Half-Life Calculator
The half-life calculator is a tool that helps you understand the principles of radioactive decay. You can use it to not only learn how to calculate half-life, but also as a way of finding the initial and final quantity of a substance or its decay constant. This article will also present you with the half-life definition and the most common half-life formula.
Half-life definition
Each radioactive material contains a stable and an unstable nuclei. Stable nuclei don't change, but unstable nuclei undergo radioactive decay, emitting alpha particles, beta particles or gamma rays and eventually decaying into a stable nuclei. Half-life is defined as the time required for half of the unstable nuclei to undergo their decay process.
Each substance has a different half-life. For example, carbon-10 has a half-life of only 19 seconds, making it impossible for this isotope to be encountered in nature. Uranium-233, on the other hand, has the half-life of about 160 000 years.
This term can also be used more generally to describe any kind of exponential decay - for example, the biological half-life of metabolites.
Half-life is a probabilistic measure - it doesn't mean that exactly half of the substance will have decayed after the time of the half-life has elapsed. Nevertheless, it is an approximation that gets very accurate when a sufficient number of nuclei are present.
Half-life formula
The number of unstable nuclei remaining after time t can be determined according to this equation:
N(t) = N(0) * 0.5(t/T)
where:
- N(t) is the remaining quantity of a substance after time t has elapsed.
- N(0) is the initial quantity of this substance.
- T is the half-life.
It is also possible to determine the remaining quantity of a substance using a few other parameters:
N(t) = N(0) * e(-t/τ)
N(t) = N(0) * e(-λt)
- τ is the mean lifetime - the average amount of time a nucleus remains intact.
- λ is the decay constant (rate of decay).
All three of the parameters characterizing a substance's radioactivity are related in the following way:
T = ln(2)/λ = ln(2)*τ
How to calculate the half-life
- Determine the initial amount of a substance. For example,
N(0) = 2.5 kg. - Determine the final amount of a substance - for instance,
N(t) = 2.1 kg. - Measure how long it took for that amount of material to decay. In our experiment, we observed that it took 5 minutes.
- Input these values into our half-life calculator. It will compute a result for you instantaneously - in this case, the half-life is equal to 19.88 minutes.
- If you are not certain that our calculator returned the correct result, you can always check it using the half-life formula.
Confused by exponential formulas? Try our exponent calculator.