# The Naked Scientists Forum

#### jlevkov

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« on: 20/02/2004 13:00:42 »
How are the half-lifes for longlived radioisotopes measured?

#### Ylide

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« Reply #1 on: 21/02/2004 02:36:31 »
I believe by a function of how much radiation is given off per mass of isotope in a given time.  For instance, if X grams of an isotope are emitting Y gamma particles per minute, there is a logarithmic fucntion using X*6.02E23 as the total number of molecules and Y as a function of time to determine halflife.  I don't recall the exact equation, but it's solution to a first order differential:  dm/dt=log C where dm is change in @atoms, dt is change in time and C is halflife...split the differential, integrate,  and solve for C to find it using measured data.

I think there's a way to do it using quantum mechanics, too....soemthing to do with probability of the nucleus being in the correct state to emit a particle.  The longer the halflife, the lower this probability for a given atom is.  We haven't covered this in class just yet, so I can't be more specific.

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#### chris

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« Reply #2 on: 21/02/2004 08:14:19 »
A great question.

Radioactive decay is modelled exponentially. When a nucleus decays, emitting a gamma ray, an alpha particle or a beta particle, it changes into a different isotope. Every nucleus has the same probability that it will decay.

But which ones do decay is a random or stochastic process. When an isotope has a long half life the probability of an individual nucleus decaying at a given time point is very low. Isotopes with a short half life have a much higher probability of decay.

Physicists have derived a formula which allows you to tell how many (but not precisely which) nuclei in a sample will have decayed after a certain period of time has elapsed. This formula is as follows :

...where N is the number of nuclei that decay, No is the number of nuclei that your started with, e is the natural (Naperian) logarithm, lambda is a mathematical value called the decay constant (given by ln2/half-life), and t is time.

The half life is the time taken for half of the radioactive nuclei to decay.

Therefore, if you take a known amount of the isotope you are interested in you can work out how many atoms (and hence nuclei) it contains. Then, by measuring how many 'counts' or decays it undergoes over a known period of time you can use the above formula to work out the half life.

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#### jlevkov

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« Reply #3 on: 26/02/2004 13:32:56 »
quote:
Originally posted by jlevkov

How are the half-lifes for longlived radioisotopes measured?

Thank you. I about all this.  My real question is about the practical aspect of making these measurements on something that may have a half-life of thousands, or millions of years.

#### tweener

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« Reply #4 on: 27/02/2004 01:35:36 »
I think Chris covered that pretty well.  The equations are used to model the radioactive decay and thus predict the half-life.  The physical models of atoms and quantum mechanical effects are very good and produce meaningful results to many significant digits, so the calculation is quite accurate.

----
John - The Eternal Pessimist.