What Is Nuclear Stability?

A nucleus contains positively charged protons and electrically neutral neutrons.

Some combinations of protons and neutrons form nuclei that remain essentially unchanged for extremely long periods. These nuclei are described as stable.

Other combinations are unstable. An unstable nucleus can spontaneously transform into another nucleus while releasing particles or electromagnetic radiation.

This process is called radioactive decay.

Whether a nucleus is stable depends on several factors, including:

• the number of protons
• the number of neutrons
• the neutron-to-proton ratio
• the competition between the strong nuclear interaction and electrical repulsion
• nuclear binding energy
• nuclear shell structure

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The Competition Inside the Nucleus

Two important interactions influence nuclear stability.

Strong Nuclear Interaction

The strong nuclear interaction provides the short-range attraction that binds nucleons together.

At nuclear distances, it is extremely strong.

Electromagnetic Interaction

Protons are positively charged.

Therefore, every proton electrically repels every other proton.

As the number of protons increases, this electrical repulsion becomes increasingly important.

Nuclear stability therefore involves a competition between:

nuclear attraction

and

proton-proton electrical repulsion

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Why Are Neutrons Important?

Neutrons contribute to nuclear binding through the strong interaction but do not add electrical repulsion because they have no electric charge.

This makes neutrons particularly important in larger nuclei.

A neutron can contribute to the attractive nuclear interactions without adding another positively charged proton.

As nuclei become larger, they generally require more neutrons relative to protons to remain stable.

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The Neutron-to-Proton Ratio

An important indicator of nuclear stability is the neutron-to-proton ratio, usually written:

N/Z

where:

N = number of neutrons

Z = number of protons

For example, carbon-12 contains:

6 neutrons

6 protons

Therefore:

N/Z = 6/6 = 1.0

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Example: Carbon-14

Carbon-14 contains:

Z = 6

A = 14

Therefore:

N = A − Z

N = 14 − 6 = 8

Its neutron-to-proton ratio is:

N/Z = 8/6

N/Z ≈ 1.33

Carbon-14 is radioactive.

Eventually, it undergoes a nuclear transformation that moves the nucleus toward a more stable configuration.

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Stable Light Nuclei

For many light stable nuclei:

N ≈ Z

This means they contain approximately equal numbers of neutrons and protons.

Examples include:

However, N = Z is not a universal rule for stability.

As nuclei become heavier, stable nuclei generally contain more neutrons than protons.

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Stable Heavy Nuclei

Consider lead-208:

²⁰⁸₈₂Pb

Protons:

Z = 82

Neutrons:

N = 208 − 82 = 126

Therefore:

N/Z = 126/82

N/Z ≈ 1.54

Lead-208 is stable despite having considerably more neutrons than protons.

This illustrates an important trend:

Light stable nuclei → N/Z close to 1

Heavier stable nuclei → N/Z becomes greater than 1

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The Band of Stability

If we plot the number of neutrons against the number of protons for known nuclei, stable nuclei occupy a region called the band of stability or valley of stability.

For light nuclei, the band lies close to:

N = Z

As proton number increases, the band gradually moves toward:

N > Z

This happens because larger nuclei require additional neutrons to help maintain nuclear binding without increasing electrical repulsion.

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Reading a Stability Graph

A typical nuclear stability graph has:

Horizontal axis → number of protons, Z

Vertical axis → number of neutrons, N

Stable nuclei form a narrow band.

Nuclei outside this band tend to be radioactive.

The position of an unstable nucleus relative to the band can help us predict the type of nuclear transformation it may undergo.

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Neutron-Rich Nuclei

A nucleus above the band of stability contains too many neutrons relative to protons.

Such a nucleus may move toward stability through beta-minus decay.

During beta-minus decay, a neutron is effectively transformed into a proton:

n → p + e⁻ + ν̄ₑ

where:

e⁻ = electron

ν̄ₑ = electron antineutrino

The result is:

Neutrons decrease by 1

Protons increase by 1

The mass number stays the same.

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Example: Carbon-14

Carbon-14 contains:

6 protons

8 neutrons

It undergoes beta-minus decay:

¹⁴₆C → ¹⁴₇N + e⁻ + ν̄ₑ

After the transformation, nitrogen-14 contains:

7 protons

7 neutrons

Nitrogen-14 is stable.

The transformation has moved the nucleus toward a more stable neutron-to-proton balance.

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Proton-Rich Nuclei

A nucleus below the band of stability has too many protons relative to neutrons.

Such nuclei may move toward stability through processes such as:

• beta-plus decay
• electron capture

In beta-plus decay, a proton is effectively transformed into a neutron:

p → n + e⁺ + νₑ

within an energetically allowed nuclear process.

The result is:

Protons decrease by 1

Neutrons increase by 1

Again, the mass number remains unchanged.

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Electron Capture

Some proton-rich nuclei undergo electron capture instead.

An inner atomic electron is captured by the nucleus and interacts with a proton:

p + e⁻ → n + νₑ

The proton becomes a neutron.

Therefore:

Z decreases by 1

while:

A remains unchanged

Both beta-plus decay and electron capture can move a proton-rich nucleus toward the band of stability.

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Very Heavy Nuclei

For very heavy nuclei, another problem develops.

There are so many protons that the electrical repulsion between them becomes increasingly difficult for the short-range nuclear interaction to counteract.

Very heavy nuclei are therefore generally unstable.

They may undergo processes such as:

• alpha decay
• spontaneous fission

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Alpha Decay

An alpha particle contains:

2 protons + 2 neutrons

It is equivalent to a helium-4 nucleus:

⁴₂He

When a heavy nucleus emits an alpha particle:

A decreases by 4

Z decreases by 2

For example:

²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

This reduces both the size and charge of the original nucleus.

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Why Do Unstable Nuclei Decay?

An unstable nucleus is in a state from which an energetically allowed transformation can produce a more stable configuration.

Through radioactive decay, the nucleus can move toward a state with lower total energy.

The process may change:

• the neutron-to-proton ratio
• the number of protons
• the number of neutrons
• the total size of the nucleus
• the internal energy of the nucleus

Energy can be released as kinetic energy of particles, neutrinos, and electromagnetic radiation.

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Binding Energy and Stability

Nuclear stability is also connected to binding energy.

A nucleus with a high binding energy per nucleon is generally more tightly bound than one with a lower binding energy per nucleon.

The binding-energy curve reaches its highest region around medium-mass nuclei near iron and nickel.

However, binding energy per nucleon alone does not determine whether an individual isotope is radioactive.

The neutron-to-proton ratio, nuclear energy levels, shell structure, and possible decay pathways must also be considered.

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Nuclear Shells

Protons and neutrons occupy quantum energy levels within the nucleus.

Certain numbers of protons or neutrons produce particularly stable nuclear arrangements.

These are called magic numbers.

Common magic numbers include:

2, 8, 20, 28, 50, 82, 126

For example, lead-208 contains:

82 protons

126 neutrons

Both are magic numbers.

This contributes to the exceptional stability of the lead-208 nucleus.

The nuclear shell model is more advanced, but it helps explain why some nuclei are more stable than a simple neutron-to-proton calculation might suggest.

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Even and Odd Numbers of Nucleons

Another trend appears when examining stable nuclei.

Nuclei containing even numbers of protons and even numbers of neutrons are particularly common among stable nuclides.

Nuclei with both an odd proton number and an odd neutron number are much less commonly stable.

This is related to the tendency of nucleons to form energetically favourable pairs inside the nucleus.

Therefore, nuclear stability depends on more than simply counting neutrons and protons.

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Predicting Nuclear Stability

We can use several general trends.

Trend 1: Light nuclei

Stable nuclei usually have approximately:

N ≈ Z

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Trend 2: Increasing nuclear size

As proton number increases:

N/Z generally increases

Heavy stable nuclei therefore contain more neutrons than protons.

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Trend 3: Too many neutrons

A neutron-rich nucleus may undergo:

beta-minus decay

This changes a neutron into a proton.

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Trend 4: Too many protons

A proton-rich nucleus may undergo:

beta-plus decay or electron capture

These processes effectively change a proton into a neutron.

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Trend 5: Very heavy nuclei

Very heavy nuclei are generally unstable and may undergo:

alpha decay

or sometimes:

spontaneous fission

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A Simple Prediction Table

These are general trends, not absolute rules. Actual decay depends on which transformations are energetically and quantum-mechanically allowed.

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Gamma Decay and Stability

Sometimes a nucleus has the correct numbers of protons and neutrons but is left in an excited nuclear state.

It can release excess energy by emitting a gamma-ray photon.

excited nucleus → lower-energy nucleus + γ

During gamma emission:

A does not change

and:

Z does not change

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

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Example: Predicting the Trend

Suppose a relatively light nucleus contains:

8 protons

12 neutrons

Its neutron-to-proton ratio is:

N/Z = 12/8 = 1.5

For a light nucleus, this is strongly neutron-rich.

We would therefore expect it to be unstable.

A likely route toward greater stability would be beta-minus decay, because this changes:

one neutron → one proton

After one beta-minus transformation:

Protons = 9

Neutrons = 11

The neutron-to-proton imbalance has been reduced.

Whether that particular daughter nucleus is itself stable requires consideration of the actual nuclides involved.

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Example: Comparing Two Nuclei

Consider:

Carbon-12: 6 protons, 6 neutrons

and:

Carbon-16: 6 protons, 10 neutrons

Carbon-12 has:

N/Z = 6/6 = 1.00

Carbon-16 has:

N/Z = 10/6 ≈ 1.67

Carbon-16 is extremely neutron-rich for such a light nucleus.

Therefore, we would predict:

Carbon-12 → stable

Carbon-16 → unstable

Carbon-16 can undergo nuclear transformations that move its products toward more stable neutron-to-proton combinations.

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The Chart of Nuclides

Physicists often use a chart of nuclides rather than a conventional periodic table when studying nuclear physics.

A chart of nuclides organizes nuclei according to:

• proton number
• neutron number
• stability
• radioactive decay behaviour

It allows scientists to see the band of stability and identify neutron-rich and proton-rich isotopes.

The periodic table is mainly organized around chemical behaviour.

The chart of nuclides is organized around nuclear composition and behaviour.

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Did You Know?

Only a relatively narrow range of proton-neutron combinations produces stable nuclei.

Thousands of other nuclides are known, but most are radioactive.

Some unstable nuclei survive for billions of years, while others exist for only tiny fractions of a second.

So unstable does not necessarily mean that a nucleus decays immediately.

The rate of decay is described using another important concept:

half-life.

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Connecting Nuclear Stability

Nuclear stability can be understood as the result of several connected factors:

Number of protons and neutrons

↓

Neutron-to-proton ratio

↓

Strong nuclear attraction vs electrical repulsion

↓

Nuclear shell and pairing effects

↓

Available lower-energy nuclear states

↓

Stable nucleus or radioactive transformation

If a nucleus has an energetically available pathway to a more stable state, it may undergo radioactive decay.

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Key Terms

Nuclear stability – The tendency of a nucleus to remain in its existing nuclear state.

Unstable nucleus – A nucleus capable of spontaneously transforming through radioactive decay.

Radioactive decay – A spontaneous nuclear transformation accompanied by the release of particles and/or radiation.

Neutron-to-proton ratio (N/Z) – The number of neutrons divided by the number of protons in a nucleus.

Band of stability – The region on a neutron-versus-proton graph containing stable nuclei.

Beta-minus decay – A radioactive process that effectively changes a neutron into a proton while emitting an electron and an electron antineutrino.

Beta-plus decay – A radioactive process that effectively changes a proton into a neutron while emitting a positron and an electron neutrino.

Electron capture – A process in which the nucleus captures an electron, converting a proton into a neutron and emitting a neutrino.

Alpha decay – The emission of a helium-4 nucleus from an unstable nucleus.

Magic number – A proton or neutron number associated with particularly stable closed nuclear shells.

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Key Takeaways

• Nuclear stability depends strongly on the balance between protons and neutrons.
• The strong nuclear interaction helps bind nucleons together, while positively charged protons electrically repel each other.
• Neutrons contribute to nuclear binding without adding electrical repulsion.
• Light stable nuclei often have N/Z close to 1.
• As nuclei become heavier, stable nuclei generally require more neutrons than protons.
• Stable nuclei occupy a region called the band of stability.
• Neutron-rich nuclei often move toward stability through beta-minus decay.
• Proton-rich nuclei often undergo beta-plus decay or electron capture.
• Very heavy nuclei commonly undergo alpha decay, and some can undergo spontaneous fission.
• Gamma emission allows an excited nucleus to lose energy without changing its proton or neutron numbers.
• Nuclear binding energy, proton-neutron balance, nuclear shells, and nucleon pairing all contribute to stability.
• Radioactive transformations allow unstable nuclei to move toward lower-energy, more stable nuclear configurations.