Atomic Nuclei and Radioactivity

What Is Radioactivity?

Radioactivity is the spontaneous emission of radiation from an unstable atomic nucleus.

Some combinations of protons and neutrons produce stable nuclei. Other combinations are unstable. An unstable nucleus can change into a more stable arrangement by undergoing radioactive decay.

During radioactive decay, the nucleus may emit particles or electromagnetic radiation.

The original unstable nucleus is often called the parent nucleus, while the nucleus produced after the decay is called the daughter nucleus.

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Radioactivity Is a Nuclear Process

Radioactivity occurs within the nucleus of an atom.

The nucleus contains:

• Protons
• Neutrons

Radioactive decay can change the number or arrangement of these particles.

This is fundamentally different from an ordinary chemical reaction.

In a chemical reaction, atoms rearrange and electrons may be transferred or shared, but the nuclei normally remain unchanged.

In radioactive decay, the nucleus itself changes.

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Spontaneous Radioactive Decay

Radioactive decay is described as spontaneous.

This means that an unstable nucleus can decay without needing an external trigger.

It does not need to be:

• Heated
• Burned
• Mixed with another chemical
• Exposed to light
• Given an electrical current

The instability is a property of the nucleus itself.

Under ordinary conditions, changing the temperature, pressure, or chemical state of a radioactive material has essentially no effect on its nuclear decay rate.

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Radioactive Decay Is Random

Radioactive decay is also random.

Suppose you have one particular unstable nucleus.

You cannot predict exactly when that individual nucleus will decay.

It might decay:

• In the next second
• Several minutes later
• Years later
• Thousands of years later

There is no countdown clock inside the nucleus that allows us to predict the exact moment of decay.

However, although individual decay events are random, the behaviour of a large number of radioactive nuclei is statistically predictable.

This distinction is extremely important.

Individual decay → unpredictable

Large population → predictable statistical pattern

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A Useful Analogy

Imagine a large container holding thousands of coins.

Suppose every few seconds the coins are tossed and all coins showing heads are removed.

You cannot predict which particular coin will show heads on the next toss.

However, with a sufficiently large number of coins, you can make a good prediction about the approximate fraction that will remain after several rounds.

Radioactive decay behaves in a similar statistical way.

We cannot predict which nucleus will decay next, but we can predict the behaviour of a very large population of radioactive nuclei.

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Probability of Decay

Each unstable nucleus has a certain probability of decaying during a given period of time.

Importantly, an unstable nucleus does not become increasingly "ready" to decay simply because it has existed for a long time.

For a particular radioactive isotope, the decay probability per unit time remains characteristic of that isotope.

This statistical behaviour leads to the concepts of:

• Activity
• Decay constant
• Half-life

These allow scientists to describe radioactive samples even though individual decay events remain unpredictable.

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What Happens During Radioactive Decay?

During radioactive decay, an unstable nucleus changes.

Depending on the type of decay, the nucleus may:

• Lose protons and neutrons
• Convert a neutron into a proton
• Convert a proton into a neutron
• Release excess nuclear energy

The decay may produce:

• Alpha particles
• Beta particles
• Gamma radiation

Different types of radioactive decay affect the nucleus in different ways.

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Alpha Decay

An alpha particle consists of:

• 2 protons
• 2 neutrons

It is therefore identical to a helium-4 nucleus.

When a nucleus emits an alpha particle:

Proton number decreases by 2

and:

Nucleon number decreases by 4

Because the proton number changes, alpha decay produces a different element.

For example, uranium-238 can undergo alpha decay.

The uranium nucleus contains:

• 92 protons
• 146 neutrons

After emitting an alpha particle, the daughter nucleus contains:

• 90 protons
• 144 neutrons

Atomic number 90 corresponds to thorium.

Therefore:

Uranium-238 → Thorium-234 + alpha particle

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Beta-Minus Decay

In beta-minus decay, a neutron in the nucleus is transformed into a proton.

An electron and an antineutrino are emitted.

The main change inside the nucleus is:

neutron → proton

Therefore:

• Number of neutrons decreases by 1.
• Number of protons increases by 1.
• Nucleon number remains unchanged.

Because the number of protons changes, the nucleus becomes a different element.

Carbon-14 undergoes beta-minus decay to form nitrogen-14.

Before decay, carbon-14 has:

• 6 protons
• 8 neutrons

After decay, nitrogen-14 has:

• 7 protons
• 7 neutrons

The total number of nucleons remains 14.

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Gamma Decay

Sometimes a nucleus has excess energy but does not need to change its numbers of protons or neutrons.

It can release this energy as gamma radiation.

Gamma radiation is high-energy electromagnetic radiation.

During gamma emission:

• Proton number does not change.
• Neutron number does not change.
• Nucleon number does not change.

The nucleus simply moves from a higher-energy state to a lower-energy state.

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Radioactive Decay Can Change the Element

An element is defined by its number of protons.

Therefore, if radioactive decay changes the proton number, the identity of the element changes.

This occurs in processes such as:

• Alpha decay
• Beta-minus decay
• Beta-plus decay

This transformation from one element into another is sometimes called nuclear transmutation.

Gamma decay is different because it does not change the proton number.

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Radioactivity vs Chemical Reactions

Radioactive decay and chemical reactions are fundamentally different processes.

This distinction is important because radioactivity is a nuclear phenomenon, not a chemical one.

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Example: Burning Uranium vs Uranium Decay

Suppose uranium takes part in a chemical reaction.

Its electrons may rearrange and uranium compounds may form.

However, the nuclei remain uranium nuclei because they still contain 92 protons.

Radioactive decay is different.

If uranium-238 undergoes alpha decay, its nucleus loses two protons.

It now contains:

90 protons

The nucleus is therefore no longer uranium.

It has become thorium.

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Activity

The activity of a radioactive sample tells us how many nuclear decays occur each second.

Activity is measured in becquerels (Bq).

1 Bq = 1 nuclear decay per second

For example:

500 Bq = 500 nuclear decays per second

A sample with an activity of 10,000 Bq has a greater rate of radioactive decay than a sample with an activity of 100 Bq.

Activity does not tell us the energy or biological effect of the radiation. It tells us the rate at which nuclei are decaying.

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Why Activity Decreases

As a radioactive sample decays, unstable nuclei are converted into daughter nuclei.

Therefore, the number of undecayed radioactive nuclei gradually decreases.

With fewer unstable nuclei remaining, fewer decays occur per second.

Therefore:

Number of radioactive nuclei decreases → activity decreases

The decrease follows a characteristic pattern called exponential decay.

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Half-Life

The half-life of a radioactive isotope is the time required for the expected number of undecayed nuclei in a large sample to decrease to half its original value.

It can also be described as the time required for the activity of a large sample to fall to half its initial value.

For example, suppose a sample begins with an activity of:

800 Bq

After one half-life:

400 Bq

After two half-lives:

200 Bq

After three half-lives:

100 Bq

The sample does not normally reach exactly zero after a particular number of half-lives.

Instead, the amount of radioactive material continues to decrease.

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Natural Radioactivity

Radioactivity is not something humans invented.

Radioactive materials have existed naturally on Earth throughout its history.

We are constantly exposed to small amounts of natural background radiation.

Natural sources include:

• Rocks and soil
• Radon gas
• Cosmic rays
• Radioactive isotopes in food and living organisms
• Naturally occurring radioactive elements in Earth's crust

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Radioactivity from Rocks and Soil

Earth's crust contains naturally occurring radioactive isotopes.

Examples include isotopes of:

• Uranium
• Thorium
• Potassium

Small amounts of these elements occur naturally in rocks and minerals.

Their radioactive decay contributes to the natural background radiation around us.

Some building materials made from rock can also contain small quantities of naturally radioactive isotopes.

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Radon Gas

Radon is a naturally occurring radioactive gas.

It can be produced during radioactive decay chains involving uranium found naturally in rocks and soil.

Radon can move through the ground and sometimes accumulate inside buildings.

Because radon itself is radioactive and its decay products can be inhaled, prolonged exposure to elevated radon concentrations can increase health risks.

The amount of radon varies considerably depending on local geology and building conditions.

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Cosmic Radiation

Earth is continuously struck by high-energy particles arriving from space.

These are known as cosmic rays.

When cosmic rays interact with Earth's atmosphere, they can produce additional particles and radiation.

Therefore, cosmic radiation contributes to natural background radiation.

Exposure generally increases with altitude because there is less atmosphere above to absorb the incoming radiation.

This is why people travelling frequently at high altitude can receive slightly greater exposure to cosmic radiation than people remaining near sea level.

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Radioactivity Inside Living Organisms

Living organisms naturally contain small quantities of radioactive isotopes.

For example, the human body contains naturally occurring:

• Carbon-14
• Potassium-40

These enter organisms through normal biological processes involving food, water and the environment.

Therefore, a small amount of radioactivity is naturally present within living things.

This is another component of natural background radiation.

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Naturally Occurring Radioactive Isotopes

Some important naturally occurring radioactive isotopes include:

Carbon-14

Carbon-14 is produced naturally in the atmosphere through interactions involving cosmic radiation.

It becomes incorporated into living organisms and is used in radiocarbon dating.

Potassium-40

Potassium-40 occurs naturally alongside other potassium isotopes.

Because potassium is essential to living organisms, small amounts of potassium-40 occur naturally in the human body.

Uranium-238

Uranium-238 occurs naturally in rocks and minerals.

Its radioactive decay is part of a long decay chain that eventually produces stable nuclei.

Thorium-232

Thorium-232 is another naturally occurring radioactive isotope found in Earth's crust.

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Natural Does Not Automatically Mean Harmless

A substance being natural does not mean that it is automatically harmless.

Ionising radiation can damage biological tissue regardless of whether its source is natural or artificial.

The effect depends on factors such as:

• Type of radiation
• Energy
• Activity of the source
• Duration of exposure
• Distance from the source
• Whether the radioactive material is outside or inside the body

At the same time, background radiation is a normal part of Earth's environment.

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Detecting Radioactivity

Radioactivity cannot normally be detected directly by human senses.

We cannot reliably:

• See it
• Smell it
• Hear it
• Taste it
• Feel low-level radiation exposure

Special instruments are therefore required.

Examples include:

• Geiger-Müller tubes
• Scintillation detectors
• Semiconductor detectors

These devices detect the effects produced when radiation interacts with matter.

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Background Count

A radiation detector may record events even when no laboratory radioactive source has been placed nearby.

This is called the background count.

Background radiation can come from natural sources such as:

• Cosmic radiation
• Rocks
• Radon
• Radioactive isotopes in the surroundings

When measuring the activity of a source experimentally, scientists may need to account for this background radiation.

For example:

Measured count rate = 150 counts/s

Background count rate = 20 counts/s

Then the count rate attributed to the source is approximately:

Source count rate = 150 − 20

Source count rate = 130 counts/s

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Random Does Not Mean Patternless

It is easy to misunderstand the word random.

Radioactive decay is random at the level of individual nuclei, but large samples show very clear mathematical behaviour.

If you measure a large radioactive sample repeatedly, the exact number of decays in each short interval may fluctuate.

However, over longer periods and large numbers of nuclei, predictable patterns emerge.

This is why scientists can reliably measure:

• Activity
• Half-life
• Decay constants

without being able to predict the decay time of a particular nucleus.

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Common Mistakes

Saying Radioactive Decay Can Be Predicted for an Individual Nucleus

We cannot predict exactly when a particular unstable nucleus will decay.

Decay is random.

Thinking Random Means Scientists Cannot Predict Anything

Large populations of radioactive nuclei behave statistically in predictable ways.

Confusing Radioactive Decay with a Chemical Reaction

Radioactive decay changes the nucleus.

Chemical reactions mainly involve electrons.

Assuming Radioactivity Requires an External Trigger

Radioactive decay is spontaneous.

An unstable nucleus does not need to be heated or chemically reacted before it can decay.

Thinking All Radiation Is Artificial

Natural background radiation has always been present.

Sources include rocks, radon, cosmic radiation and naturally occurring isotopes.

Assuming Radioactive Decay Always Changes the Element

Alpha and many beta decays change the proton number and therefore the element.

Gamma emission does not change the proton number.

Thinking Activity and Count Rate Are Exactly the Same

Activity describes actual nuclear decays per second.

A detector usually records only some of the emitted radiation, so its measured count rate may be lower than the source's activity.

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Check Your Understanding

1. Define radioactivity.

2. What makes a nucleus radioactive?

3. What does it mean to say radioactive decay is spontaneous?

4. What does it mean to say radioactive decay is random?

5. Can scientists predict exactly when a particular radioactive nucleus will decay? Explain.

6. Why can scientists still make reliable predictions about large radioactive samples?

7. Explain the main difference between radioactive decay and a chemical reaction.

8. Which part of an atom changes during radioactive decay?

9. How does alpha decay change proton number and nucleon number?

10. How does beta-minus decay change the numbers of protons and neutrons?

11. Does gamma emission change the proton number? Explain.

12. What is measured in becquerels?

13. Identify three naturally occurring sources of background radiation.

14. Explain how radon contributes to natural background radiation.

15. Explain why a radiation detector may record a count even when no laboratory radioactive source is nearby.

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Key Terms

• Radioactivity – the spontaneous emission of radiation from an unstable atomic nucleus.
• Radioactive decay – the spontaneous transformation of an unstable nucleus.
• Unstable nucleus – a nucleus capable of spontaneously undergoing radioactive decay.
• Parent nucleus – the original radioactive nucleus before decay.
• Daughter nucleus – the nucleus produced by radioactive decay.
• Spontaneous – occurring without the need for an external trigger.
• Random decay – decay for which the exact time of an individual nuclear event cannot be predicted.
• Alpha decay – radioactive decay involving emission of an alpha particle.
• Beta decay – radioactive decay involving a change between a proton and neutron and emission of beta radiation and other particles.
• Gamma radiation – high-energy electromagnetic radiation emitted by an excited nucleus.
• Activity – the number of nuclear decays occurring each second.
• Becquerel (Bq) – the SI unit of activity; one decay per second.
• Half-life – the time required for the expected number of undecayed nuclei in a large sample, or its activity, to decrease to half its initial value.
• Background radiation – ionising radiation naturally or artificially present in the environment.
• Radon – a naturally occurring radioactive noble gas.
• Cosmic rays – high-energy particles originating from space.

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Key Takeaways

• Radioactivity is the spontaneous emission of radiation from unstable atomic nuclei.
• Radioactive decay is a nuclear process, not a chemical reaction.
• Individual radioactive decay events occur randomly.
• Scientists cannot predict exactly when one particular unstable nucleus will decay.
• Large populations of radioactive nuclei nevertheless behave in statistically predictable ways.
• Radioactive decay changes the energy, composition, or both of the nucleus.
• Alpha decay removes two protons and two neutrons from a nucleus.
• Beta decay changes the balance of protons and neutrons.
• Gamma emission releases excess nuclear energy without changing proton or neutron numbers.
• Activity measures the number of nuclear decays occurring each second and is measured in becquerels.
• Radioactivity occurs naturally throughout the environment.
• Natural sources include rocks and soil, radon gas, cosmic radiation, and naturally occurring radioactive isotopes in living organisms.
• Background radiation is therefore a normal feature of Earth's environment.