SAT Subject Test Chemistry,10 edition

where λ is known as the decay constant, which is just the rate constant for the decay reaction. The
solution of this equation tells us how the number of radioactive nuclei changes with time. The
solution is known as an exponential decay:

n   =   n 0 e–λt

where n 0 is the number of undecayed nuclei at time t = 0. The decay constant is related to the half-

life by .

Example: If at time t = 0 there is a 2-mole sample of radioactive isotopes of decay constant 2
(hour)–1, how many nuclei remain after 45 minutes?
Solution: Since 45 minutes is 3/4 of an hour, the exponent is:

The exponential factor  will    be  a   number  smaller than    1:

e–λt    =   e–3/2   =   0.22

So only 0.22 or 22% of the original 2-mole sample will remain. To find n 0 we can multiply the
number of moles we have by the number of particles per mole (Avogadro’s number):

n 0     =   2(6.02  ×   10^23 ) =   1.2 ×   10^24

From the equation that describes exponential decay, you can calculate the number that remain
after 45 minutes: