Calculating Radioactive Decay of 18F Isotope in PET Scanners

[hms.tech]

Homework Statement

Positron Emission Tomography (PET) scanners frequently operate us-
ing the radioactive isotope 18F, which has a half life of about two hours.
The isotope is incorporated into a drug, half of which is excreted by
the body every two hours. How long will it take before the quantity of
radioactive drug in the body halves?
A 0.5 hours B 1 hour
C 1.5 hours D 2 hours

Homework Equations

Radio active decay is given by :
where λ ≈ 0.347
N = $N_{0}$ $e^{-\lambda t}$

The Attempt at a Solution

Assuming that the body excretes every two hours and not during that time, then it is impossible for the drug to get half.
But unfortunately that answer choice is not present.

Any help is greatly appreciated .

 

[ehild]

Assume that the body excretes the drug continuously.

ehild

 

[hms.tech]

then the obvious answer is "B" ; 1 hour .

 

[Ibix]

It's not linear. Try writing down the quantity at 'easy' times - 0, 2hrs, 4hrs, etc. What is the function for the concentration here?

Tip: [strike]N=N₀2^-t[/strike] N=N₀2^-t/T, where T is the half-life, is an easier way to write your half-life formula.

 

[hms.tech]

It's not linear. Try writing down the quantity at 'easy' times - 0, 2hrs, 4hrs, etc. What is the function for the concentration here?

Tip: N=N₀2^-t is an easier way to write your half-life formula.

I considered the "excretion" to vary linearly with time but I never assumed the half life to be the same.

I deduced the answer by using the correct expression of exponential decay of the radioactive sample.

Am I still wrong ?

 

[ehild]

then the obvious answer is "B" ; 1 hour .

Your answer is correct.

ehild

 

[Ibix]

Sorry - fell victim to the algebraic slip now corrected above. The answer is half a half life, not half an hour. You are correct.