Half-Life Calculator
Calculate the remaining quantity of a substance, its half-life, or elapsed time based on radioactive decay principles. This calculator is useful for chemistry, physics, medicine, and environmental science applications.
Results
| Initial Quantity (N₀) | 100 |
|---|---|
| Remaining Quantity (N) | 50 |
| Half-Life (t½) | 5730 years |
| Time Elapsed (t) | 5730 years |
| Decay Constant (λ) | 1.21 × 10-4 /year |
| Mean Lifetime (τ) | 8267 years |
Decay Equation
The exponential decay formula is:
N(t) = N₀ × e-λt
Where:
- N(t) = quantity remaining after time t
- N₀ = initial quantity
- λ = decay constant (ln(2)/t½)
- t = time elapsed
- t½ = half-life
About the Half-Life Calculator
This Half-Life Calculator computes the remaining quantity of a substance, its half-life, or the elapsed time based on the principles of radioactive decay. The calculator is useful for various applications in chemistry, physics, medicine, and environmental science.
Understanding Half-Life
Half-life (t½) is the time required for a quantity to reduce to half of its initial value. The concept is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive.
Key characteristics of half-life:
- Each radioactive isotope has its own unique half-life
- Half-life is independent of the initial amount of the substance
- The decay process is random for individual atoms, but predictable for large quantities
Common Half-Life Examples
| Substance | Half-Life | Application |
|---|---|---|
| Carbon-14 | 5,730 years | Radiocarbon dating |
| Uranium-238 | 4.5 billion years | Geological dating |
| Iodine-131 | 8 days | Medical treatments |
| Technetium-99m | 6 hours | Medical imaging |
Calculation Methods
The calculator uses the exponential decay formula:
N(t) = N₀ × (1/2)t/t½ = N₀ × e-λt
Where:
- N(t) = quantity remaining after time t
- N₀ = initial quantity
- t½ = half-life of the substance
- t = elapsed time
- λ = decay constant (ln(2)/t½)
Applications of Half-Life Calculations
Half-life calculations have numerous practical applications:
- Radiometric dating: Determining the age of archaeological artifacts or geological samples
- Medical applications: Calculating dosages for radioactive treatments and imaging
- Nuclear power: Managing radioactive waste and fuel cycles
- Environmental science: Tracking pollutant degradation and environmental cleanup
- Pharmacology: Determining drug elimination rates from the body
Limitations and Considerations
While half-life calculations are generally reliable, several factors should be considered:
- For very short half-lives, relativistic effects may become significant
- Environmental conditions can sometimes affect decay rates
- For dating purposes, the initial quantity must be known or estimated
- Some decay processes involve multiple steps with different half-lives