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September 23, 2014

September 23, 2014

Posted by **anonymous** on Monday, February 4, 2008 at 2:47pm.

1. Set up the appropriate integral to represent the radiation dosage delivered by the absorbed iodine in eight days.

2. Use the fact that eight days is the half-life of the isotope to find the initial radiation intensity in millrems/hour.

3. To the nearest 10 millirems, how much of the total radiation is delivered in six weeks?

- CALC -- integrals! -
**Damon**, Monday, February 4, 2008 at 5:02pmwell, we know the intensity is exponential in time.

I = Io e^-kt

the half life is 8 days

I/Io = .5 = e^-8k

ln .5 = -8k

-.693147=-8k

k = .0866

so

I = Io e^-.0866 t

now total over 8 days, call it D for dose

D = int I dt

D = int dt Io e^-.0866 t from t=0 to t = 8

D = (Io/-.0866) [ e^-.0866(8)-e^0]

e^0 = 1 of course

e^-.6931 = .5 of course

so

D = .5 Io/.0866

or

Io = 5.77 D

D is given of course so you are there in millirems /24 hours

I will leave the doing it in hours and the six weeks thing for you

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