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Beta Decay and Neutrinos: Changing Neutrons and Protons

Capítulo 6

Estimated reading time: 6 minutes

+ Exercise

What Beta Decay Changes (and What It Does Not)

Beta processes convert one nucleon type into the other inside the nucleus. The key bookkeeping is:

Atomic number Z (protons) can change by ±1.
Neutron number N changes in the opposite direction (∓1).
Mass number A = Z + N stays the same (a nucleon changes identity, none are added/removed).

Three closely related processes do this: beta-minus (β−), beta-plus (β+), and electron capture (EC). Each is a different way the nucleus adjusts its proton-to-neutron ratio.

Beta-Minus (β−): Neutron → Proton

What happens in the nucleus

In β− decay, a neutron converts into a proton and emits an electron and an antineutrino:

n → p + e− + ν̅e

How Z and N change

Z increases by 1 (one more proton).
N decreases by 1 (one fewer neutron).
A unchanged.

Balanced nuclear equation (nuclide form)

Write the parent and daughter nuclides, then add the emitted particles:

^A_ZX → ^A_(Z+1)Y + e− + ν̅e

Example:

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^14_6C → ^14_7N + e− + ν̅e

Check: A stays 14; Z goes 6 → 7; N goes 8 → 7.

Step-by-step: predicting the daughter

Keep A the same.
Increase Z by 1.
Find the element with the new Z (that is the daughter element).
Optionally compute N = A − Z to confirm N decreased by 1.

Beta-Plus (β+): Proton → Neutron

What happens in the nucleus

In β+ decay, a proton converts into a neutron and emits a positron and a neutrino:

p → n + e+ + νe

How Z and N change

Z decreases by 1 (one fewer proton).
N increases by 1 (one more neutron).
A unchanged.

Balanced nuclear equation (nuclide form)

^A_ZX → ^A_(Z−1)Y + e+ + νe

Example:

^22_11Na → ^22_10Ne + e+ + νe

Check: A stays 22; Z goes 11 → 10; N goes 11 → 12.

Practical note: when β+ is possible

β+ emission requires enough decay energy to create a positron. In practice, the available energy must exceed the positron rest-mass energy (and related atomic effects). If the energy is insufficient, the nucleus may instead use electron capture to achieve the same Z and N change without emitting a positron.

Electron Capture (EC): Proton + Electron → Neutron

What happens

In electron capture, the nucleus captures an inner-shell electron (often from the K shell). A proton converts into a neutron and a neutrino is emitted:

p + e− → n + νe

This is a nuclear transformation triggered by an atomic electron. The atom is left with an inner-shell vacancy, so electrons from higher shells fall inward, producing characteristic X-rays or Auger electrons (atomic, not nuclear, emissions).

How Z and N change

Z decreases by 1 (one proton becomes a neutron).
N increases by 1.
A unchanged.

Balanced nuclear equation (nuclide form)

^A_ZX + e− → ^A_(Z−1)Y + νe

Example:

^7_4Be + e− → ^7_3Li + νe

Step-by-step: predicting the daughter for EC

Keep A the same.
Decrease Z by 1.
The daughter element is the one with the new Z.
Expect accompanying characteristic X-rays/Auger electrons due to the electron vacancy.

Mapping the Three Processes to Z and N

Process	Nucleon-level change	Emitted particles	ΔZ	ΔN
β−	n → p	e−, ν̅e	+1	−1
β+	p → n	e+, νe	−1	+1
Electron capture	p + e− → n	νe (plus atomic X-rays/Auger)	−1	+1

Why Beta Particles Have a Continuous Energy Spectrum

Alpha decay typically produces alpha particles with discrete energies (linked to specific nuclear energy levels). Beta decay is different: the decay energy is shared among three particles (daughter nucleus recoil plus two light leptons), so the electron/positron can leave with a range of energies.

Energy sharing in β decay

Let the available decay energy be Q. In a simplified picture:

Some energy becomes the kinetic energy of the beta particle (electron or positron).
Some becomes the kinetic energy of the neutrino/antineutrino.
A small amount becomes recoil kinetic energy of the daughter nucleus.

Because the neutrino can take varying fractions of the energy, the beta particle energy is not fixed. The beta spectrum runs from near zero up to a maximum value (the endpoint energy), which occurs when the neutrino carries away very little energy.

Momentum conservation and the neutrino

Momentum must also be conserved. If only the beta particle and daughter nucleus were produced, the kinematics would force a nearly fixed beta energy (two-body decay). The observed continuous spectrum indicates a third particle carrying variable momentum. The neutrino (or antineutrino) provides:

Missing energy (variable share of Q).
Missing momentum (variable direction and magnitude).
Consistency with conservation laws in each individual decay event.

Practical implication: in a detector, the beta particle often deposits only part of the decay energy; the neutrino typically escapes without interacting.

Penetration, Ionization, and Shielding: Beta Compared (Practical Radiation Handling)

Beta radiation consists of electrons (β−) or positrons (β+). Their interaction with matter is dominated by electromagnetic forces, leading to moderate penetration and moderate-to-high ionization along their tracks. Shielding choices aim to stop the beta while minimizing secondary radiation.

Radiation type	Typical penetration in matter	Ionization density (qualitative)	Typical shielding	Practical note
β− / β+	Moderate (mm to cm depending on energy and material)	Moderate (less than alpha, more spread out)	Plastic (acrylic), glass, or thin aluminum	High-Z shielding can generate bremsstrahlung X-rays; often use plastic first, then thin metal if needed.
α (for comparison)	Very low (stopped by paper/skin outer layer)	Very high (dense ionization)	Paper, air gap, thin barrier	Main hazard is internal contamination rather than external exposure.
γ (for comparison)	High (deep penetration)	Low per unit path length	Lead, concrete	Requires thick shielding; not primarily stopped by plastic/aluminum.

Step-by-step: choosing simple beta shielding

Estimate whether the source is primarily beta (from decay mode information).
Place a low-Z shield (plastic/acrylic) close to the source to absorb beta particles.
If dose rates remain high due to secondary photons, add a thin metal layer (e.g., aluminum) outside the plastic to attenuate any bremsstrahlung and protect the plastic.
Verify with measurement (survey meter appropriate for beta/photons) and adjust thickness.

Application-Style Questions

A nuclide has too many neutrons relative to protons. Which beta process (β−, β+, or EC) moves it toward stability by changing N and Z in the right direction? State ΔZ and ΔN.
Write the balanced decay equation (including the neutrino/antineutrino) for: ^32_15P undergoing β− decay.
Write the balanced decay equation for: ^18_9F undergoing β+ decay.
Electron capture decreases Z by 1. If ^55_26Fe undergoes EC, what is the daughter nuclide (A and Z)?
In a β− decay with endpoint energy 1.0 MeV, can the emitted electron always have 1.0 MeV kinetic energy? Explain using energy sharing with the antineutrino.
You need to shield a beta source in a lab. Choose between lead, acrylic (plastic), and aluminum as the first layer. Which is best and why?

Now answer the exercise about the content:

A beta source must be shielded in a lab. Which material is best to use as the first shielding layer to stop the beta particles while minimizing unwanted secondary radiation?

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Beta particles are best stopped first with a low-Z shield like plastic/acrylic. Using high-Z materials first can produce bremsstrahlung X-rays, so plastic is preferred as the initial layer.