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Physics question relating to medical isotopes

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LAN_403

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Wed Oct 26 2011, 03:22AM

Registered Member #561 Joined: Sat Mar 03 2007, 02:46AM
Location: Adelaide Australia
Posts: 230

I'm currently in my final year of high school physics, we're just about to have our final exams next week. We were going through some questions when something like his came up:

Two radioactive isotopes are available; one has a half-life of 8 minutes, the other 40 minutes. Which one would be safer to use?

I thought the question was poorly worded, as it didn't specify the elements in question. So I chose to assume they were both of the same element, and that during each half-life they would emit the same amount of radiation. From this I came to this conclusion:

The isotope with the longer half-life would be preferred because: both isotopes would be metabolised by the body at the same rate, and a longer hlf-life means you have less of the isotope decaying in your body. Say for example it takes 80 minutes for the body to metabolise all of it, then during that time you would have received 2 1/2 half-lifes of radiation. We can say that for the first half-life there was 1 gray of radiation, the second 1/2 gray, the third 1/4 gray etc. This would be about 1 1/2 grays of radiation received. The isotope with the shorter half-life however would give you a much larger dose, something like 2-3 grays.

I was told that the isotope with the shorter half-life would be preferable, as it minimised exposure time, I argued that it was not exposure time, but rather accumulative exposure.

So can anyone tell me if I'm wrong or right? Maybe we have a radiologist around here. I also think that if the tracer was a heavy metal it may turn out different, but my understanding though is that tracer are usually things like isotopes of xenon or nitrogen.

Mattski

Wed Oct 26 2011, 05:55AM

Registered Member #1792 Joined: Fri Oct 31 2008, 08:12PM
Location: University of California
Posts: 527

Half life is just a measure of the rate at which some species undergoes decay. If you start out with a certain number of particles then whether it takes 5 minutes or 10 years to decay then the total dose is just a function of the number of atoms times the energy released when each atom decays. And there are some weight factors for human risk based on the different kind of decay products (alpha, beta, gamma, etc).

The dose is just that total amount of energy, so if you assume that the two samples are identical in decay product and energy and only differ in half-life then the received dose is the same, assuming you are in contact with each sample until it is fully decayed. Some quick Wikipedia'ing seems to indicate that the best guess is that risk is proportional to total dose rather than dose rate, though there is not a clear consensus:

But the debate seems to be that lower dose rates might have no effect, so that would tend to suggest that the samples are equal in risk or the 40 minute half life sample might be marginally safer due to lower dose rate.

You could also argue that the 40 minute half life is in general safer because if you spend only a limited time with each sample then since the 40 minute sample is emitting radiation slower you will get a smaller dose.

I'm assuming that you can't predict anything about the energy or type of decay product from the half-life, something I really have no idea about.

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Wed Oct 26 2011, 05:58AM

Registered Member #561 Joined: Sat Mar 03 2007, 02:46AM
Location: Adelaide Australia
Posts: 230

It would seem I had to assume quite a bit. As I said the questions was quite lacking

radiotech

Wed Oct 26 2011, 08:41AM

Registered Member #2463 Joined: Wed Nov 11 2009, 03:49AM
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Posts: 1546

Would the one with the longer half life undergo more transitions to replenish the energy expended
to sustain particle emission while approaching the end state, than the one with the shorter half life ?

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Wed Oct 26 2011, 09:34AM

Registered Member #561 Joined: Sat Mar 03 2007, 02:46AM
Location: Adelaide Australia
Posts: 230

radiotech wrote ...

Would the one with the longer half life undergo more transitions to replenish the energy expended
to sustain particle emission while approaching the end state, than the one with the shorter half life ?

I'm not sure what you are asking

Forty

Wed Oct 26 2011, 11:49AM

Registered Member #3888 Joined: Sun May 15 2011, 09:50PM
Location: Erie, PA
Posts: 649

yes the question is definitely lacking.
it would depend a lot on the element:
-whether or not it can be metabolized or removed from the body
-how it is administered into the body.
-and toxicity

if both elements could be pissed out completely in an hour, then you'd want the slower decaying one for less radiation exposure.

radiotech

Fri Oct 28 2011, 03:22AM

Registered Member #2463 Joined: Wed Nov 11 2009, 03:49AM
Location:
Posts: 1546

The original question concerned the safety of use. It did not mention if it was for human therapy. There
are many uses of isotopes. Safety could involve some intermediate product as the isotope ages. So one
may be a far simpler type of disintegration than the other, having none of these intermediates.

What context were you discussing in your physics class?

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