Half-life is fundamental in chemistry, particularly in radioactive decay and first-order reactions. It represents the time required for a quantity to reduce to half its initial value. This calculator helps you determine key variables in half-life calculations.
Key Formulas and Calculations
1. Exponential Decay
Formula: N = N₀ * (1/2)^(t / t₁/₂)
Where:
- N = Remaining quantity
- N₀ = Initial quantity
- t = Elapsed time
- t₁/₂ = Half-life
This formula directly calculates the remaining quantity after a given time, based on the initial quantity and half-life.
2. Decay Constant (λ)
Formula: λ = ln(2) / t₁/₂
Where:
- λ = Decay constant
- ln(2) ≈ 0.693
The decay constant (λ) is a measure of how quickly a substance decays. It is inversely proportional to the half-life.
Alternative Formula: N = N₀ * e^(-λt)
This is an alternative decay formula using the decay constant.
3. Calculating Half-Life (t₁/₂)
Formula: t₁/₂ = ln(2) / λ
Formula: t₁/₂ = t / log₂(N₀ / N)
This is useful when you have the initial and final quantities, and the elapsed time.
4. Calculating Elapsed Time (t):
Formula: t = (t₁/₂) * log₂(N₀ / N)
Formula: t = -ln(N / N₀) / λ
Use these formulas to find the time it takes for a substance to decay to a specific amount.
5. Initial Quantity (N₀):
Formula: N₀ = N / (1/2)^(t / t₁/₂)
Formula: N₀ = N / e^(-λt)
These formulas allow you to calculate the original amount of a substance.
Practical Applications
- Radioactive Decay: Determining the age of fossils (carbon-14 dating), calculating radiation exposure.
- First-Order Kinetics: Studying the rate of chemical reactions, drug metabolism.
Using our half-life Calculator
Input the known values into the corresponding fields. The calculator will automatically compute the unknown variables using the formulas above. Ensure all time units are consistent.
Key Concepts
- Exponential decay
- Decay constant
- Logarithmic relationships
- First-order reactions.
- Radioactive Isotopes.
