How do you use the exponential decay formula?

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Answer 1 · 2014-12-16T23:06:15

I'll use an example from radioactive decay:

$N_t=N_0e^(-lambdat)$

$N_t$ = number of undecayed atoms after time $t$

$N_0$ = initial number of atoms

$lambda$ = decay constant.

$t$ = time elapsed.

" $I^131$ is a radioactive isotope with a half - life of 8 days. Starting with a mass of 5g, what mass will remain after 10 days? "

$t_((1)/(2)) =0.693/lambda$

So $lambda=0.693/t_((1)/(2)) =0.693/8 = 0.0866d^(-1)$

Taking natural logs of the decay equation we get:

$lnN_t=lnN_0-lambdat$

So $lnN_t=ln(5) - 0.0866xx10$

$lnN_t = 1.61-0.866=0.744$

From which $N_t =2.1g$

I can use grams instead of number of atoms as they are proportional so the constant will cancel out.