Beta Decay

What Is Beta Radiation?

Beta radiation is produced when an unstable atomic nucleus undergoes beta decay.

There are two main types:

• beta-minus (β⁻) decay
• beta-plus (β⁺) decay

At this level, beta-minus decay is usually the main focus.

A beta-minus particle is a high-speed electron emitted from the nucleus during radioactive decay.

It can be represented as:

⁰₋₁e

or:

β⁻

A beta particle is not an electron that was previously orbiting the nucleus. It is produced during a change involving particles inside the nucleus.

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Properties of a Beta-Minus Particle

A beta-minus particle has:

• charge = −1e
• extremely small mass compared with a proton or neutron
• mass number = 0
• atomic-number contribution = −1 in nuclear equations

It is represented:

⁰₋₁e

Its mass number is written as zero because the electron is not a nucleon.

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What Happens During Beta-Minus Decay?

During beta-minus decay, a neutron changes into a proton.

At a more complete level:

neutron → proton + electron + electron antineutrino

or:

n → p + e⁻ + ν̄ₑ

The electron is emitted from the nucleus as beta radiation.

The antineutrino is also emitted.

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Why the Atomic Number Changes

Before beta-minus decay, the nucleus contains a neutron.

During decay:

neutron → proton

The number of protons therefore increases by one.

Since atomic number is the number of protons:

Z → Z + 1

Therefore, the nucleus becomes a different element.

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Why the Mass Number Does Not Change

A neutron changes into a proton.

Both the neutron and proton are nucleons.

Therefore, the total number of nucleons remains unchanged.

So:

A → A

The mass number does not change.

This gives the basic beta-minus rule:

mass number: no change

atomic number: increases by 1

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General Beta-Minus Decay Equation

A beta-minus decay can be represented:

ᴬ_ZX → ᴬ_Z₊₁Y + ⁰₋₁e + ν̄ₑ

where:

• X = parent element
• Y = daughter element
• A = mass number
• Z = atomic number
• ⁰₋₁e = beta-minus particle
• ν̄ₑ = electron antineutrino

In simpler introductory nuclear equations, the antineutrino is sometimes omitted, giving:

ᴬ_ZX → ᴬ_Z₊₁Y + ⁰₋₁e

However, including the antineutrino gives a more complete description.

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Example: Carbon-14

Carbon-14 has:

A = 14

Z = 6

During beta-minus decay:

Mass number:

14 → 14

Atomic number:

6 → 7

Element 7 is nitrogen.

Therefore:

¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄ₑ

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Checking the Carbon-14 Equation

Check mass numbers:

Left:

14

Right:

14 + 0 = 14

Therefore:

14 = 14 ✓

Check atomic numbers:

Left:

6

Right:

7 + (−1)

7 − 1 = 6

Therefore:

6 = 6 ✓

The equation balances.

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Example: Hydrogen-3

Hydrogen-3, also called tritium, undergoes beta-minus decay.

Hydrogen has atomic number:

Z = 1

After beta-minus decay:

Z = 2

Element 2 is helium.

Mass number remains:

A = 3

Therefore:

³₁H → ³₂He + ⁰₋₁e + ν̄ₑ

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Example: Phosphorus-32

Phosphorus-32 has:

A = 32

Z = 15

During beta-minus decay:

A remains 32.

Z increases:

15 → 16

Element 16 is sulfur.

Therefore:

³²₁₅P → ³²₁₆S + ⁰₋₁e + ν̄ₑ

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Example: Strontium-90

Strontium has atomic number:

38

During beta-minus decay:

Z = 38 + 1

Z = 39

Element 39 is yttrium.

Therefore:

⁹⁰₃₈Sr → ⁹⁰₃₉Y + ⁰₋₁e + ν̄ₑ

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Identifying an Unknown Daughter

Complete:

¹³¹₅₃I → ? + ⁰₋₁e + ν̄ₑ

Mass number remains:

A = 131

Atomic number increases:

53 + 1 = 54

Element 54 is xenon.

Therefore:

¹³¹₅₃I → ¹³¹₅₄Xe + ⁰₋₁e + ν̄ₑ

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A Useful Beta-Minus Shortcut

For beta-minus decay, remember:

A stays the same

Z goes up by 1

So:

ᴬ_ZX → ᴬ_Z₊₁Y + β⁻

This is the fastest way to determine the daughter nucleus in introductory problems.

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Why Does the Element Change?

An element is defined by its number of:

protons

During beta-minus decay:

neutron → proton

Therefore, the nucleus gains one proton.

Changing the number of protons changes the element.

For example:

carbon → nitrogen

phosphorus → sulfur

strontium → yttrium

This is another example of:

nuclear transmutation

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Where Does the Beta Electron Come From?

A common misconception is that the emitted electron was already sitting inside the nucleus.

That is not the correct description.

The electron is produced during the beta-decay process as a neutron transforms into a proton through the weak interaction.

So:

the beta electron is created during the nuclear transformation

rather than being an orbital electron ejected from the atom.

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The Weak Interaction

Beta decay occurs through one of the fundamental interactions of nature:

the weak nuclear interaction

At the particle level, the weak interaction allows one type of quark inside a neutron to change, transforming the neutron into a proton.

This is fundamentally different from alpha decay, where a group of two protons and two neutrons leaves the nucleus together.

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The Antineutrino

Beta-minus decay also produces an:

electron antineutrino

symbol:

ν̄ₑ

Antineutrinos:

• have no electric charge
• have extremely small mass
• interact very weakly with matter

They can therefore travel through enormous amounts of matter without interacting.

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Why the Antineutrino Matters

Early measurements of beta decay produced a puzzle.

The emitted beta particles did not always carry the same energy.

Instead, they showed a continuous range of energies.

Scientists initially wondered whether energy was not being conserved.

The solution was that another particle carries away part of the energy and momentum:

the antineutrino

Therefore:

energy and momentum are conserved

when all decay products are included.

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Beta Particles Have a Range of Energies

In alpha decay, alpha particles from a particular decay often emerge with characteristic energies.

Beta decay is different.

The available decay energy is shared mainly among:

• beta particle
• antineutrino
• recoiling daughter nucleus

Therefore, beta particles are emitted with a:

continuous range of kinetic energies

This is an important characteristic of beta decay.

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Beta-Plus Decay

Another form of beta decay is:

beta-plus decay

In beta-plus decay:

proton → neutron + positron + electron neutrino

A positron is the antimatter counterpart of an electron.

It has:

• same mass as an electron
• charge +1e

It is represented:

⁰₊₁e

or:

β⁺

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Changes During Beta-Plus Decay

During beta-plus decay:

proton → neutron

Therefore:

Mass number:

A stays the same

Atomic number:

Z decreases by 1

General equation:

ᴬ_ZX → ᴬ_Z₋₁Y + ⁰₊₁e + νₑ

where νₑ is an electron neutrino.

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Beta-Minus vs Beta-Plus

For most introductory beta-decay questions, carefully check whether β⁻ or β⁺ is specified.

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Penetrating Power of Beta Radiation

Beta radiation has:

moderate penetrating power

It penetrates matter farther than alpha radiation but generally much less than gamma radiation.

A typical comparison is:

alpha < beta < gamma

in penetrating ability.

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What Stops Beta Radiation?

Beta radiation can often pass through:

• paper
• the outer dead layer of skin

but can be significantly reduced by a relatively thin layer of material such as:

• plastic
• acrylic
• aluminium

The exact penetration depends on beta-particle energy.

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Beta Radiation in Air

Beta particles can travel farther through air than alpha particles.

Alpha radiation typically has a range of only a few centimetres in air.

Beta radiation may travel substantially farther, depending on its energy.

This means beta sources can present a more significant external exposure concern than alpha sources at comparable source conditions.

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Why Beta Radiation Penetrates Farther Than Alpha

Beta particles are much less massive than alpha particles and carry only one elementary charge magnitude.

Alpha particle:

charge = +2e

Beta-minus particle:

charge = −e

Beta particles generally interact less intensely along each unit of path than alpha particles.

Therefore, they typically lose energy less rapidly and travel farther through matter.

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Ionizing Ability

Beta radiation is ionizing.

As beta particles pass through matter, they interact with atoms and can remove electrons.

However, their ionizing ability is generally lower than that of alpha particles.

A simplified comparison is:

alpha → very strongly ionizing

beta → moderately ionizing

gamma → less densely ionizing

This comparison is useful, although actual biological effects depend on radiation energy and exposure conditions.

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Alpha vs Beta Radiation

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Alpha and Beta Deflection

Both alpha and beta particles carry electric charge.

Therefore, both can be deflected by:

• electric fields
• magnetic fields

However, beta particles are much lighter.

For charged particles in a magnetic field:

r = mv/(|q|B)

Because beta particles have extremely small mass, their trajectories can be strongly curved compared with alpha particles under comparable conditions.

Also:

• β⁻ is negatively charged
• α is positively charged

so they curve in opposite directions in the same magnetic field if their velocity directions are comparable.

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Gamma Radiation Is Different

Gamma radiation consists of:

high-energy electromagnetic photons

Gamma photons have:

• no electric charge
• no rest mass
• very high penetrating ability

Therefore, gamma radiation is not deflected by electric or magnetic fields.

This provides another useful comparison:

alpha → positive

beta-minus → negative

gamma → neutral

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Beta Radiation and External Exposure

Unlike alpha radiation, beta particles can penetrate into living tissue to some extent.

Therefore, a beta source outside the body can potentially damage:

• skin
• eyes
• nearby tissue

The severity depends on factors such as:

• beta energy
• source activity
• exposure time
• distance
• shielding

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Internal Beta Exposure

Beta-emitting radioactive materials can also be hazardous if they enter the body through:

• inhalation
• ingestion
• wounds

The beta particles can then deposit energy in surrounding tissue.

The biological risk depends strongly on:

• isotope
• activity
• energy
• location in the body
• time retained in the body

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Shielding Beta Radiation

Beta shielding requires care.

Materials such as:

• plastic
• acrylic

are often useful for reducing beta radiation.

Thin aluminium can also stop many beta particles.

However, high-energy beta particles rapidly decelerating in high-atomic-number materials can produce secondary X-ray radiation called:

bremsstrahlung

For this reason, radiation shielding is selected according to the particular source and situation rather than simply using the densest available material.

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Bremsstrahlung

The word bremsstrahlung means approximately:

braking radiation

When a fast electron passes near a positively charged nucleus, it can be strongly accelerated or decelerated.

The electron loses kinetic energy.

That energy can be emitted as an X-ray photon.

This is one reason low-atomic-number materials such as plastic may be used as an initial layer for beta shielding.

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Beta Decay and Radioactive Dating

Carbon-14 beta decay is particularly important.

Living organisms continually exchange carbon with their environment while alive.

After death, this exchange stops, and the amount of carbon-14 decreases through radioactive decay.

Carbon-14 undergoes:

¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄ₑ

By measuring the remaining carbon-14, scientists can estimate the age of certain once-living materials.

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Beta Radiation in Medicine

Beta-emitting isotopes have specialized medical applications.

Depending on the isotope and treatment, beta radiation may be used to deliver ionizing radiation to particular tissues.

Radioactive tracers and therapeutic isotopes are selected according to properties such as:

• radiation type
• energy
• half-life
• chemical behaviour

Medical use of radioactive materials requires carefully controlled doses and professional radiation-safety procedures.

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Beta Radiation in Industrial Measurement

Beta radiation can also be used in some industrial monitoring systems.

For example, radiation passing through a material can depend on its thickness.

A detector on the opposite side can measure the transmitted radiation.

This principle can be used to monitor the thickness of materials such as:

• paper
• plastic film
• thin metal sheet

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How a Thickness Gauge Works

A simplified system contains:

beta source → material → detector

If the material becomes thicker:

less beta radiation reaches detector

If the material becomes thinner:

more beta radiation reaches detector

The detector signal can be used in a feedback system to adjust manufacturing equipment.

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Detecting Beta Radiation

Beta radiation can be detected using instruments such as:

• Geiger-Müller tubes
• semiconductor detectors
• scintillation detectors
• cloud chambers

A Geiger-Müller detector records ionizing events and can be used to investigate:

• background radiation
• source activity
• absorption by shielding
• distance effects

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Beta Tracks in a Cloud Chamber

Beta particles can produce visible tracks in a cloud chamber.

Compared with alpha tracks, beta tracks tend to be:

• thinner
• longer
• more irregular

because beta particles are:

• much lighter
• less strongly ionizing
• more easily scattered

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Example: Complete a Beta Decay Equation

Complete:

⁶⁰₂₇Co → ? + ⁰₋₁e + ν̄ₑ

Mass number remains:

60

Atomic number increases:

27 → 28

Element 28 is nickel.

Therefore:

⁶⁰₂₇Co → ⁶⁰₂₈Ni + ⁰₋₁e + ν̄ₑ

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Example: Find the Parent Nucleus

Suppose:

? → ⁹⁰₃₉Y + ⁰₋₁e + ν̄ₑ

The parent mass number must be:

90

For atomic number:

Z_parent = 39 − 1

Z_parent = 38

Element 38 is strontium.

Therefore:

⁹⁰₃₈Sr → ⁹⁰₃₉Y + ⁰₋₁e + ν̄ₑ

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Example: Multiple Beta-Minus Decays

Suppose a nucleus undergoes three beta-minus decays.

Each decay:

• leaves A unchanged
• increases Z by 1

After three decays:

A_new = A_original

Z_new = Z_original + 3

For example:

Initial:

A = 100

Z = 40

After three β⁻ decays:

A = 100

Z = 43

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Comparing Multiple Alpha and Beta Decays

Suppose a nucleus undergoes:

• 2 alpha decays
• 3 beta-minus decays

Each alpha decay:

A − 4

Z − 2

Two alpha decays:

A − 8

Z − 4

Three beta-minus decays:

A unchanged

Z + 3

Overall:

A decreases by 8

Z decreases by 1

This type of reasoning is useful when analyzing radioactive decay chains.

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Example: Decay Chain Calculation

A nucleus begins with:

A = 238

Z = 92

It undergoes:

2 alpha decays

and:

2 beta-minus decays.

After two alpha decays:

A = 238 − 8 = 230

Z = 92 − 4 = 88

After two beta-minus decays:

A = 230

Z = 88 + 2 = 90

Final values:

A = 230

Z = 90

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Beta Decay Is Random

Like alpha decay, beta decay is a spontaneous nuclear process.

It is impossible to predict exactly when a particular unstable nucleus will decay.

For a large collection of nuclei, however, the overall behaviour is statistically predictable.

This allows radioactive samples to be described using:

• activity
• decay constant
• half-life

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Conservation in Beta Decay

Beta decay obeys conservation laws.

Important conserved quantities include:

• electric charge
• energy
• momentum
• nucleon number
• lepton number

The neutrino or antineutrino is essential to the complete conservation picture.

For example:

n → p + e⁻ + ν̄ₑ

Charge:

0 = (+1) + (−1) + 0

Therefore:

charge is conserved.

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Problem-Solving Strategy

When solving a beta-minus decay equation:

Keep the mass number unchanged

A_new = A

Increase atomic number by one

Z_new = Z + 1

Identify the new element

Use the periodic table.

Add the beta particle

⁰₋₁e

Include the antineutrino when appropriate

ν̄ₑ

Check the equation

Verify that mass number and charge/atomic-number totals balance.

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Common Mistakes

Mistake: Saying a beta-minus particle is a proton.
A β⁻ particle is an electron.

Mistake: Saying the beta electron comes from the electron cloud.
It is produced during the nuclear decay process.

Mistake: Decreasing mass number during beta-minus decay.
Mass number stays the same.

Mistake: Decreasing atomic number during beta-minus decay.
For β⁻ decay, atomic number increases by 1.

Mistake: Confusing β⁻ and β⁺ decay.
β⁻ increases Z by 1; β⁺ decreases Z by 1.

Mistake: Saying beta radiation is more ionizing than alpha radiation.
Alpha radiation is generally much more strongly ionizing.

Mistake: Saying beta radiation is less penetrating than alpha radiation.
Beta radiation generally penetrates farther than alpha radiation.

Mistake: Saying beta radiation requires thick lead shielding in every situation.
Shielding depends on the source; low-atomic-number materials are often useful for beta particles, partly to limit bremsstrahlung production.

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Key Terms

Beta particle — high-speed electron or positron emitted during beta decay.

Beta-minus (β⁻) — electron emitted when a neutron transforms into a proton.

Beta-plus (β⁺) — positron emitted when a proton transforms into a neutron.

Electron — negatively charged fundamental particle.

Positron — positively charged antimatter counterpart of the electron.

Neutrino — electrically neutral, extremely weakly interacting particle emitted in certain nuclear processes.

Antineutrino — antimatter counterpart of a neutrino; an electron antineutrino is emitted during β⁻ decay.

Weak interaction — fundamental interaction responsible for beta decay.

Parent nucleus — radioactive nucleus before decay.

Daughter nucleus — nucleus produced by radioactive decay.

Transmutation — conversion of one element into another through a nuclear process.

Penetrating power — ability of radiation to travel through matter.

Ionizing power — ability of radiation to remove electrons from atoms or molecules.

Bremsstrahlung — electromagnetic radiation produced when charged particles, particularly electrons, are rapidly accelerated or decelerated.

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Key Takeaways

• Beta decay is a type of radioactive nuclear decay.
• A beta-minus particle is a high-speed electron.
• It is represented as ⁰₋₁e or β⁻.
• During β⁻ decay, a neutron changes into a proton.
• An electron and electron antineutrino are also produced.
• The mass number remains unchanged during β⁻ decay.
• The atomic number increases by one.
• Therefore, β⁻ decay changes one element into another.
• The beta electron is produced during the decay; it does not come from the electron cloud.
• Beta decay occurs through the weak interaction.
• Beta particles have a continuous range of energies.
• The antineutrino helps ensure conservation of energy and momentum.
• Beta-plus decay involves emission of a positron.
• During β⁺ decay, atomic number decreases by one.
• Beta radiation has moderate penetrating power.
• Beta radiation penetrates farther than alpha radiation.
• Beta radiation is generally less ionizing than alpha radiation.
• Beta particles are deflected by electric and magnetic fields because they are charged.
• Beta emitters can present both external and internal radiation hazards.
• Beta radiation has applications in scientific research, medicine and industrial measurement.

Check Your Understanding

1. What is a beta-minus particle?
2. What electric charge does a β⁻ particle carry?
3. What happens to a neutron during beta-minus decay?
4. What happens to mass number during β⁻ decay?
5. What happens to atomic number during β⁻ decay?
6. Explain why β⁻ decay changes one element into another.
7. Write the beta-minus decay equation for carbon-14.
8. Complete: ³²₁₅P → _____ + ⁰₋₁e + ν̄ₑ.
9. Complete: ⁹⁰₃₈Sr → _____ + ⁰₋₁e + ν̄ₑ.
10. Explain where the emitted beta electron comes from.
11. What is the role of the antineutrino in beta-minus decay?
12. Compare the mass and charge of alpha and beta-minus particles.
13. Compare the penetrating powers of alpha and beta radiation.
14. Compare the ionizing abilities of alpha and beta radiation.
15. Why does beta radiation generally penetrate matter farther than alpha radiation?
16. Explain why beta particles can be deflected by electric and magnetic fields.
17. A nucleus with A = 80 and Z = 35 undergoes two β⁻ decays. Determine its new A and Z.
18. A nucleus undergoes one alpha decay followed by two beta-minus decays. Determine the overall changes in A and Z.
19. Explain why suitable beta shielding may use plastic rather than simply using a dense metal.
20. Describe two practical uses of beta radiation and explain why beta radiation is suitable for each.