Real-Life Math
Health physicists need polished math skills to be accurate and efficient
in their daily work.
Paul Mansfeld is a radiochemist.
"You use math all the time. I'm in and out of a chemistry lab all day,
where we do all kinds of chemical conversions to figure out the rate of decay
of radioactive materials," he says.
"Math helps you compare how much
you have versus how much you started with -- i.e., how much has gone away
since you last measured it."
You're a health physicist measuring
radioactive compounds left behind at a decommissioned nuclear weapons facility.
Your readings indicate 30 mg of tritium at the site, which has a half-life
of 12.3 years.
Given that the facility closed 24.6 years ago, how much
tritium was there to start? Base your result on the following criteria provided
by the Health Physics Society:
A half-life is the time required for
a population of atoms of a given radionuclide (a human-produced radioactive
compound like tritium) to decrease, by radioactive decay, to exactly one-half
of its original number. No operation, either chemical or physical, can change
the decay rate of a radioactive substance.
Half-lives range from much
less than a microsecond to more than a billion years. The longer the half-life,
the more stable the nuclide. After 1 half-life, half the original atoms will
remain. After 2 half-lives, one fourth (or 1/2 of 1/2) will remain. After
3 half-lives, one-eighth of the original number (1/2 of 1/2 of 1/2) will remain,
and so on.