# How do I find the half-life of an element?

sciencesolve | Teacher | (Level 3) Educator Emeritus

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There exists three equivalent formulas that you can use to evaluate the half life of an element. You may select one formula out of the three, depending the inputs provided by the problem.

The formulas that you may want to work with are the following:

1) `A(t) = A_0*(0.5)^(t/t_(0.5))`

`A(t)` represents the amount of element that is not decayed

`A_0` represents the original amount of element, before the decaying process

`t` represents the time

`t_(0.5)` represents the half life of decaying amount

2) `A(t) = A_0*e^(-lambda*t)`

You should notice that in this equivalent formula the factorÂ `e^(-lambda*t)` replaces `(0.5)^(t/t_(0.5))`

`lambda` represents the decay constant, `lambda > 0`

3) `A(t) = A_0*e^(-t/tau)`

`tau = 1/lambda, tau > 0`

Hence, you may evaluate the half life of an element, using the formulas above with respect to the information provided by the problem.