Untitled - Kelly Walsh High School

300 CHEMISTRY FOR THE UTTERLY CONFUSED
use of magnetic fields (“magnetic bottles”) to contain the nuclei at this temperature.
If they can overcome these obstacles, fusion may well provide a limitless
energy source for our world. The production of neutrons by this process is a
problem. It is difficult to keep a neutron in a magnetic bottle. Escaping neutrons
will convert some of the material in the fusion plant into radioactive wastes.
20-6 Utterly Confused About
Nuclear Decay
Nuclear decay problems normally use one or both of the following equations:
(1) ln (N t/N 0) kt and (2) t 1/2 (ln 2)/k or t 1/2 0.693/k
The terms N t and N 0 may have many different units. The only restriction on the
units is that these two terms have the same units. If they do not have the same
units, you will need to convert one of the units. Both t and t 1/2 will have units of
time. Any time unit may be present. The rate constant (decay constant), k, will
have units of time 1 . Any time unit may be present. The time units for t, t 1/2, and
k must agree. If the units do not agree, you will need to make a conversion.
Let’s look at some sample questions.
Determine the decay constant for iron-55. The half-life of iron-55 is 2.7 years.
You should begin a problem of this type by recopying and labeling each of the
known and unknown variables:
k ? t 1/2 2.7 y
These two variables appear in the equation t 1/2 (ln 2)/k. We can rearrange this
equation to find k, and enter the value for the half-life:
k (ln 2)/t 1/2 (ln 2)/2.7 y 0.693/2.7 y 0.256667 0.26 y 1
What is the half-life for argon-41? The decay constant for argon-41 is 6.33
10 3 min 1 .
We can recopy and label the variables to get:
k 6.33 10 3 min 1 t 1/2 ?
These two variables appear in the equation t 1/2 (ln 2)/k. We do not need to
rearrange this equation. We only need to enter the value for the decay constant.