©Department of Physics, University of Guelph.

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1. The physical half life of an isotope is 15 days. What is the corresponding decay constant in day-1 and s-1?

2. The values of lp and  lb for a particular radioactive isotope in humans is 0.080 day-1 and 0.050-1 respectively. What is the effective half life of the isotope in humans?

3. Two goats at Port Hopeless, Ontario accidentally get into a field containing radioactive grass. The goat "Aristophanes" eats twice as much grass as the goat "Demetrius". However Aristophanes' metabolism is 1.5 times faster than that of Demetrius and the ingested isotope has in this case a biological decay constant which is directly proportional to metabolism. If the biological decay constant is 0.10 day-1 in Demetrius, how long will it be until the two goats contain the same concentration of isotope? Assume that the physical half life is very long compared to the biological half lives.

4. Three bats Bewitched, Bothered and Bemildred, each drink one cup of radioactive coffee, leaving exactly one cup in the pot. 40.0 minutes later, two of the bats are eaten by Howland Owl. 6.00 hours after the meal, the owl has a total body count of 200 disintigrations per minute which, by a curious coincidence, is the same count rate as the cold coffee at that time. The effective half life for the radioactive isotope is 4.00 hours in an owl and 1 hour and 20 minutes in a bat.
a) What is the biological half life for the isotope in a bat?
b) What is the initial count rate for the full pot of coffee?

With affectionate apologies to POGO

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