Half-Life Calculator
Calculate decay, remaining amount, elapsed time, and decay constant using half-life equations for radioactive materials and compounds with our scientific calculator.
Category: Math
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Understanding Half-Life
What is Half-Life?
Half-life 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, but it applies to many other situations where exponential decay occurs.
Key Formulas
Exponential Decay Law:
N = N₀ × e^(-λt)
Where:
- N is the quantity remaining after time t
- N₀ is the initial quantity
- λ (lambda) is the decay constant
- t is the elapsed time
Half-Life Formula:
t₁/₂ = ln(2) / λ ≈ 0.693 / λ
The relationship between half-life (t₁/₂) and decay constant (λ)
Alternative Half-Life Formula:
N = N₀ × (1/2)^(t/t₁/₂)
Where t/t₁/₂ represents the number of half-lives elapsed
Common Applications
- Radiometric dating in archaeology and geology
- Nuclear medicine and radiation therapy
- Nuclear power and waste management
- Pharmacokinetics (drug elimination from the body)
- Carbon dating of organic materials
Examples of Half-Lives
- Carbon-14: 5,730 years (used in carbon dating)
- Uranium-238: 4.5 billion years
- Iodine-131: 8 days (used in medical treatments)
- Caffeine in adults: approximately 5-6 hours
- Technetium-99m: 6 hours (used in medical imaging)
Frequently Asked Questions
What is half-life?
Half-life is the time required for a quantity to reduce to half of its initial value. It's commonly used to describe the decay of radioactive isotopes, but also applies to other exponential decay processes like drug metabolism or the decay of certain chemicals.
How is half-life calculated?
Half-life can be calculated using the formula: t₁/₂ = ln(2)/λ, where t₁/₂ is the half-life and λ is the decay constant. Alternatively, if you know the initial amount, remaining amount, and time elapsed, you can calculate half-life using N(t) = N₀·(1/2)^(t/t₁/₂).
What is the decay constant?
The decay constant (λ) is a value that determines how quickly a substance decays. It represents the probability per unit time that a particle will decay. The relationship between decay constant and half-life is: λ = ln(2)/t₁/₂, where t₁/₂ is the half-life.
What are some applications of half-life calculations?
Half-life calculations are used in radiocarbon dating to determine the age of archaeological artifacts, in nuclear medicine to determine appropriate dosing of radiopharmaceuticals, in ecology to study the persistence of pollutants, and in pharmacology to understand drug elimination from the body.