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

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Answer 1 · 2014-07-21T17:01:25

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.