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A large room is filled with air polluted with Caesium-137 at an average density of 1 Cs-137 particle per $\text{cm}^3$. A human is sitting inside the room for duration of $T$. What is the total energy absorbed by the person?

Originally given at Problemania wiki.

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When asking a question, it's preferred that you actually state it as a question. Also, I'm leaning toward thinking that this is a problem of primarily educational value and thus it falls under our guideline on homework-like questions, which means that you would need to show some effort toward obtaining a solution. (unless the community disagrees?) –  David Z Aug 7 '11 at 6:26
    
I looked in that "problemania wiki, which is practically empty. I think that "wiki" is a brainchild of user Problemania and this "question" here is a kind of ad. This "question of the day" is practically the only one there. –  Georg Aug 7 '11 at 14:30
    
It's tagged as homework. Therefore Problemania should have shown some attempt at a solution. –  Ben Crowell Aug 7 '11 at 19:44
    
@Ben: yeah, but the homework tag wasn't added by (and hasn't been acknowledged by) the OP so we can't be sure. I'm more inclined to think that Georg has the right idea. Since it is physics-related, at least, I won't treat it as spam, but I will close it in accordance with the homework-type question policy until Problemania explains further. –  David Z Aug 7 '11 at 20:51
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closed as off topic by David Z Aug 7 '11 at 20:51

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1 Answer

I will give it a try. Multiply the density of Cs-137 by the volume of the room to find the initial number of Cs-137 particles $N_0$. Then from decay law $N(t)=N_0 e^{−\lambda t}$ find the number of Cs-137 particles $n=N_0−N(T)$ that have decayed after time $t=T$. Finally multiply the energy of the decay product (electrons of energy ~$1.176 MeV$) by the $n$ to find the total absorbed energy. Also you can divide it by the humans body mass to find the absorbed dose.

Of course this is just an approximation because of the fact that the source of Cs-137 is the whole room (it's not a point like source) so there will be some absorption of decay products by the air and Cs-137 (I think). Moreover, the human is inside the source (room).

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