Absorbed dose given an initial dose rate

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Homework Help Overview

The discussion revolves around calculating the total equivalent dose of absorbed radiation from 137 Cs in an unspecified organ, given an initial dose rate of 1μGy/h and an active half-life of 100 days. Participants are exploring the implications of the decay rate and the meaning of the terms used in the problem statement.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants are attempting to understand how to integrate the dose rate over time, considering the exponential decay of the activity. Questions are raised about the clarity of the problem statement, particularly regarding the definition of "active half-life" and the implications of the initial dose rate.

Discussion Status

The discussion is ongoing, with participants providing insights and clarifications about the problem's wording and assumptions. Some suggest that the question may not clearly specify the time frame for calculating the total dose, while others emphasize the importance of the half-life in determining the decay of the dose rate over time.

Contextual Notes

Participants note that the term "active half-life" may imply different interpretations, and there is uncertainty about whether the question is asking for the absorbed dose over a finite time or an infinite duration. The distinction between physical and effective half-lives is also mentioned, with some participants questioning the relevance of these terms to the problem at hand.

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Homework Statement


[/B]
Assume that we have 137 Cs absorbed in an unknown organ. We know that the initial dose rate is 1μGy/h. Calculate the total equivalent dose in this organ, if we know that the activity is reduced exponentially over time with an active half life of 100 days.

Homework Equations


[/B]
∫D⋅dt

The Attempt at a Solution



∫D⋅dt= ?

I suppose that I should try somehow to solve the above, for t between 0 and 100 days, since the active half life is 100 days. But since the activity changes over time, I think that the dose rate too will change over time.
 
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There won't be many experts in this field on this forum, but many who coukd help you if you were to explain a bit more.

On the face of it, the question makes no sense. It tells you an absorbed dose and asks for the absorbed dose.
It tells you a decay rate but does not specify or ask for a time.
Is this the question as given to you, word for word?
What is a "C"?
 
haruspex said:
There won't be many experts in this field on this forum, but many who coukd help you if you were to explain a bit more.

On the face of it, the question makes no sense. It tells you an absorbed dose and asks for the absorbed dose.
It tells you a decay rate but does not specify or ask for a time.
Is this the question as given to you, word for word?
What is a "C"?

It asks for the dose absorbed in this unspecified organ.And it gives the initial dose rate at this organ

What I mean by: ''active half life of 100 days" is the following:

we consider that after 100 days there will be no 137 Cs in this organ, meaning that it will be no longer radioactive.The question is as given to me
 
superduke1200 said:
What I mean by: ''active half life of 100 days" is the following:

we consider that after 100 days there will be no 137 Cs in this organ
I am quite sure it does not mean that. It means that the rate halves over 100 days.
But at least your response there helped me resolve one misunderstanding: "137 Cs" means caesium 137.

So, the question is saying: if the initial rate is 1μGy/h, and it decays exponentially so that after 100 days it is half that, what will be the total number of Gy from t=0 to t=∞.
(But I do find it odd that it asks for "equivalent" dose, which depends on a factor associated with the type of radiation. Maybe the factor is 1 for 137 Cs decay.)

Can you write down the expression for the dose rate as a function of time?
 
It seems that the question given has some shortcomings. But it is given as mentioned

Furthermore, it doesn't say half life time of 100 days, but active half life time. That's why I thought it implies that practically after 100 days there will be no caesium. Probably I am wrong.

Perhaps it supposes that we don't care about the equivalent dose. And all we want is to calculate the absorbed dose (Gy) in these 100 days, knowing that the initial dose rate is:

1μGy per hour

But again. When 137 caesium decays, it emits only γ photons and electrons. Both of them have a weighting factor of Wr=1
 
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superduke1200 said:
it doesn't say half life time of 100 days, but active half life time
Right, but it still uses the word "half", not "full". So I think you are safe to interpret this as half life.
superduke1200 said:
all we want is to calculate the absorbed dose (Gy) in these 100 days,
No, it does not say 100 days has gone by. It only mentions 100 days as a way to express the decay rate. No specific time is mentioned for the total dose, so you should take it as infinite time.

Please post the equation for dose rate as function of time.
 
haruspex said:
Right, but it still uses the word "half", not "full". So I think you are safe to interpret this as half life.

No, it does not say 100 days has gone by. It only mentions 100 days as a way to express the decay rate. No specific time is mentioned for the total dose, so you should take it as infinite time.

Please post the equation for dose rate as function of time.

All we know is the initial dose rate. It is 1μGy per hour
 
superduke1200 said:
All we know is the initial dose rate. It is 1μGy per hour
No, you know that it decays exponentially and, trust me, you are given the half life.
 
haruspex said:
No, you know that it decays exponentially and, trust me, you are given the half life.
Physical Half life of 137 Caesium is 30 years. Not given, but it may help.

100 days is the effective half life of 137 Caesium
 
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  • #10
superduke1200 said:
Physical Half life of 137 Caesium is 30 years. Not given, but it may help.

100 days is the effective half life of 137 Caesium
No matter, you should use 100 days as the half life in this question. Same equation, different rate.
(I believe the difference is that the effective half life comes mostly from the turnover within the organ, i.e. it gets moved out of the body much faster than it actually decays.)
 
  • #11
Yes, as far as I have learned Caesium is highly dissolved in water. Which means that we are able to move out some of it with urination.
 
  • #12
How does that seem as a solution? Do you think it is correct?
IMG_20180221_034755.jpg
 

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  • #13
superduke1200 said:
How does that seem as a solution? Do you think it is correct? View attachment 220763
Looks right to me.
 
  • #14
Fine! Appreciate your time a lot
 

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