Question

Can you determine the annual decay rate of a certain radioactive isotope that has a half life of 231 years?

Answer 1

The equation for radioactive decay is

`N_t = N_0e^(-λt)`

where

`N_0` is the initial quantity of the substance,
`N_"t"` is the quantity that remains decayed after a time `t`,
`t_½` is the half-life, and

`λ` is a number called the decay constant or the rate constant for the decay. `λ` is also the decay rate.

`λ = ln2/t_½`

If the half-life is 231 years, the decay constant is

`λ = ln2/(231"yr")` = 0.003 00 yr⁻¹

That is, the decay rate is 0.300 % per year.