# Determine half life from gamma radiation

• alivedude
In summary, the author is working on a lab and trying to determine the half life of an element. He has all the data, but cannot relate the gamma radiation to the half life. He needs help and asks for advice.

#### alivedude

I'm working on a lab and the task is to determine the half life of an element studying the beta radiation or the gamma radiation (emitted from the daughter). I have all the data and I'm done with the beta part, that was pretty straight forward. I have no clue how to relate the gamma radiation to the half life. This is how far I have come:

When a nucleus decays (in this case beta) it often leaves the daughter in an excited state. The daughter lowers it's energy by emitting photons but this doesn't necessary happens instant, right? So I can't count the photons and use the same equation as for beta radiation?

I don't even understand how I can relate the radiation from the daughter to the half life of the parent? I just need a push in the right direction.

Cheers! :)

alivedude said:
When a nucleus decays (in this case beta) it often leaves the daughter in an excited state. The daughter lowers it's energy by emitting photons but this doesn't necessary happens instant, right? So I can't count the photons and use the same equation as for beta radiation?
Depends on the isotope. As an example, if your beta decay has a half-life of 1 year, and the gamma decay has a half-life of one nanosecond, you can assume it to be instantly. Most gamma transitions happen even faster, just a few metastable nuclei have relevant lifetimes.

In general, the distribution of the gamma radiation will depend on both lifetimes (or even more if you have more than one gamma transition). If you know the distribution well enough, you can measure both at the same time. In practice, that will rarely work, so you need some approximation or other external input.

mfb said:
Depends on the isotope. As an example, if your beta decay has a half-life of 1 year, and the gamma decay has a half-life of one nanosecond, you can assume it to be instantly. Most gamma transitions happen even faster, just a few metastable nuclei have relevant lifetimes.

In general, the distribution of the gamma radiation will depend on both lifetimes (or even more if you have more than one gamma transition). If you know the distribution well enough, you can measure both at the same time. In practice, that will rarely work, so you need some approximation or other external input.

Hmm okay, thanks!

I think I need to ask my assistant about this because it sounds a bit beyond our scope in this course. Because I know there is several gamma transitions in my isotopes and I'm studying two isotopes at the same time, how should I know which photons that comes from what nucleus? Can I measure their energy and go from that in somehow?

If you have a detector that can measure the energy: sure. Those transitions usually have well-defined energies (if they don't, then they are really shortliving), and you can look them up.

mfb said:
If you have a detector that can measure the energy: sure. Those transitions usually have well-defined energies (if they don't, then they are really shortliving), and you can look them up.

Yeah we have such a detector in the lab and I found decay schemes so I know their transitions energies. But I still don't understand how you can relate these energies to the half-lifes?

Well, with the energy you can figure out which isotope lead to the decay, and then you can study how the rate changes over time (if the lifetime is short enough) or find a relation between total activity and sample size (if the lifetime is too long to observe the reducing decay rate over time).

mfb said:
Well, with the energy you can figure out which isotope lead to the decay, and then you can study how the rate changes over time (if the lifetime is short enough) or find a relation between total activity and sample size (if the lifetime is too long to observe the reducing decay rate over time).

It was actually much easier than I thought. After some checking the decays schemes I noticed that it was only one photon per isotope and it was emitted in nano seconds, so I could only count the photons basically. I just overcomplicated it all :) Thanks anyway for the help!