How Do You Calculate the Effective Half-life of a Radioactive Isotope?

[larianne]

Homework Statement

If a patient is given a radioactive isotope which has a half-life of six days and a biological half-life of ten days, what is the effective half-life for the isotope.

Homework Equations

I know the formula for half-life calculations is T1/2 = 0.693/k

The Attempt at a Solution

I don't know where to start with this. My tutor just briefly went over it. It was a question on a past paper so I just want it covered in case it comes up in my exams.

Any help I'd be grateful. Thanks.

 

[LowlyPion]

Homework Statement

If a patient is given a radioactive isotope which has a half-life of six days and a biological half-life of ten days, what is the effective half-life for the isotope.

Homework Equations

I know the formula for half-life calculations is T1/2 = 0.693/k

The Attempt at a Solution

I don't know where to start with this. My tutor just briefly went over it. It was a question on a past paper so I just want it covered in case it comes up in my exams.

Any help I'd be grateful. Thanks.

For what you are asking I think it works something like this:

N = N_o*e^-t/T1*e^-t/T2 = N_o*e^-t/T1+t/T2 = N_o*e^t/T

Where 1/T = 1/T1 + 1/T2