Question

Find the half-life for strontium-90 if k=0.026, where `A = A_0 e^(-kt)` (ignore the parethesis) and `t` is expressed in years?

Answer 1

Half life is`26.55` years.

Explanation:

Half life means the period in which a radioactive material decays and reduces to half of its original strength.

The equation `A=A-0e^(-kt)` indicates original strength of `A_0` and let `t_h` be its half life in which it reduces to `A_0/2`

Hence `A_0/2=A_0e^(-kt_h)`

or `e^(-kt_h)=1/2` i.e. `e^(kt_h)=2` or `kt_h=ln2`

and as `k=0.026`

`t_h=ln2/0.026=0.6931472/0.026=26.66` years