Absorbed dose given an initial dose rate

[superduke1200]

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

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∫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.

 

[haruspex]

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"?

 

[superduke1200]

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

 

[haruspex]

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?

 

[superduke1200]

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

 

[haruspex]

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.

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.

 

[superduke1200]

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

 

[haruspex]

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.

 

[superduke1200]

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

 

[haruspex]

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.)

 

[superduke1200]

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.

 

[superduke1200]

How does that seem as a solution? Do you think it is correct?

 

[haruspex]

How does that seem as a solution? Do you think it is correct? View attachment 220763

Looks right to me.

 

[superduke1200]

Fine! Appreciate your time a lot