SELF-TEST III, QUESTION 4

Three bats, 'Bewitched', 'Bothered', and 'Bemildred', each drink one cup of radioactive coffee, leaving exactly one cup of coffee in the pot. Forty (40.0) minutes later, two of the bats are eaten by 'Howland Owl'. Six (6.00) hours after this meal, the owl has a total body count of 200 disintegrations per minute, which, by coincidence, is exactly 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 initial amount ingested by the owl?
(b) What was the initial amount in the pot?
(c) What is the physical half life of the isotope?
(d) What is the biological half-life for this isotope in a bat?

This is a difficult problem and if you can do it without looking at the solution you are well prepared.

There are 3 timelines to be followed and described mathematically:
1. The one quarter portion of coffee in the pot decays physically for 400 min.
2. The bats contribute to the decay of 2 portions for 40 min.
3. What is left in the bats becomes the initial amount for the owl where it decreases for 360 min.

If you write down the correct equation for each of these timelines you will have the answers. Of the 3 equations only one will have one unknown-clearly you must start the numerical part of the solution with that one.
 

Solution

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