24.3. Decay Equations http://www.ck12.org
24.3 Decay Equations
Nuclear decay is often measured in terms of half lives. During the span of one half life, the amount of a decaying
substance decreases by half. Therefore, afterkhalf lives, the amount of a substance starting atN 0 left is
N(k) =N 0 ×^12
kIf we need to know the amount left after some timet, we first need to see find many half lives transpired (this will
be given bytHt, then use the formula above:
N(t) =N 0 ×^12
tt
HIf on the other hand, we know how much of a substance is left and would like to find how much time has transpired,
we can solve the equation above fort(left to reader):
t=tHlnNN 0
ln^12This equation is used in radioactive dating:
Question: The half-life of^239 Pu is 24,119 years. You have 31.25 micrograms left, and the sample you are studying
started with 2000 micrograms. How long has this rock been decaying?
Answer: We will use the equation for time and simply plug in the known values.
t=tHlnNN 0
ln^12=24119yln^312000.^25 μμgg
ln^12= 144 ,700yearsRadioactive carbon datingis a technique that allows scientists to determine the era in which a sample of biological
material died. A small portion of the carbon we ingest every day is actually the radioactive isotope^14 C rather than
the usual^12 C. Since we ingest carbon every day until we die (we do this by eating plants; the plants do it through
photosynthesis), the amount of^14 C in us should begin to decrease from the moment we die. By analyzing the ratio
of the number of^14 C to^12 C atoms in dead carbon-based life forms (including cloth made from plants!) and using
the technique illustrated above, we can determine how long ago the life form died.