Alpha Decay Calculator

What is Alpha Decay?

Alpha decay is a type of radioactive decay where an unstable nucleus emits an alpha particle (α), which consists of two protons and two neutrons (identical to a helium-4 nucleus). The process can be represented as:

^A_ZX → ^A-4_Z-2Y + ⁴₂He

This decay mode is common in heavy elements (Z > 83) and occurs when the strong nuclear force can no longer overcome electromagnetic repulsion between protons.

Q-Value Explained

The Q-value in alpha decay represents:

• Energy released: Measured in MeV, derived from mass difference using E=mc²
• Decay feasibility: Positive Q-value means spontaneous decay is energetically favorable
• Decay energy: Total kinetic energy shared between daughter nucleus and alpha particle
• Half-life correlation: Higher Q-values generally correspond to shorter half-lives
• Calculation method: Q = [M(parent) - M(daughter) - M(α)]c²

Decay Process Details

During alpha decay, several changes occur:

• Atomic number (Z): Decreases by 2, changing the element identity
• Mass number (A): Decreases by 4, reducing the total nucleons
• Neutron number (N): Decreases by 2, affecting nuclear stability
• Nuclear binding energy: Often increases per nucleon, enhancing stability
• Nuclear radius: Decreases according to R ∝ A^1/3
• Quantum tunneling: Alpha particles escape the nucleus via quantum tunneling through the potential barrier

Practical Applications

Alpha decay has numerous important applications:

• Radiometric dating: Uranium-lead and thorium-lead dating of geological samples
• Smoke detectors: Americium-241 alpha emitters ionize air to detect smoke particles
• Medical treatments: Targeted alpha therapy for certain cancers
• Space power: Radioisotope thermoelectric generators for spacecraft
• Material analysis: Alpha particle X-ray spectrometry for elemental analysis
• Nuclear forensics: Identifying sources of nuclear materials

Energy Distribution Physics

The energy distribution follows conservation of momentum principles:

• Alpha particle energy: E_α = Q × [M_daughter/(M_daughter + M_α)]
• Daughter recoil energy: E_daughter = Q - E_α
• Typical distribution: Alpha particle receives ~98% of the energy for heavy nuclei
• Detection implications: Alpha particles are easier to detect due to higher energy
• Spectroscopy applications: Alpha energy spectra can identify specific isotopes
• Excited states: Sometimes decay produces daughter nuclei in excited states, reducing alpha energy

Alpha Decay Chains

Many heavy elements decay through sequential alpha emissions:

• Uranium series: ²³⁸U → ²³⁴Th → ... → ²⁰⁶Pb (stable)
• Thorium series: ²³²Th → ²²⁸Ra → ... → ²⁰⁸Pb (stable)
• Actinium series: ²³⁵U → ²³¹Th → ... → ²⁰⁷Pb (stable)
• Neptunium series: ²³⁷Np → ²³³Pa → ... → ²⁰⁹Bi (nearly stable)
• Branching ratios: Some isotopes can decay by multiple modes (alpha, beta, etc.)
• Secular equilibrium: In old samples, decay rates of all chain members equalize