Calculating safe levels of radioactivity

In summary: I don't know, but you can look it up on the internet. The activity of cesium in water depends on how much cesium is in the water and how long it has been there.
  • #1
Guest432
48
2
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
 
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  • #2
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).
 
  • #3
mfb said:
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.
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-

I am willing to do the mathematics myself, but I'm really not too sure what I should be doing... thanks for any help :)
 
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  • #4
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.
 
  • #5
mfb said:
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.
I have understood this. However, which formulae should I be using to get an accurate answer?
 
  • #6
The decay formula also works as activity formula, both are proportional to each other, so both decay exponentially.
 
  • #7
mfb said:
The decay formula also works as activity formula, both are proportional to each other, so both decay exponentially.
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?
 
  • #8
mfb said:
The decay formula also works as activity formula, both are proportional to each other, so both decay exponentially.
Actually, using this calculator confirms my answer is correct... I hope...
wHxnl50.png

is there anything wrong guys?
 
  • #9
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
 
  • #10
mfb said:
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.
Do you mean the caesium IN contamined drinking water?
 
  • #11
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.
 
  • #12
mfb said:
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.
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
 
  • #13
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.
 
  • #14
mfb said:
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.
I understand. Where would I find the value for the activity of a normal amount of cesium contaminated water?
 
  • #15
There is no normal amount, every sample will be different.
 
  • #16
mfb said:
There is no normal amount, every sample will be different.
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.
 
  • #17
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.
 
  • #18
mfb said:
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.
So this can't be hypothesised accurately?
 
  • #19
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.
 
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  • #20
mfb said:
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.
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.
 
  • #21
Trontor said:
I just want to show how long it takes for Cesium from say, a fallout to be rendered safe.
That is not the right question. If you accumulate pure Cs-137 in large amounts, it will always be dangerous, because it will have an activity of 3 TBq/g. But no one sifts through millions of tons of soil to extract and purify all the Cs-137 in it. Why should you.

The relevant question is "when will normal things (like our drinking water) have an activity that is low enough". And that depends on how much cesium initially gets into the drinking water, and how it gets distributed there.
 
  • #22
mfb said:
That is not the right question. If you accumulate pure Cs-137 in large amounts, it will always be dangerous, because it will have an activity of 3 TBq/g. But no one sifts through millions of tons of soil to extract and purify all the Cs-137 in it. Why should you.

The relevant question is "when will normal things (like our drinking water) have an activity that is low enough". And that depends on how much cesium initially gets into the drinking water, and how it gets distributed there.

OK,
But where do I get these values? I don't know of any average grams per litre of contamination or something. I just want to create a scenario that is plausible :(
 
  • #23
Trontor said:
But where do I get these values?
After accidents, people take samples from different places and measure the activities of individual radioisotopes. Those values end up in publications, reports (academic/governments) and rarely the popular press. You cannot find a single number as answer. It is not that easy.
 
  • #24
mfb said:
After accidents, people take samples from different places and measure the activities of individual radioisotopes. Those values end up in publications, reports (academic/governments) and rarely the popular press. You cannot find a single number as answer. It is not that easy.
Nice!

After looking, I found this table:
msAQ8Lb.png

I am really curious as to why the concentration level (kBq/m^3) goes from 22.2 to 1.8 within a year?
 
  • #25
Trontor said:
I am really curious as to why the concentration level (kBq/m^3) goes from 22.2 to 1.8 within a year?
Because it goes down stream.
 
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  • #26
snorkack said:
Because it goes down stream.
Oh, haha.
 
  • #27
Ok, so I did the following.

  1. Found how many atoms of Cesium-137 is in a gram of water in 1986 (1.8 kBq)
  2. Found how many atoms in the prescribed safe activity per gram (0.2Bq)
  3. Used the half life formula to calculate the time taken for the initial activity to decay to the second activity.
 
  • #28
Note the units: the values are in kBq/m3.
 
  • #29
mfb said:
Note the units: the values are in kBq/m3.
Ahh yes,
I know its a river, however I calculated m^3 to grams as for water 1m^3 = 10^6 grams.

If I do not do it this way, then I cannot use the prescribed safe activity level I have on hand.
 
  • #30
So what do you get for the activity per gram if you convert 1.8 kBq/m3 to Bq/g?
 
  • #31
mfb said:
So what do you get for the activity per gram if you convert 1.8 kBq/m3 to Bq/g?
0.0018 Bq/g
 
  • #32
Right. A factor 100 below the 0.2 Bq/g limit.
 
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  • #33
mfb said:
Right. A factor 100 below the 0.2 Bq/g limit.
...

Help

Please
 
  • #34
What? You figured out that all the reported values in this thread were below the safety limits all the time.

If you want to calculate some time, you'll need water with more contamination. Or take something else, e. g. mushrooms in Bavaria.
 
  • #35
mfb said:
What? You figured out that all the reported values in this thread were below the safety limits all the time.

If you want to calculate some time, you'll need water with more contamination. Or take something else, e. g. mushrooms in Bavaria.

OK. I have looked now at examples from Fukushima Daichii 2011, but they're reporting the levels to now be near identical to pre incidental levels. Considering this is the largest incident since Chernobyl, is it safe to assume there have been no other incidents where water contamination was worthy to investigate?

I am considering just making a scenario and analysing that.
 
<h2>What is radioactivity?</h2><p>Radioactivity is the process by which unstable atoms emit energy in the form of radiation in order to become more stable. This can occur naturally or be induced through human activities.</p><h2>How do scientists calculate safe levels of radioactivity?</h2><p>Scientists use a variety of methods and models to calculate safe levels of radioactivity, including risk assessment, dose-response modeling, and exposure limits. They also take into account factors such as the type of radiation, the duration and frequency of exposure, and the sensitivity of different body tissues to radiation.</p><h2>What are the potential health effects of exposure to radioactivity?</h2><p>The potential health effects of exposure to radioactivity depend on the type and amount of radiation, as well as the duration and frequency of exposure. Some potential health effects include radiation sickness, genetic mutations, and an increased risk of certain types of cancer.</p><h2>How do scientists determine the safe levels of radioactivity for different populations?</h2><p>Scientists consider a variety of factors when determining safe levels of radioactivity for different populations, including age, gender, overall health, and level of exposure. They also take into account the potential risks and benefits of exposure to radiation, as well as any regulatory guidelines or standards.</p><h2>What measures are in place to ensure safe levels of radioactivity?</h2><p>There are a number of measures in place to ensure safe levels of radioactivity, including regulatory agencies that set and enforce guidelines for exposure, monitoring and testing of radiation levels in the environment, and safety protocols for industries that work with radioactive materials. Additionally, ongoing research and advancements in technology help to improve our understanding of the effects of radioactivity and how to mitigate potential risks.</p>

FAQ: Calculating safe levels of radioactivity

What is radioactivity?

Radioactivity is the process by which unstable atoms emit energy in the form of radiation in order to become more stable. This can occur naturally or be induced through human activities.

How do scientists calculate safe levels of radioactivity?

Scientists use a variety of methods and models to calculate safe levels of radioactivity, including risk assessment, dose-response modeling, and exposure limits. They also take into account factors such as the type of radiation, the duration and frequency of exposure, and the sensitivity of different body tissues to radiation.

What are the potential health effects of exposure to radioactivity?

The potential health effects of exposure to radioactivity depend on the type and amount of radiation, as well as the duration and frequency of exposure. Some potential health effects include radiation sickness, genetic mutations, and an increased risk of certain types of cancer.

How do scientists determine the safe levels of radioactivity for different populations?

Scientists consider a variety of factors when determining safe levels of radioactivity for different populations, including age, gender, overall health, and level of exposure. They also take into account the potential risks and benefits of exposure to radiation, as well as any regulatory guidelines or standards.

What measures are in place to ensure safe levels of radioactivity?

There are a number of measures in place to ensure safe levels of radioactivity, including regulatory agencies that set and enforce guidelines for exposure, monitoring and testing of radiation levels in the environment, and safety protocols for industries that work with radioactive materials. Additionally, ongoing research and advancements in technology help to improve our understanding of the effects of radioactivity and how to mitigate potential risks.

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