How can I calculate nuclear half life?

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Answer 1 · 2018-03-14T23:00:09

Consider that radioactive decay follow first order kinetics. Recall,

#ln[A]_"t" = -kt + ln[A]_0" " (1)#

Now, consider,

#=> -ln(([A]_"t")/([A]_0)) = kt#

#=> ln(([A]_0)/([A]_t))/k = t#

#=> ln(2/1)/k = t#

#therefore t_(1/2) = ln(2)/k" "(2)#

Now, if we knew the rate constant for the specific decay, we could calculate the half life of that radioactive sample.

Or, practically, we could measure a sample at different intervals and calculate the rate constant in (1) and apply it to (2).