[kdog3682]

a .1ml sample of solution containing a radioactive nuclide (5000 counts per mililiter) is injected to a rat.  several minutes later, 1 cm of blood is removed.

blood shows 48counts per minute of radioactivity.

calculate volume of blood in the rat.

What asusumptions need to be made?

hElp@!@

[xiankai]

first of all you have to assume that the radioactive decay is very slow/or has a very long half-life, since you need to ensure the amount of radioactive nuclide injected remains relatively constant in the time taken to wait for it to spread throughout the bloodstream.

also, assume that the amount of radioactive nuclide inserted into the blood is relatively small in comparison to the total volume of blood in the rat, again to ensure the volume of blood you're trying to measure remains constant.

if 1cm³ of blood gives 48 counts, how much volume of blood would give 5000 counts?

[Yggdrasil]

This is, in essence, a dilution problem.  Think of counts per mL as a measure of concentration, then use the formula for dilution:

C_initialV_initial = C_finalV_final