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

 

[nlightner]

The effective half-life of a radioactive isotope is a combination of its physical half-life and its biological half-life. In this case, the physical half-life is six days and the biological half-life is ten days. To calculate the effective half-life, we can use the formula T1/2 = 0.693/k, where k is the decay constant.

First, we need to find the decay constant by dividing 0.693 by the physical half-life of six days. This gives us a decay constant of approximately 0.1155 days^-1.

Next, we can use this decay constant to calculate the effective half-life by dividing 0.693 by the sum of the decay constant and the biological half-life of ten days. This gives us an effective half-life of approximately 4.8 days.

Therefore, the effective half-life for the given radioactive isotope is approximately 4.8 days. This means that after 4.8 days, half of the initial amount of the isotope will have decayed. After another 4.8 days, half of the remaining amount will have decayed, and so on. It is important to note that the effective half-life may vary depending on the individual and their specific biological processes.