Question

If 1/8 remains after 21 years, what is the half-life?

Answer 1

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.