Question

How can half-life be calculated?

Answer 1

If the decay is exponential, i.e. `x=x_{0}e^{-kt}`, then the half-life is given by `ln(2)/k`.

Explanation:

Let `tau` be the half-life. `tau` is the time taken for `x_0` to reach `x_0/2`

`x_0/2=x_{0}e^{-ktau}`

`1/2=e^{-ktau}`

`2=e^{ktau}`

`ln(2)=ktau`

`tau=ln(2)/k`