Untitled - Kelly Walsh High School

302 CHEMISTRY FOR THE UTTERLY CONFUSED
The current decay rate of the 14 C in a sample is 4.82 disintegrations per minute
per gram (d/ming). The 14 C activity of living organisms is 15.3 d/ming. The halflife
of 14 C is 5730 years. How many years old is the sample?
We can recopy and label the variables to get:
N 0 15.3 d/ming N t 4.82 d/ming t 1/2 5730 y t ?
There is no single equation containing these four variables. For this reason, we
need to use the two equations: ln (N t/N 0) kt and t 1/2 (ln 2)/k. We will
begin with the half-life equation t 1/2 (ln 2)/k. We need to rearrange this equation
and enter the half-life to determine the decay constant:
k (ln 2)/t 1/2 (ln 2)/5730 y 0.693/5730 y
1.209424 10 4 y 1 (unrounded)
Now that we have the value of the decay constant, we can now use the other
equation. We rearrange this equation:
ln a
t
Nt b
N0 k
We can now enter the values and calculate the time.
t 9550.8 9.55 103 4.82 d /min·g
ln a
15.3 d/min·g
y
b
1.209402 104 y1 Nuclear reactions involve the decay of an unstable isotope to a more stable one.
The natural decay modes include alpha emission, beta emission, gamma emission,
positron emission, and electron capture. By considering the ratio of neutrons
to protons in a particular isotope, we may be able to predict whether a
certain isotope is stable and its possible decay modes. The half-life (t 1/2) is the
amount of time that it takes for one-half of a sample of a radioactive isotope to
decay. This decay follows first-order kinetics. Using the equations derived for
first-order kinetics allows us to calculate time, half-life or amount. Einstein’s
equation allows us to calculate the amount of energy released when a certain
amount of matter is converted to energy. Practical applications of nuclear decay
include fission, the decay of a larger isotope into two or more smaller ones, and
fusion, the combining of lighter isotopes into a heavier one. Fission is currently
used in nuclear power generators and atomic bombs. Fusion may eventually
provide an unlimited power source.