Interactive Half-Life Calculator

Visualize and calculate radioactive decay with ease. Understand how much substance remains over time.

Calculate Half-Life

Decay Rate:

% per unit time

Half-Life:

Calculate Remaining Quantity

Half-Life:

Initial Quantity:

Time Elapsed:

units of time

Remaining Quantity:

Half-Life Formula

The half-life ($t_0.5$) is the time required for a quantity to reduce to half of its initial value. It is related to the decay rate ($\lambda$) by the formula:

$$ t_{1/2} = \frac{\ln(2)}{\lambda} = \frac{0.693}{\lambda} $$

Where:

$t_0.5$ is the half-life.
$\lambda$ is the decay constant (decay rate).

Understanding Half-Life

Half-life is a crucial concept in various fields, especially in nuclear physics and pharmacology. It describes the duration after which half of a substance has decayed or been eliminated. For instance, in radioactive materials, it's the time it takes for half of the atoms to undergo radioactive decay. In medicine, it refers to the time it takes for the concentration of a drug in the body to reduce by half.

Uses of Half-Life Calculator

Radioactive Dating: Determine the age of ancient artifacts or geological formations by measuring the remaining amount of radioactive isotopes.
Nuclear Medicine: Calculate dosages and understand the duration of radioactivity in medical treatments using radioactive tracers.
Pharmacology: Predict how long a drug will remain effective in the body and determine appropriate dosing intervals.
Environmental Science: Assess the persistence of pollutants in the environment and their decay rates.

Sources: Wikipedia, Britannica

About Half-Life

Half-life is the time it takes for a quantity to reduce to half its initial value. This term is commonly used in nuclear physics to describe how quickly radioactive atoms undergo decay, but it can apply to any quantity that decreases exponentially over time. For example, if a radioactive substance has a half-life of 10 years, then every 10 years, the amount of the substance remaining will be halved.

Key Concepts:

Decay Rate: The rate at which a substance decreases. It's often expressed as a percentage per unit of time.
Exponential Decay: The process where the quantity decreases at a rate proportional to its current value. Half-life is a characteristic of exponential decay.
Applications: Understanding half-life is crucial in fields like medicine (drug metabolism), environmental science (pollutant degradation), and archaeology (carbon dating).

This calculator helps you explore these concepts by allowing you to calculate half-life from a given decay rate, or determine the remaining quantity of a substance after a certain period.