Thread: Question about half life

Problem I did not know how to do:

A student wants to measure the half life of a radioactive isotope. He is told the isotope has a half life of between 10 and 20 minutes. Illustrating your answers appropriate, describe:

A). the measurements that he should take
B). how he should use the measurements to arrive at an estimate of the half life for the isotope.

I understand that to measure the half life of a radioactive material you measure the activity of the sample at regular times.

What I do not understand is the significance of the half life being between 10 and 20 minutes.

I'm not sure how he should take the measurements?..

Does he measure the becquerel at various intervals and then plot this in the graph? If so, what is the significance of telling us that the half life is between 10 and 20 minutes? I know what a half life is but why is telling us this what the half life is in between any different from just measuring the becquerel on our own and figuring out the half life from that?

One simple way to measure half life is to take activity readings as follows. Take an initial reading at time t=0, then take readings as close as possible together between 10 and 20 minutes later. The time at which the activity is half the initial reading is the half life.

You can use an equation for exponential decay.
From Wikipedia:


Nt = the remaining radioactive material
N0 = the initial amount
{lambda} = decay constant

So the first measurement would be at t=0 to find the initial quantity. Then you could measure it at any other time, plug that value in for Nt, and use the value at t=0 for N0, and you know t, then just solve for {lambda}.

Once you know {lambda} you are basically done. To find the half-life simply put in your initial value, N0, and set Nt = (1/2)N0, plug in your {lambda} and solve for t. That's it.

It seems to me that the only point in saying that the half-life is between 10 and 20 minutes is to rule out the possibility of it being very short or very long. If it was 0.1 seconds, 10 minutes later, there won't be much left. If it's 1000 years, 10 minutes later, nothing would have changed.

Originally Posted by MagiMaster

It seems to me that the only point in saying that the half-life is between 10 and 20 minutes is to rule out the possibility of it being very short or very long. If it was 0.1 seconds, 10 minutes later, there won't be much left. If it's 1000 years, 10 minutes later, nothing would have changed.

What that provision does is make the simple experiment suggested by mathman practical.

Take a reading. Start the clock. Keep looking at the dial. When it shows half of the original reading, look at the clock again. That is the half-life.

That is not practical if the half-life is a nanosecond -- you might blink and miss the whole show. And it is not practical if the half-life is a century. But if the half-life is a few minutes the experiment is simple and reasonably accurate.

I know this is a bit late.

But the key feature that everyone is missing, is that you can not instantaneously accurately measure the activity of a radioactive sample.

You count the number of decays over a period of time. To get the activity you divide the number of decays by the time elapsed. But doing this assumes that the activity does not change significantly over the counting time. This is where the 10-20 minute half life is important.

Ideally, I would want to take measurements over the longest period of time possible. This will reduce statistical noise. But if I count too long then the activity will change significantly and my results will be meaningless.

For example, if I had a sample that had a half life of 100 years. Then I could spend an entire day doing one count, and that would give me better statistics than if I counted for 1 hour, or 1 second. Also because the counting time is a lot smaller than the half life I don't have to worry about the activity changing.

Conversely, in you example where the half life is 10-20 minutes, if I tried to spend all day doing one count I would get useless data. Instead I would try to count for 30 second to 1 minute. Anything longer and I would have to account for changes in activity during my count.