Radioactive decay processes underpin much of nuclear physics, and understanding decay equations and activity allows physicists to describe how unstable nuclei transform and how quickly these changes occur.

Radioactive Decay Processes

Radioactive decay is a transformation in which an unstable nucleus emits radiation to reach a more energetically favourable configuration. This subsubtopic focuses specifically on α decay, β⁻ decay, and β⁺ decay, along with how nuclear transformations are represented using decay equations and how activity quantifies decay rate.

Fundamental Ideas in Nuclear Transformations

Nuclear transformations always obey key conservation laws, including conservation of charge, nucleon number, and lepton number. These principles determine the forms and products of decay equations.

When discussing decay processes, students must be confident with the nuclide notation ZAX^A_Z XZA​X, where AAA represents the nucleon number and ZZZ the proton number.

Alpha Decay

Alpha decay is characteristic of heavy, unstable nuclei such as uranium or radium. In this process, the nucleus emits an α particle, which is identical to a helium-4 nucleus.

A nucleus undergoing α decay decreases its proton number by 2 and its nucleon number by 4.

Diagram of α decay showing emission of a helium-4 nucleus from a heavy parent nucleus. The ejection lowers Z by 2 and A by 4. Colours distinguish protons and neutrons for clarity. Source.

This leads to a daughter nucleus shifted two places lower in the periodic table. Alpha decay equations must clearly show this change in nuclear composition using nuclide notation.

The emission of an α particle results from strong nuclear repulsion in very large nuclei where the binding energy per nucleon is insufficient to hold all nucleons tightly.

Beta Minus Decay (β⁻)

β⁻ decay occurs in neutron-rich nuclei. A neutron transforms into a proton, accompanied by the emission of an electron (the β⁻ particle) and an antineutrino.

In β⁻ decay, the nucleon number remains constant, but the proton number increases by 1, creating a daughter nucleus one place higher in the periodic table.

Diagram of β⁻ decay: a neutron converts to a proton, emitting an electron and an antineutrino. Proton number increases by one while A is unchanged. Colours mark protons and neutrons for clarity. Source.

The decay equation must reflect this transformation clearly and preserve all conservation laws.

After β⁻ decay has been introduced, it becomes important to connect the transformation to changes in quark structure within nucleons, although only qualitatively at this stage.

Beta Plus Decay (β⁺)

β⁺ decay takes place in proton-rich nuclei. Here, a proton inside the nucleus converts into a neutron, with the simultaneous emission of a positron (β⁺ particle) and a neutrino.

A β⁺ decay equation shows the proton number decreasing by 1, while the nucleon number remains unchanged. The conservation of charge and lepton number must be demonstrated in the equation.

Both β⁻ and β⁺ processes highlight the role of the weak nuclear interaction in mediating changes in quark composition, although deeper treatment is outside the scope of this subsubtopic.

Writing Decay Equations

Decay equations must follow strict rules to be accepted as physically valid. Students writing decay equations should follow these principles:

Key Requirements for Decay Equations

• Use full nuclide notation ZAX^A_Z XZA​X.

• Balance nucleon number on both sides of the equation.

• Balance proton number to maintain charge conservation.

• Include emitted particles such as α, β⁻, β⁺, neutrinos, or antineutrinos.

• Ensure lepton number conservation, especially for β decays.

Correctly written decay equations show how unstable nuclei evolve and provide a framework for modelling nuclear processes encountered in physics and applied nuclear technologies.

Activity of a Radioactive Sample

Radioactive decay is inherently statistical, and the decay of individual nuclei cannot be predicted. However, for a large collection of identical nuclei, the decay rate follows predictable laws described through activity.

Activity is measured in becquerels (Bq), where 1 Bq corresponds to one decay per second. It provides a practical way to quantify how “radioactive” a sample is.

Once activity is defined, students must understand its relationship with the number of undecayed nuclei and the decay constant.

The Activity Equation

The relationship between activity AAA, the decay constant λ\lambdaλ, and the number of undecayed nuclei NNN is central in nuclear physics.

EQUATION
—-----------------------------------------------------------------
Activity (A) = λN
A = Activity, number of decays per second (Bq)
λ = Decay constant, probability per unit time that a nucleus decays (s⁻¹)
N = Number of undecayed nuclei in the sample (dimensionless count)
—-----------------------------------------------------------------

This expression reflects the proportionality between the number of remaining radioactive nuclei and the likelihood of decay occurring within a given instant. After stating the equation, it becomes important to recognise that activity decreases over time as the number of undecayed nuclei falls.

Graph of activity versus time illustrating exponential decrease proportional to the number of undecayed nuclei. The curve supports understanding of A = λN in real measurements. Extra detail: half-life marking appears but does not add unnecessary complexity. Source.

Modelling Activity in Nuclear Physics

Understanding activity allows physicists to describe how radioactive samples diminish in strength, compare isotopes with different decay constants, and predict how the intensity of radiation changes during experiments.

Key conceptual points include:

• Each nucleus decays independently at random.

• Decay cannot be accelerated or delayed.

• The decay constant determines the rate of exponential decrease in both activity and the number of nuclei.

• Activity measurements underpin experimental investigations such as absorption studies and detection methods.

These principles ensure students can interpret decay equations confidently and apply activity relationships across diverse contexts in nuclear physics.