tissue, this can damage cells and may cause mutations in DNA.

Radiation can kill cells or make them divide uncontrollably, which can lead to cancer. The risk depends on the type of radiation, the activity, whether the source is inside or outside the body, and the half-life.

Precautions include:

keeping exposure time as short as possible
standing as far away as possible from sources
using shielding, such as lead or thick concrete
using tongs or remote handling tools
wearing film badges or electronic dose monitors
storing sources in labelled, shielded containers

For Separate Physics content, you should also link danger to half-life. A short half-life source may have high activity at first but becomes much less active quickly. A long half-life source can remain hazardous for a very long time.

Tip

Choosing a medical tracer

A medical tracer should have a short enough half-life to reduce the patient’s dose, but long enough for doctors to carry out the test.

Exam technique

In the exam

For decay equations, always balance the top numbers and bottom numbers separately.
For half-life calculations, count how many times the activity halves; do not assume the graph is a straight line.
For uses and dangers, link your answer to penetration, ionisation, half-life, and exposure precautions.

Self review

Check yourself

What changes to mass number and atomic number happen in alpha, beta-minus, beta-plus, gamma and neutron emission?
Why can half-life predict the activity of a large sample but not the decay time of one nucleus?
Why is beta radiation often suitable for thickness gauging thin materials?

Radioactive decay, half-life and uses

What you'll learn

How the atomic model changed from “plum pudding” to the nuclear model.
What happens in alpha, beta, gamma and neutron emission.
How to balance nuclear equations using mass number and charge.
How half-life links to activity, uses of radioactivity, and radiation risks.

The atom: the starting point

An atom is the smallest part of an element that still behaves like that element. It has a tiny central nucleus, containing protons and neutrons, with electrons around the outside.

A proton has relative charge +1.
A neutron has relative charge 0.
An electron has relative charge -1.

The nucleus is very small compared with the whole atom, but it contains almost all the atom’s mass.

Definition

Atomic number and mass number

The atomic number, $Z$ , is the number of protons in the nucleus. It decides which element the atom is.
The mass number, $A$ , is the total number of protons and neutrons in the nucleus.
The number of neutrons is found using $A - Z$ .
An isotope is an atom of the same element with the same number of protons but a different number of neutrons.

Nuclear notation is written like this:

ZAX^{A}_{Z}\text{X}

where X is the chemical symbol of the element.

Example

Finding protons and neutrons

A nucleus is written as $614C^{14}_{6}\text{C}$ .

Use the bottom number for the number of protons: $Z = 6$ , so carbon has 6 protons.
Use the top number for total protons plus neutrons: $A = 14$ .
Subtract to find neutrons: $14 - 6 = 8$ , so this nucleus has 8 neutrons.

How the atomic model changed

Scientific models change when new evidence cannot be explained by the old model.

Early in the 1900s, the plum pudding model described the atom as a ball of positive charge with negative electrons embedded in it.

Bohr later developed this into a model where electrons are arranged in shells around the nucleus.

Diagram showing the plum pudding model, Rutherford alpha scattering, and the Bohr nuclear model

Key Idea

Evidence changed the model

The alpha scattering experiment showed that atoms are mostly empty space and that positive charge and mass are concentrated in a tiny nucleus.

Example

Using scattering evidence

A student says: “If the plum pudding model were correct, alpha particles should mostly be strongly deflected.”

In the plum pudding model, positive charge is spread out through the atom, so no tiny region has a very large positive charge.
Alpha particles are positively charged, so they would only feel weak repulsion from a spread-out positive charge.
Large deflections need a concentrated positive charge, so the results support the nuclear model instead.

What radioactive decay means

Some nuclei are unstable. This means they can change into a more stable nucleus by emitting radiation.

Definition

Radioactive decay

Radioactive decay is the random process where an unstable nucleus emits radiation and changes into a more stable nucleus.

The decay of one particular nucleus is random: you cannot predict exactly when it will decay. However, with a very large number of nuclei, you can predict the overall pattern using half-life.