Radiation Dose Rate Calculations for a 1 cm Square

[pone]

Homework Statement

Four “point” gamma ray sources are permanently implanted in tissue so that the sources are at the corners of a 1 cm X 1 cm square. Each source has an initial activity of 15 MBq (1 Bq = one decay per second), every decay produces a 30 keV gamma ray, and the half-life is 60 days. The dose rate from each source falls off with distance, r, according to

Dose Rate = (Constant)(exp -ur)(r-2)

where u = 0.25 cm-1. Calculate the total dose delivered by the implanted sources to a point at the centre of the square. Sketch the isodose distribution in the plane that contains all of the sources.

Hint: Use conservation of energy to evaluate the constant in the equation above.

3. The Attempt at a Solution
This question confuses me because a) there is no real time frame given. There is a half life, but I am unsure how to use it. Also, b) when evaluating the Constant, I do not get proper units. The way I have been looking at it is:
constant = (15 x 10^6 decay/s)(30,000 eV)(1.602 x 10^-19 J/eV) which gives me J/s.
I know this must be wrong, but do not know where to go from here. Any help?

 

[gabbagabbahey]

This question confuses me because a) there is no real time frame given. There is a half life, but I am unsure how to use it.

The given half-life allows you to calculate the activity of each source at a given time.

Also, b) when evaluating the Constant, I do not get proper units. The way I have been looking at it is:
constant = (15 x 10^6 decay/s)(30,000 eV)(1.602 x 10^-19 J/eV) which gives me J/s.
I know this must be wrong, but do not know where to go from here. Any help?

(15 x 10^6 decay/s)(30,000 eV)(1.602 x 10^-19 J/eV) just gives you the initial rate at which each source point loses energy (in other words, the initial power radiated from each source), why would this be equal to the constant you are trying to determine?

What are the units of dose rate? What what you expect to get if you integrated the dose rate over all space?

 

[pone]

I know that the units for dose rate is Gray/s or Joules/kg-second, and I figured I could just juggle around with those initial values that were given, to get my final result for the constant. Clearly that did not work out. As for what would happen if the dose rate were integrated over all space though, I am a little unsure. If I integrated over time wouldn't I just get the total dose? I am still just really blank in how to find this constant!

 

[gabbagabbahey]

Sorry, I meant to ask, "what would you expect to get if you integrated the mass density of the tissue times the dose rate over the entire volume of the tissue"?...Think about energy/power conservation.