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Randomness of radioactive decay

  1. Nov 24, 2014 #1
    Hi everyone!

    I have two questions about radioactive decay that some of you might be able to answer (I'm a mathematician and no physicist by the way). The first one is very general:
    As I understand it the time at which a single instable atom decays is believed to be a truly random process. But what about the type of decay that occurs? For example if you lookup Technetium-99m in wikipedia it says under Nuclear properties:
    "Tc-99m decays mainly by gamma emission, slightly less than 88% of the time."
    and
    "The remaining approximately 12% of 99mTc decays are by means of internal conversion, resulting in ejection of high speed internal conversion electrons in several sharp peaks (as is typical of electrons from this type of decay) also at about 140 keV"
    Is it also truly random which type of decay will occur in the same sense it is random when it will occour? Should these values 88% and 12% be valid under all circumstances or are there any environmental factor that are known or at least believed to influence them? For example it is known that observing a single instable atom (testing if it has decayed) will collapse its wave function and in some sense "reset the timer". So an atom that is constantly observed is believed to never decay which means that the decay rate is only true for unobserved atoms. Is there anything that is believed to influence the type of decay as well? (if it even is truly random)
    My second question is very specific and relates to the mentioned Technetium-99m. Does anyone happen to know where I can find the most accurate chances of it decaying one or the other way that are known from experiments or follow from theory. Do these chances (and also the decay rate) even follow from theory or can they only be found experimentally?
     
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  3. Nov 24, 2014 #2

    e.bar.goum

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    Yes, branching ratios are also random in terms of which one will occur. Just like if I toss a coin, 50% of the time it is heads, so I'd say that the heads branching ratio is 50%.

    The caveat is for isotopes that decay via Electron Capture or Internal Conversion (your 99mTc example was prescient!). In those cases, the decay is due to the interaction between the electrons around the nucleus, so if you ionize the atom, you perturb the decay rate. This is often subtle (most IC or EC is due to the innermost electrons). If you fully ionize 7Be, it will never decay as the only possible decay channel is through EC.

    The National Nuclear Data Center is where you will find information like the decay of 99mTc. It is home to the "accepted" data for every isotope. Since 99mTc is very important for medical uses, the half-life and branching ratios are well studied. http://www.nndc.bnl.gov/nudat2/chartNuc.jsp Search 99Tc in the search box, and click "level scheme" or "decay radiation". Looks like there's also a very small chance that beta minus decay can occur! The IT vs B- branching ratios are shown here to 6 significant figures!

    In nuclear physics, our theoretical models aren't good enough to give us that sort of accuracy.
     
  4. Nov 24, 2014 #3

    mfb

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    There is no timer. That's the point of "random". It can decay within a nanosecond - and the probability to decay within the next nanosecond (if it still exists) is always the same.

    It is possible to make rough theoretical predictions for branching ratios, but usually it is easier to measure them.
     
  5. Nov 24, 2014 #4

    DrChinese

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    I don't know that this environmental factor affects the branching ratios, but gravity (GR) does affect the half-life of any decay reaction. In other words, there are relativistic considerations since time dilates in its presence. This is relevant in collider experiments.
     
  6. Nov 24, 2014 #5
    Thank you all for your replies!

    On "There is no timer" from mfb:
    If that is true then I don't understand the Quantum Zeno effect:

    http://en.m.wikipedia.org/wiki/Quantum_Zeno_effect

    "Consider a system in a state A, which is the eigenstate of some measurement operator. Say the system under free time evolution will decay with a certain probability into state B. If measurements are made periodically, with some finite interval between each one, at each measurement, the wave function collapses to an eigenstate of the measurement operator. Between the measurements, the system evolves away from this eigenstate into asuperposition state of the states A and B. When the superposition state is measured, it will again collapse, either back into state A as in the first measurement, or away into state B. However, its probability of collapsing into state B, after a very short amount of time t, is proportional to t², since probabilities are proportional to squared amplitudes, and amplitudes behave linearly. Thus, in the limit of a large number of short intervals, with a measurement at the end of every interval, the probability of making the transition to B goes to zero."

    If there is no timer that stores the time since the last measurement then why are the chances of decay smaller after a measurement and why can the decay be slowed down or even stopped this way?

    To e.bar.goum:
    Thank you for the link! But I really have problems understanding the data. So there are three possible ways it can decay? But where can I find the chances for each case?

    To DrChinese:
    That's a good point but I don't see why gravitation would also influence the chance for a certain decay type.
     
  7. Nov 24, 2014 #6

    mfb

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    Gravity is not relevant for collider experiments. Special relativity is, but this is not an issue - you can simply go to the rest frame of the particle again.

    The quantum zeno effect needs quite special conditions (in particular, non-exponential probability evolutions). You don't get it for nuclear decays. There are other processes that have timer-like state evolutions.
     
  8. Nov 24, 2014 #7

    bhobba

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    That never occurred to me - but now I think about it it must be true.

    Really appreciate the insight.

    Thanks
    Bill
     
  9. Nov 24, 2014 #8

    e.bar.goum

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    It should be pointed out that it's SR not GR that's in play here.

    But no only is it relevant in collider experiments, it's actually actively exploited at places like the ESR at GSI. https://www.gsi.de/en/start/forschung/forschungsfelder/appa_pni_gesundheit/atomphysik/research/experimental_facilities/esr.htm [Broken]
     
    Last edited by a moderator: May 7, 2017
  10. Nov 25, 2014 #9

    bhobba

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    Hmmm. I haven't seen calculations on the size of GR corrections but any process that involves time must be different in a gravitational field compared to the conceptual inertial frame of SR.

    Thanks
    Bill
     
  11. Nov 25, 2014 #10

    e.bar.goum

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    Sure, but the issue in particle accelerators is that we're accelerating particles to relativistic speeds. (~65% of the speed of light at GSI, 99.9999991% at LHC etc), not that they're in a gravitational potential. I've never come across a nuclear physics problem where anything other than corrections as per SR are used (happy to be corrected!).

    See for example, http://www.researchgate.net/publication/223833956_Rare_ISotopes_INvestigation_at_GSI_%28RISING%29_using_gamma-ray_spectroscopy_at_relativistic_energies [Broken]
     
    Last edited by a moderator: May 7, 2017
  12. Nov 25, 2014 #11

    mfb

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    Measurements of gravitational redshift via the Mößbauer effect? Well, that is a very special application directly designed to see effects of gravity.

    Time dilation and other SR effects are taken into account in accelerator experiments all the time. Usually they are so dominant nonrelativistic approaches would be pointless.
     
  13. Nov 25, 2014 #12

    e.bar.goum

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    Ok, given. (And that's very neat.)

    Unless you're doing low-medium energy nuclear physics, rather than particle physics. Most of the time, you're in the nonrelativistic regime there.
     
  14. Nov 25, 2014 #13

    DrChinese

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    Thanks for correcting my poorly written comment, which mixed GR and SR references. A radioactive sample will decay at different rates in different gravitational fields, which has nothing to do with a collider.
    Yeah that's why I posted. It's very interesting that even a process like radioactive decay would be affected by nearby mass. It makes sense of course but I find it very cool anyway.

    mfb: Thanks for correcting my poorly written prior post. As you say, colliders don't test GR.
     
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