How much gasoline is in the underground storage tank?

[astrostar2]

Homework Statement

Suppose that you wish to find out how much gasoline is in an underground storage tank. You pour in one gallon of gasoline that contains some half-life radioactive material that causes a Geiger constant to register 48400 counts per minute above background radiation. The next day you remove a gallon from the underground tank and measure its radioactivity to be 100 counts per minute above background

Homework Equations

none

The Attempt at a Solution

The only formula that comes to mind is N=n0e^(kt), so I solved for the decay rate to be .00429 counts/min. But I'm not quite sure how to connect it to the gallons of gasoline.

 

[voko]

How did you compute the decay rate?

 

[astrostar2]

I plugged in the counts as the N values.

 

[astrostar2]

...which might be completely wrong :/

 

[voko]

You can't take those counts directly. The counts depend on the amount of material and its activity. What you get the next day is decayed AND diluted.

Quite frankly, I am not sure how to solve this problem if the decay is very significant. We have an unknown amount of material with unknown activity. So given the number of counts, we can get the relationship between the amount and activity. The next day counts will relate these two with another unknown, the amount of gasoline. So we have three unknowns and only two equations. That can't be solved.

I think you should treat it as if the decay did not significantly affect the amount of the radioactive material. This can be solved easily.

 

[astrostar2]

Ah, that was right! Thank you :)