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

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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

$N_{t} = N_{0} e^{- λ t}$ $N_t = N_0e^(-λt)$

where

$N_{0}$ $N_0$ is the initial quantity of the substance,
$N_{t}$ $N_"t"$ is the quantity that remains decayed after a time $t$ $t$ ,
$t_{½}$ $t_½$ is the half-life, and

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

$λ = \frac{ln 2}{t_{½}}$ $λ = ln2/t_½$

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

$λ = \frac{ln 2}{231 yr}$ $λ = ln2/(231"yr")$ = 0.003 00 yr⁻¹

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

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

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