Half-life

Definition

Half-life is the time required for a quantity to reduce to half of its initial value. It is commonly used in contexts involving exponential decay, such as radioactive decay or pharmacokinetics.

5 Must Know Facts For Your Next Test

1. The formula for calculating half-life in terms of the decay constant $\lambda$ is $t_{1/2} = \frac{\ln(2)}{\lambda}$.
2. In exponential decay models, half-life remains constant regardless of the initial amount.
3. Half-life can be derived using integration techniques from the differential equation $\frac{dy}{dt} = -\lambda y$.
4. Understanding half-life is crucial for solving problems involving decay rates and predicting future amounts.
5. The concept of half-life applies to various fields such as physics, chemistry, biology, and environmental science.

Review Questions

• What is the relationship between the decay constant $\lambda$ and the half-life?
• How would you use integration to derive the formula for half-life from a given exponential decay model?
• If a substance has a known half-life, how can you determine the remaining quantity after a certain period?

Related terms

Exponential Decay: A process where quantities decrease at a rate proportional to their current value.

Decay Constant ($\lambda$): A parameter representing the rate at which a substance undergoes exponential decay.

$e$ (Euler's Number): $e$ is an irrational number approximately equal to 2.71828, and it serves as the base for natural logarithms in calculus.