Half-Life Calculator
What is Half-Life?
Half-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay, but it also applies to other fields including medicine, pharmacology, and carbon dating.
Half-Life Formula
The basic formula for calculating the remaining quantity after a certain time is:
N(t) = N₀ × (1/2)t/t₁₍₂₎
Where:
- N(t) = Quantity remaining after time t
- N₀ = Initial quantity
- t = Elapsed time
- t₁₍₂₎ = Half-life
This can be rearranged to find the half-life:
t₁₍₂₎ = t × log(2) / log(N₀/N(t))
Applications of Half-Life
Nuclear Physics
Half-life is crucial in understanding radioactive decay. Different isotopes have different half-lives, ranging from fractions of a second to billions of years.
Examples: Carbon-14 (5,730 years), Uranium-238 (4.5 billion years), Iodine-131 (8 days)
Medicine & Pharmacology
The half-life of drugs determines how long they remain active in the body and helps establish dosing schedules.
Examples: Caffeine (5-6 hours), Ibuprofen (2-4 hours), Amoxicillin (1-1.5 hours)
Archaeology
Carbon dating uses the half-life of Carbon-14 to determine the age of organic materials up to about 60,000 years old.
Environmental Science
Half-life helps scientists understand how long pollutants and other substances persist in the environment.
Exponential Decay
Half-life is a specific case of exponential decay. The general exponential decay formula is:
N(t) = N₀ × e-λt
Where:
- λ = Decay constant
- e = Euler's number (approximately 2.71828)
The relationship between half-life (t₁₍₂₎) and decay constant (λ) is:
t₁₍₂₎ = ln(2) / λ
λ = ln(2) / t₁₍₂₎
How to Use the Half-Life Calculator
Our half-life calculator offers three calculation modes:
- Calculate Remaining Quantity: Enter the initial quantity, half-life, and time elapsed to find how much remains.
- Calculate Time Elapsed: Enter the initial quantity, current quantity, and half-life to find how much time has passed.
- Calculate Half-Life: Enter the initial quantity, current quantity, and time elapsed to determine the half-life.
Simply select the calculation mode you need, enter the required values, and click "Calculate" to see the results.