Initial quantity
Half life time
sec
Total time
sec
Remaining quantity
Decay constant
/
sec
sec

# Half Life Calculator

By Bogna Haponiuk

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

1. Determine the initial amount of a substance. For example, `N(0) = 2.5 kg`.
2. Determine the final amount of a substance - for instance, `N(t) = 2.1 kg`.
3. Measure how long it took for that amount of material to decay. In our experiment, we observed that it took 5 minutes.
4. 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.
5. 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.

Bogna Haponiuk

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