Half-Life Calculator

This half-life calculator helps you solve radioactive decay problems by calculating any unknown variable when the others are provided.

1. Select what you want to calculate from the dropdown menu
2. Enter the known values in the appropriate fields
3. Choose the correct time units for your problem
4. View the calculated result and additional decay information
5. Use the timeline to see how the substance decays over multiple half-lives

What is Half-Life?

Half-life is the time required for half of the radioactive nuclei in a sample to undergo radioactive decay. It's a constant characteristic of each radioactive isotope.

Key Concepts

• Exponential Decay: Radioactive decay follows an exponential pattern, not linear
• Decay Constant (λ): The probability per unit time that a nucleus will decay
• Mean Lifetime (τ): The average lifetime of a radioactive nucleus (τ = 1/λ)
• Activity: The rate of decay, measured in becquerels (Bq) or curies (Ci)

Applications

• Carbon Dating: Determining the age of organic materials
• Medical Imaging: Using radioactive tracers in diagnostic procedures
• Nuclear Power: Understanding fuel decay and waste management
• Geology: Dating rocks and minerals using uranium-lead dating

Carbon-14 Dating

A fossil contains 25% of its original Carbon-14. How old is it?

Given: N/N₀ = 0.25, t₁/₂ = 5,730 years

Solution: t = t₁/₂ × ln(N₀/N) / ln(2) = 5,730 × ln(4) / ln(2) = 11,460 years

Medical Isotope Decay

How much Iodine-131 remains after 24 days from an initial 100 mg sample?

Given: N₀ = 100 mg, t = 24 days, t₁/₂ = 8.02 days

Solution: N = 100 × (1/2)^(24/8.02) = 100 × (1/2)^2.99 ≈ 12.6 mg