A certain radioactive isotope has leaked into a small stream. Two hundred days after the leak, 15% of the original amount of the substance remained. Determine the half-life of this radioactive isotope.

Question

A certain radioactive isotope has leaked into a small stream.  Two hundred days after the leak, 15% of the original amount of the substance remained.  Determine the half-life of this radioactive isotope.

irishboy123 · Answer

the fundamental decay equation is: $ N(t) = N_0 e^{- k t}$

the steps:

find k from the first data point, viz $N(200) = 0.15 N_o = N_0 e^{- k( 200)}$

then, use same equation to calc half life $T$: 

$N(T) = 0.5 * N_o = N_o e^{-k T}$

anonymous · Answer

Great! Thanks--I was on the right track.