Radioactive Decay Calculator - Nuclear Physics

This advanced physics calculator analyzes radioactive decay processes, including alpha, beta, and gamma decay. It calculates decay rates, half-lives, activity, and nuclear transformations with precision.

Radioactive Decay Fundamentals

Radioactive decay follows an exponential decay law:

N(t) = N₀ × e^(-λt)

Where:

• N(t): Quantity remaining at time t
• N₀: Initial quantity
• λ (lambda): Decay constant
• t: Time elapsed

Decay Types

Alpha Decay (α)

Emission of helium nucleus (2 protons + 2 neutrons):

⁴₂He nucleus emitted

• Mass Number: Decreases by 4
• Atomic Number: Decreases by 2
• Energy: 4-9 MeV typical
• Range: Short (few cm in air)

Beta Decay (β)

Emission of electron or positron:

β⁻: neutron → proton + electron + antineutrino

β⁺: proton → neutron + positron + neutrino

• Mass Number: Unchanged
• Atomic Number: Increases (β⁻) or decreases (β⁺) by 1
• Energy: 0.5-2 MeV typical
• Range: Medium (few meters in air)

Gamma Decay (γ)

Emission of high-energy electromagnetic radiation:

Excited nucleus → Ground state + γ-ray

• Mass Number: Unchanged
• Atomic Number: Unchanged
• Energy: 0.1-10 MeV typical
• Range: Long (penetrating)

Key Concepts

• Half-Life (t₁/₂): Time for half the nuclei to decay
• Decay Constant (λ): Probability of decay per unit time
• Activity (A): Decay rate (decays per unit time)
• Mean Lifetime (τ): Average time before decay
• Specific Activity: Activity per unit mass

Mathematical Relationships

• Half-Life: t₁/₂ = ln(2)/λ = 0.693/λ
• Mean Lifetime: τ = 1/λ
• Activity: A = λN
• Decay Rate: dN/dt = -λN
• Survival Probability: P(t) = e^(-λt)

Real-World Applications

• Radiocarbon Dating: Carbon-14 for archaeological dating
• Nuclear Medicine: Medical imaging and therapy
• Nuclear Power: Energy generation
• Geological Dating: Uranium-lead dating
• Smoke Detectors: Americium-241
• Food Irradiation: Sterilization

Interesting Facts

• Carbon-14 dating can date objects up to 50,000 years old
• Uranium-238 has a half-life of 4.5 billion years
• Some isotopes decay in fractions of a second
• Radioactive decay is random but predictable statistically
• Bananas are naturally radioactive due to potassium-40

Units and Measurements

• Becquerel (Bq): 1 decay per second
• Curie (Ci): 3.7 × 10¹⁰ decays per second
• Gray (Gy): 1 joule per kilogram absorbed
• Sievert (Sv): Biological effect of radiation
• Electron Volt (eV): Energy unit for nuclear processes

Safety Considerations

• Time: Minimize exposure time
• Distance: Increase distance from source
• Shielding: Use appropriate materials
• ALARA: As Low As Reasonably Achievable
• Monitoring: Regular radiation monitoring