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

##### 1 Answer
Jul 21, 2014

The equation for radioactive decay is

N_t = N_0e^(-λt)

where

${N}_{0}$ is the initial quantity of the substance,
${N}_{\text{t}}$ 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.