15.8 Types of Radioactive Decay

Radioactive decay is a fascinating process where unstable atomic nuclei release energy and particles. This topic explores the different types of decay, including alpha, beta, and gamma, and the subatomic particles involved in each.

Understanding radioactive decay is crucial for grasping nuclear physics and its applications. We'll examine how specific isotopes determine decay types and the conservation principles that govern these processes, providing a foundation for further study in nuclear physics.

Processes of Nuclear Decay

Subatomic Particles in Decay

When nuclei undergo radioactive decay, they release various subatomic particles, each with unique properties that play specific roles in the decay process.

• Alpha particles ($\alpha$) are essentially helium nuclei consisting of two protons and two neutrons bound together. They can be represented as $\alpha$ or $\mathrm{He}^{2+}$ and have a mass of approximately 4 atomic mass units.
• Neutrinos ($v$) are electrically neutral particles with extremely small mass, making them difficult to detect.
• Antineutrinos ($\bar{v}$) are the antimatter counterparts of neutrinos, also electrically neutral with nearly zero mass.
• Positrons ($e^{+}$ or $\beta^{+}$) are the antimatter equivalents of electrons, having identical mass but positive charge.

Types of Radioactive Decay

Radioactive decay occurs through several mechanisms, each involving different particles and resulting in different changes to the nucleus.

Alpha Decay:

• In alpha decay, a nucleus ejects an alpha particle ($\alpha$), reducing its atomic number by 2 and its mass number by 4.
• The general equation for alpha decay is: $^A_Z X \rightarrow ^{A-4}_{Z-2} Y + ^4_2 \alpha$
• Example: Uranium-238 decays to Thorium-234 via alpha decay: $^{238}_{92} \text{U} \rightarrow ^{234}_{90} \text{Th} + ^4_2 \alpha$

Beta-Minus Decay ($\beta^-$):

• Occurs when a neutron in the nucleus converts to a proton, emitting an electron and an antineutrino.
• The atomic number increases by 1, while the mass number remains unchanged.
• General equation: $^A_Z X \rightarrow ^A_{Z+1} Y + e^- + \bar{v}$
• Example: Carbon-14 decays to Nitrogen-14: $^{14}_6 \text{C} \rightarrow ^{14}_7 \text{N} + e^- + \bar{v}$

Beta-Plus Decay ($\beta^+$):

• Happens when a proton transforms into a neutron, releasing a positron and a neutrino.
• The atomic number decreases by 1, while the mass number stays the same.
• General equation: $^A_Z X \rightarrow ^A_{Z-1} Y + e^+ + v$
• Example: Nitrogen-13 decays to Carbon-13: $^{13}_7 \text{N} \rightarrow ^{13}_6 \text{C} + e^+ + v$

Gamma Decay ($\gamma$):

• Often follows alpha or beta decay when the resulting nucleus is in an excited state.
• The nucleus releases energy in the form of a high-energy photon (gamma ray).
• Neither the atomic number nor the mass number changes.
• General equation: $^A_Z X^* \rightarrow ^A_Z X + \gamma$
• The asterisk indicates an excited state of the nucleus.

In all these decay processes, certain conservation laws must be satisfied:

1. Conservation of nucleons (protons and neutrons)
2. Conservation of leptons (electrons, positrons, neutrinos, and antineutrinos)
3. Conservation of electric charge

Isotope-Specific Decay

The stability of a nucleus depends on its specific composition of protons and neutrons. Each isotope has characteristic decay modes determined by its nuclear structure.

• Isotopes with too many neutrons compared to protons tend to undergo beta-minus decay.
• Isotopes with too many protons relative to neutrons often undergo beta-plus decay or electron capture.
• Very heavy nuclei (atomic number > 83) commonly undergo alpha decay.
• The decay mode of a particular isotope is predictable based on nuclear stability patterns.

Practice Problem 1: Alpha Decay

Solution

To solve this problem, we need to apply conservation of nucleons and charge.

In alpha decay, the parent nucleus emits an alpha particle ($^4_2\text{He}$), which contains 2 protons and 2 neutrons.

Starting with uranium-238 ($^{238}_{92}\text{U}$):

• The mass number will decrease by 4: 238 - 4 = 234
• The atomic number will decrease by 2: 92 - 2 = 90

Element with atomic number 90 is thorium (Th).

Therefore, the daughter nucleus is thorium-234 ($^{234}_{90}\text{Th}$).

The complete nuclear equation is: $^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$

Practice Problem 2: Beta-Minus Decay

Solution

In beta-minus decay, a neutron in the nucleus converts to a proton, emitting an electron and an antineutrino.

Starting with carbon-14 ($^{14}_{6}\text{C}$):

• The mass number remains unchanged: 14
• The atomic number increases by 1: 6 + 1 = 7

Element with atomic number 7 is nitrogen (N).

Therefore, the daughter nucleus is nitrogen-14 ($^{14}_{7}\text{N}$).

The complete nuclear equation is: $^{14}_{6}\text{C} \rightarrow ^{14}_{7}\text{N} + ^{0}_{-1}e + \bar{v}$

Where $^{0}_{-1}e$ represents the electron (beta particle) and $\bar{v}$ represents the antineutrino.