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.