Science & Lab Tools
Half-Life Calculator
Calculate half-life and decay rates for radioactive substances, biological compounds, and chemical reactions
Enter values to calculate half-life and decay
Related to Half-Life Calculator
The half-life calculator uses fundamental principles of exponential decay to determine how a substance decays over time. The calculation is based on the exponential decay equation and the relationship between half-life and decay constant. Here's how it works:
Decay Constant Calculation
The decay constant (λ) is calculated using the half-life (t₁/₂) through the equation: λ = ln(2) / t₁/₂. This constant represents the rate at which a substance decays over time.
Exponential Decay Equation
The remaining quantity N(t) at time t is calculated using the equation: N(t) = N₀ * e^(-λt), where N₀ is the initial quantity and e is Euler's number (approximately 2.71828).
The calculator provides several key pieces of information to help you understand the decay process:
Remaining Quantity
This value shows how much of the original substance remains after the specified time period. For example, after one half-life, approximately 50% of the original quantity remains.
Decay Constant (λ)
The decay constant represents the probability per unit time that a particle will decay. A larger decay constant means faster decay, while a smaller constant indicates slower decay.
Decay Graph
The graph visualizes the exponential decay process over time. The curve shows how the quantity decreases more rapidly at first and then slows down as time progresses.
1. What is half-life?
Half-life is the time required for a quantity to reduce to half of its initial value. This concept applies to many fields, including radioactive decay, pharmacology, and chemical reactions.
2. Why is half-life important?
Half-life is crucial in various applications, from determining the age of archaeological artifacts through carbon dating to calculating drug dosage intervals in medicine and understanding radioactive waste decay in nuclear physics.
3. How accurate is the half-life calculation?
The calculation is based on the ideal exponential decay model, which is highly accurate for most applications. However, real-world factors like temperature, pressure, or chemical environment might slightly affect the actual decay rate.
4. Can half-life change over time?
For radioactive decay, half-life is a constant that doesn't change over time. However, for biological or chemical processes, external factors can influence the effective half-life of a substance.
5. What is the scientific source for this calculator?
This calculator is based on the fundamental laws of exponential decay, first formulated by Ernest Rutherford and Frederick Soddy in their 1902 paper on radioactive decay. The mathematical model uses the exponential decay equation N(t) = N₀e^(-λt), which is derived from first-order kinetics and is documented in standard physics textbooks such as "Physics for Scientists and Engineers" by Serway and Jewett. The relationship between half-life and decay constant (λ = ln(2)/t₁/₂) is a mathematical consequence of this equation and is verified through extensive experimental evidence in nuclear physics and radiochemistry.