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.
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.
Definition and Formula
Half‑life denotes the period needed for a given amount to fall to fifty percent of its original value. While the term is most frequently linked to radioactive atoms, it equally describes any diminishing process, whether exponential or not. A well‑known practical use of half‑life is radiocarbon dating. Carbon‑14 possesses a half‑life of roughly 5,730 years, enabling dependable dating of objects up to about 50,000 years old. The method was refined by William Libby and depends on the continual production of carbon‑14 in the atmosphere. Plants take it up through photosynthesis, and animals acquire it by consuming those plants. Once the organism dies, the carbon‑14 decays, and by measuring the remaining quantity we can infer the time of its demise.
Below are shown three equivalent formulas describing exponential decay:
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where
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
If an archaeologist found a fossil sample that contained 25% carbon-14 in comparison to a living sample, the time of the fossil sample's death could be determined by rearranging equation 1, since Nt, N0, and t1/2 are known.
This means that the fossil is 11,460 years old.
Derivation of the Relationship Between Half-Life Constants
Using the above equations, it is also possible for a relationship to be derived between t1/2, τ, and λ. This relationship enables the determination of all values, as long as at least one is known.
