Half-Life Calculator
Calculate radioactive decay, half-life, and remaining amounts over time
Half-Life & Decay Calculations
How to Use the Half-Life Calculator
Getting Started
- Step 1: Select what you want to calculate (final amount, time, half-life, or initial amount)
- Step 2: Choose the appropriate time unit (seconds, minutes, hours, days, or years)
- Step 3: Enter the known values in the appropriate fields
- Step 4: Click Calculate to get your result with detailed steps
Key Radioactive Decay Concepts
- Half-Life (t₁/₂): Time required for half of a radioactive sample to decay
- Decay Constant (λ): Probability of decay per unit time (λ = ln(2)/t₁/₂)
- Exponential Decay: N(t) = N₀ × e^(-λt)
- Activity: Rate of decay, proportional to the amount of material
Common Half-Lives
- Carbon-14: 5,730 years (radiocarbon dating)
- Uranium-238: 4.5 billion years (geological dating)
- Iodine-131: 8.02 days (medical applications)
- Technetium-99m: 6.01 hours (medical imaging)
Applications
- Nuclear Medicine: Dosage calculations and safety protocols
- Archaeology: Carbon dating of artifacts and fossils
- Geology: Dating rocks and determining Earth's age
- Nuclear Power: Waste management and reactor design
Frequently Asked Questions
What's the difference between half-life and decay constant?
Half-life is the time for half the material to decay, while decay constant (λ) is the probability of decay per unit time. They're related by λ = ln(2)/t₁/₂.
Why do we use exponential decay rather than linear decay?
Radioactive decay is a random process where the rate depends on the current amount. This creates an exponential pattern: more material = faster decay rate.
How accurate are half-life calculations for small amounts?
For large numbers of atoms, exponential decay is very accurate. For small amounts, statistical fluctuations become significant, and individual decay events become unpredictable.
Can anything change a material's half-life?
Generally no. Half-life is an intrinsic nuclear property, unaffected by temperature, pressure, or chemical state. Extreme conditions (like in stellar cores) can have minor effects.
How do I calculate after multiple half-lives?
After n half-lives, you have (1/2)^n of the original amount. After 3 half-lives: 1000g → 500g → 250g → 125g remaining.
What's the relationship between activity and amount?
Activity (decays per second) = λ × N, where λ is decay constant and N is number of atoms. Activity decreases exponentially like the amount.
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