Half-Life Calculator - Nuclear Physics

This advanced physics calculator helps you understand radioactive decay, a fundamental process in nuclear physics. Half-life is the time required for half of a given quantity of radioactive material to decay.

Exponential Decay Law

Radioactive decay follows an exponential decay law, described by the equation:

N = N₀ × e^(-λt)

Where:

• N: Remaining quantity after time t
• N₀: Initial quantity
• λ (lambda): Decay constant
• t: Time elapsed
• e: Natural logarithm base (≈ 2.718)

Key Concepts

• Half-Life (T₁/₂): Time for half the nuclei to decay
• Decay Constant (λ): Probability of decay per unit time
• Activity (A): Number of decays per unit time (A = λN)
• Mean Lifetime (τ): Average time before decay (τ = 1/λ)

Relationship Between Half-Life and Decay Constant

The decay constant is related to half-life by:

λ = ln(2) / T₁/₂

This means that after one half-life, exactly half of the original quantity remains, regardless of the initial amount.

Real-World Applications

• Carbon Dating: Determine age of organic materials using C-14
• Nuclear Medicine: Medical imaging and cancer treatment
• Geological Dating: Determine age of rocks and minerals
• Nuclear Power: Fuel cycle management and waste disposal
• Environmental Monitoring: Track radioactive contamination

Interesting Facts

• After 10 half-lives, only about 0.1% of the original quantity remains
• Some isotopes have half-lives of fractions of a second, others billions of years
• Radioactive decay is a random process at the atomic level but predictable statistically
• The discovery of radioactivity led to revolutionary changes in physics and chemistry