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B Calculating safe levels of radioactivity

  1. May 6, 2016 #1
    Hello!

    I am not sure how I would go about calculating the time it takes for a radioactive element to decay to safe levels. I know of the decay formula (N=No*e^(-kt)) and K =ln2/t(1/2). I believe calculating the time until an atom has decayed to safe levels has to do with the activity (Bq) A=kN of the element. However, I do not have confirmation on this.

    Take, Cesium 137 for example. It has a half life of 30 years. However, I would like to create a general formula for x kg of this element to decay to 'safe' levels.

    Thanks,
    Trontor
     
    Last edited: May 6, 2016
  2. jcsd
  3. May 6, 2016 #2

    mfb

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    You have to define "safe" levels, and you have to know the initial activity of the radioactive materials. Once you know the ratio between initial and "safe" levels (the latter is more a radiobiology question), everything else is just a matter of mathematics. The distribution of the material will be relevant, and if you consider long timespans, the migration of the material in the environment will be relevant as well (but that is yet another field of science).
     
  4. May 6, 2016 #3
    Ok, what about the values from this article? http://www.bloomberg.com/news/articles/2011-03-21/japan-sets-safe-limits-for-consuming-radiation-contaminated-food-table- [Broken]

    I am willing to do the mathematics myself, but I'm really not too sure what I should be doing... thanks for any help :)
     
    Last edited by a moderator: May 7, 2017
  5. May 6, 2016 #4

    mfb

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    Well, if the spinach of 2011 had 1931 Bq/kg and the limit is 500 Bq/kg, you can calculate the worst case waiting time until spinach from the same place will be below the limit. About a factor of 4 in the activity, so roughly twice the half-life. The actual time will be significantly shorter as cesium gets spread out over time, but a proper estimate there would need a detailed study.
     
  6. May 6, 2016 #5
    I have understood this. However, which formulae should I be using to get an accurate answer?
     
  7. May 6, 2016 #6

    mfb

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    The decay formula also works as activity formula, both are proportional to each other, so both decay exponentially.
     
  8. May 6, 2016 #7
    Ok, I've attempted a solution for this. Don't judge ;)
    DBH8WFa.png
    1. This seems way too long, for a GRAM of cesium.
    2. The initial activity has no effect on my solution :/

    I'm doing this wrong, I presume. What do I need to fix?
     
  9. May 6, 2016 #8
    Actually, using this calculator confirms my answer is correct... I hope...
    wHxnl50.png
    is there anything wrong guys?
     
  10. May 6, 2016 #9

    mfb

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    This is the time you have to wait until 100% pure radioactive cesium* becomes safe drinking water. Well, if we replace the decay products by water.

    *which would evaporate under its own heat in practice
     
  11. May 6, 2016 #10
    Do you mean the caesium IN contamined drinking water?
     
  12. May 6, 2016 #11

    mfb

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    The concentration of cesium in drinking water is significantly below 1 gram per gram of drinking water (that would not be water at all, it would be a block of cesium). If you start with 0.1 picogram of cesium per gram of drinking water, you get a completely different result.
     
  13. May 6, 2016 #12
    Oh. I'm confused now. Where does the per gram of water come into this. I just used the 0.2Bq/gram from the website as a 'safe level'. I didn't think of a Cesium/gram of water
     
  14. May 6, 2016 #13

    mfb

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    Well, your water is mainly water, but with a small amount of cesium in it. The activity in 1 gram of water (=where the limit applies) depends on the amount of cesium in the water. This amount will go down over time.
     
  15. May 6, 2016 #14
    I understand. Where would I find the value for the activity of a normal amount of cesium contaminated water?
     
  16. May 6, 2016 #15

    mfb

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    There is no normal amount, every sample will be different.
     
  17. May 6, 2016 #16
    OK,
    Should I assume that after a nuclear meltdown, there could be 0.1 picograms of cesium in every gram of water, then calculate the activity from that.
     
  18. May 7, 2016 #17

    mfb

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    No, that is a number I made up. The actual concentrations will vary wildly depending on where you take the water from. You have to measure it.
     
  19. May 7, 2016 #18
    So this can't be hypothesised accurately?
     
  20. May 7, 2016 #19

    mfb

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    So far we didn't make any difference between water taken from the reactor pool in Chernobyl and water taken from some underground reservoir in the middle of nowhere in Africa. Clearly the activity will be different for those two cases. The same formula can be used in both cases (and the water in Africa is probably below the threshold), but the starting activity is massively different.
     
  21. May 7, 2016 #20
    I've thought about this and tried researching, however, I still do not fully understand this concept. I just want to show how long it takes for Cesium from say, a fallout to be rendered safe. I need this to make a statement highlighting the dangers of radioactive material.
     
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