Half-Life Calculator
The following tools can generate any one of the values from the other three in the half-life formula for a substance undergoing decay to decrease by half.
Modify the values and click the Calculate button to use
Half-Life Calculator
Please provide any three of the following to calculate the fourth value.
Half-Life, Mean Lifetime, and Decay Constant Conversion
Please provide any one of the following to get the other two.
Understanding Half-Life and Exponential Decay
Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value. The term is most commonly used in relation to atoms undergoing radioactive decay, but can also describe other types of decay, whether exponential or not.
One of the most well-known applications of half-life is carbon-14 dating. The half-life of carbon-14 is approximately 5,730 years, and it can be reliably used to measure dates up to around 50,000 years ago. The process of carbon-14 dating was developed by William Libby and is based on the fact that carbon-14 is constantly being produced in the atmosphere. It is incorporated into plants through photosynthesis, and then into animals when they consume plants. Once the plant or animal dies, the carbon-14 undergoes radioactive decay, and measuring the remaining amount of carbon-14 in a sample can convey information about when the organism died.
Exponential Decay Formulas
Below are three equivalent formulas commonly used to describe exponential decay:
- N0 is the initial quantity
- Nt is the remaining quantity after time, t
- t1/2 is the half-life
- τ is the mean lifetime
- λ is the decay constant
Example of Exponential Decay
If an archaeologist found a fossil sample that contained 25% of the carbon-14 in comparison to a living sample, the time of the fossil’s death could be determined by rearranging the exponential decay equation, since Nt, N0, and t1/2 are known.
Example Solution:
This calculation would reveal that the fossil is approximately 11,460 years old.
Relationship Between Half-Life Constants
Using the exponential decay equations above, it is also possible to derive a relationship between t1/2, τ, and λ. This relationship enables the determination of all values as long as at least one of them is known.
These relationships are fundamental in physics, chemistry, archaeology, and many other fields dealing with decay processes.
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Half Life Calculator on Calculator.net