Atomic Nuclei and Radioactivity

Why Are Some Nuclei Stable?

Atomic nuclei contain protons and neutrons packed into an extremely small region.

Protons are positively charged, so they repel one another through the electrostatic force. At the same time, protons and neutrons experience the strong nuclear force, which can hold nucleons together when they are extremely close.

A nucleus is stable when the combination and arrangement of its protons and neutrons allow it to remain together without spontaneously changing.

An unstable nucleus eventually changes into a more stable arrangement by undergoing radioactive decay.

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The Forces Inside the Nucleus

Two interactions are especially important when thinking about nuclear stability.

Strong Nuclear Force

The strong nuclear force:

• Acts between nucleons.
• Is attractive over typical distances between neighbouring nucleons.
• Is extremely strong at nuclear distances.
• Acts only over a very short range.

It helps bind protons and neutrons together in the nucleus.

Electrostatic Repulsion

Every proton has a positive electric charge.

Therefore, every proton electrically repels every other proton in the nucleus.

This repulsion tends to push the nucleus apart.

Nuclear stability therefore depends partly on the balance between the attractive nuclear interaction and the electrical repulsion between protons.

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Why Are Neutrons Important?

Neutrons contribute to the attractive nuclear interactions between nucleons without adding additional electrical repulsion.

This makes neutrons particularly important in larger nuclei.

A nucleus with too few neutrons relative to its number of protons may be unstable.

However, simply adding more and more neutrons does not guarantee stability.

A nucleus can also become unstable if it contains too many neutrons.

This leads to an important concept:

Nuclear stability depends strongly on the balance between the numbers of neutrons and protons.

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Neutron-to-Proton Ratio

The neutron-to-proton ratio compares the number of neutrons, N, with the number of protons, Z.

It can be written in ordinary text as:

Neutron-to-proton ratio = N / Z

For example, carbon-12 contains:

• 6 neutrons
• 6 protons

Therefore:

N / Z = 6 / 6 = 1

Carbon-12 is stable.

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Stability in Light Nuclei

For many light stable nuclei, the number of neutrons is approximately equal to the number of protons.

For example:

Carbon-12

• 6 protons
• 6 neutrons
• N / Z = 1

Oxygen-16

• 8 protons
• 8 neutrons
• N / Z = 1

Calcium-40

• 20 protons
• 20 neutrons
• N / Z = 1

This does not mean that every nucleus with equal numbers of protons and neutrons is stable. It is a general pattern rather than an absolute rule.

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Stability in Heavier Nuclei

As nuclei become larger, the situation changes.

A larger nucleus contains more protons, so there is more electrostatic repulsion.

Stable heavier nuclei therefore generally require more neutrons than protons.

For example, lead-208 contains:

• 82 protons
• 126 neutrons

Its neutron-to-proton ratio is approximately:

N / Z = 126 / 82 ≈ 1.54

Therefore, the stable neutron-to-proton ratio generally increases as nuclei become heavier.

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The Band of Stability

If neutron number is plotted against proton number for many nuclei, the stable nuclei occupy a region often called the band of stability or valley of stability.

For lighter nuclei, this region lies relatively close to:

N = Z

For heavier nuclei, the stable region shifts toward:

N > Z

This pattern shows that there is no single neutron-to-proton ratio that guarantees stability for every nucleus.

Instead, the most stable balance changes with nuclear size.

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Too Many Neutrons

A nucleus with too many neutrons relative to its proton number may be unstable.

One way such a nucleus can move toward greater stability is through beta-minus decay.

During beta-minus decay, a neutron is transformed into a proton, with other particles also being emitted.

At the nuclear level:

neutron → proton + electron + antineutrino

The emitted electron is the beta-minus particle.

The important change in the nucleus is:

• Neutrons decrease by 1.
• Protons increase by 1.
• Nucleon number stays the same.

This can move a neutron-rich nucleus closer to the stable region.

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Too Many Protons

A nucleus can also be unstable because it has too many protons relative to its number of neutrons.

Such nuclei may move toward greater stability through processes such as beta-plus decay or electron capture.

In beta-plus decay, a proton is transformed into a neutron, with other particles emitted.

The important nuclear change is:

• Protons decrease by 1.
• Neutrons increase by 1.
• Nucleon number remains unchanged.

This can move a proton-rich nucleus toward a more stable neutron-to-proton balance.

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Very Heavy Nuclei

For very large nuclei, having additional neutrons is eventually not enough to maintain stability.

The nucleus contains so many positively charged protons that electrical repulsion becomes increasingly significant.

Very heavy nuclei are therefore generally unstable.

They may undergo processes such as:

• Alpha decay
• Beta decay
• Spontaneous fission

For example, uranium-238 contains:

• 92 protons
• 146 neutrons

Despite having many more neutrons than protons, uranium-238 is still radioactive.

This shows why the neutron-to-proton ratio is important but is not the only factor determining nuclear stability.

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What Is a Stable Isotope?

A stable isotope has a nucleus that does not spontaneously undergo radioactive decay.

Examples include:

• Hydrogen-1
• Carbon-12
• Carbon-13
• Oxygen-16
• Oxygen-18

These nuclei can persist without spontaneously changing into different nuclei.

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What Is a Radioactive Isotope?

A radioactive isotope, or radioisotope, contains an unstable nucleus.

The nucleus spontaneously changes through radioactive decay.

Examples include:

• Hydrogen-3
• Carbon-14
• Cobalt-60
• Uranium-235
• Uranium-238

During radioactive decay, the nucleus emits particles and/or electromagnetic radiation and changes toward a more stable configuration.

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Example: Carbon Isotopes

Carbon provides a useful comparison.

Carbon-12

Carbon-12 contains:

• 6 protons
• 6 neutrons

It is stable.

Carbon-13

Carbon-13 contains:

• 6 protons
• 7 neutrons

It is also stable.

Carbon-14

Carbon-14 contains:

• 6 protons
• 8 neutrons

Carbon-14 is radioactive.

It undergoes beta-minus decay.

This demonstrates an important point:

Atoms can belong to the same element while having nuclei with different stabilities.

All three are carbon because they all contain 6 protons.

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Example: Hydrogen Isotopes

The three well-known isotopes of hydrogen also illustrate nuclear stability.

Hydrogen-1

• 1 proton
• 0 neutrons
• Stable

Hydrogen-2

• 1 proton
• 1 neutron
• Stable

Hydrogen-2 is also called deuterium.

Hydrogen-3

• 1 proton
• 2 neutrons
• Radioactive

Hydrogen-3 is also called tritium.

Tritium has an unstable neutron-to-proton balance and undergoes beta-minus decay.

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Identifying an Unstable Isotope

Sometimes an isotope can be identified as unstable from known nuclear data.

For example:

¹⁴₆C

contains:

• 6 protons
• 14 − 6 = 8 neutrons

Carbon-14 is known to be radioactive.

Compare this with:

¹²₆C

which contains:

• 6 protons
• 6 neutrons

Carbon-12 is stable.

However, the neutron-to-proton ratio should not be treated as a simple formula that can always determine whether an unfamiliar isotope is stable.

Actual nuclear stability depends on several aspects of nuclear structure.

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Why Do Unstable Nuclei Decay?

An unstable nucleus is in a configuration that can transform into a lower-energy, more stable configuration.

Radioactive decay allows this transformation to occur.

The nucleus may emit:

• Alpha particles
• Beta particles
• Gamma radiation
• Other particles in particular nuclear processes

The exact type of decay depends on the structure and energy of the nucleus.

Radioactive decay is therefore a nuclear process, not a chemical reaction.

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Radioactive Decay Is Spontaneous

An important feature of radioactive decay is that it occurs spontaneously.

For a particular unstable nucleus, we cannot normally predict exactly when it will decay.

It might decay:

• Almost immediately
• Several seconds later
• Years later
• Millions or billions of years later

However, when very large numbers of radioactive nuclei are present, their overall behaviour is statistically predictable.

This leads to the concept of half-life, which is used to describe the rate of radioactive decay.

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Stable Does Not Mean Unchanging in Every Situation

Calling a nucleus stable means that it does not spontaneously undergo radioactive decay under ordinary conditions.

It does not mean that the nucleus can never change.

Nuclei can undergo nuclear reactions if they interact with particles or other nuclei under suitable conditions.

The distinction is therefore between:

Spontaneous radioactive decay

and:

A nuclear reaction caused by an interaction

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Stability Is More Complicated Than N / Z Alone

The neutron-to-proton ratio is an important guide, but real nuclear stability also depends on nuclear structure.

Important factors include:

• Number of protons
• Number of neutrons
• Nuclear energy
• Arrangement of nucleons
• Binding of nucleons within the nucleus

Some numbers of protons and neutrons produce particularly stable nuclear arrangements.

Therefore, two nuclei with apparently similar neutron-to-proton ratios can have different stabilities.

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Nuclear Binding

A stable nucleus exists because energy would be required to separate its nucleons.

The nucleons are held together by nuclear interactions.

The concept of binding energy describes how strongly the nucleus is bound.

In general, nuclear stability is closely related to how energetically favourable the arrangement of nucleons is.

An unstable nucleus can sometimes transform into a configuration with greater stability by releasing energy through radioactive decay.

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Stable vs Radioactive Isotopes

Both stable and radioactive isotopes are still isotopes.

The difference concerns the stability of their nuclei.

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Predicting General Trends

The following patterns are useful when considering nuclear stability:

Light stable nuclei

Usually have similar numbers of protons and neutrons.

Heavier stable nuclei

Usually contain more neutrons than protons.

Very neutron-rich nuclei

Are often radioactive.

Very proton-rich nuclei

Are often radioactive.

Very heavy nuclei

Are generally radioactive.

These are useful trends, but they should not be treated as perfect rules for every individual isotope.

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Common Mistakes

Assuming Stable Nuclei Always Have Equal Numbers of Protons and Neutrons

This is approximately true for many light stable nuclei.

Heavy stable nuclei normally contain more neutrons than protons.

Assuming More Neutrons Always Increase Stability

Additional neutrons can help stabilize larger nuclei, but too many neutrons can also make a nucleus unstable.

Assuming the N / Z Ratio Alone Determines Stability

The ratio is an important indicator, but nuclear stability also depends on nuclear structure and binding.

Confusing Radioactive Isotopes with Different Elements

Carbon-12 and carbon-14 are both carbon because they both contain 6 protons.

Carbon-14 being radioactive does not make it a different element.

Thinking Radioactive Decay Is a Chemical Reaction

Radioactive decay changes the nucleus.

Chemical reactions primarily involve electrons.

Thinking Scientists Can Predict When One Particular Nucleus Will Decay

Individual radioactive decay events are unpredictable.

Scientists can predict the statistical behaviour of large numbers of nuclei.

Assuming Stable Means the Nucleus Can Never Change

Stable nuclei do not spontaneously decay, but they can participate in nuclear reactions under suitable conditions.

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Check Your Understanding

1. What is meant by nuclear stability?

2. Which force helps bind nucleons together?

3. Why do protons repel one another?

4. Why are neutrons important for the stability of larger nuclei?

5. What is meant by the neutron-to-proton ratio?

6. Calculate N / Z for carbon-12.

7. Why do heavier stable nuclei generally contain more neutrons than protons?

8. What is the band of stability?

9. Why can a nucleus with too many neutrons be unstable?

10. Carbon-14 contains 6 protons and 8 neutrons. How does its composition differ from carbon-12?

11. Explain the difference between a stable isotope and a radioactive isotope.

12. Why are very heavy nuclei generally unstable?

13. Explain why uranium-238 can be radioactive even though it contains considerably more neutrons than protons.

14. Why is radioactive decay described as spontaneous?

15. Explain why the neutron-to-proton ratio is useful but cannot by itself perfectly predict nuclear stability.

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Key Terms

• Nuclear stability – the ability of a nucleus to remain without spontaneously undergoing radioactive decay.
• Stable isotope – an isotope whose nucleus does not spontaneously decay.
• Radioactive isotope – an isotope with an unstable nucleus that undergoes radioactive decay.
• Neutron-to-proton ratio – the ratio of the number of neutrons to the number of protons in a nucleus.
• Strong nuclear force – the interaction responsible for binding nucleons within nuclei.
• Electrostatic repulsion – the repulsive interaction between positively charged protons.
• Band of stability – the region containing stable nuclei when neutron number is plotted against proton number.
• Radioactive decay – the spontaneous transformation of an unstable atomic nucleus.
• Radioisotope – another term for a radioactive isotope.
• Beta-minus decay – a radioactive process that converts a neutron into a proton while emitting a beta-minus particle and an antineutrino.
• Binding energy – the energy associated with binding nucleons together in a nucleus.
• Half-life – the time required for the expected number of undecayed nuclei in a large sample to decrease to half its original value.

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Key Takeaways

• Nuclear stability depends on the balance of interactions and the arrangement of protons and neutrons in the nucleus.
• The strong nuclear interaction helps bind nucleons together, while positively charged protons electrically repel one another.
• The neutron-to-proton ratio is an important indicator of nuclear stability.
• Many light stable nuclei have approximately equal numbers of neutrons and protons.
• Heavier stable nuclei generally require more neutrons than protons.
• Too many or too few neutrons relative to the proton number can result in an unstable nucleus.
• Very heavy nuclei are generally radioactive.
• Stable isotopes do not spontaneously undergo radioactive decay.
• Radioactive isotopes contain unstable nuclei that spontaneously decay.
• Radioactive decay allows an unstable nucleus to transform toward a more stable, lower-energy configuration.
• Carbon-12 and carbon-13 are stable, while carbon-14 is radioactive.
• The neutron-to-proton ratio is useful for understanding stability, but it is not the only factor involved.
• Nuclear stability is ultimately connected to nuclear structure, interactions between nucleons, and nuclear binding energy.