Rearrangement of a complex radiation formula

[murdrobe]

Homework Statement

6. If the exposure rate from 137Cs at one metre is 2.50 mGy/h, how many bequerels are present?

Homework Equations

X=5.263 x 10-6 A∑(yiEi(μen/ρ)i)/r2

The Attempt at a Solution

what I am looking to do isn't to solve the question, i need to rearrange the formula above so that A is the subject and i have no idea where to begin due to its complexity.

i would also like to know what the symbols represent, my interpretation from what i have found is that:

X = the exposure measured in Roetengens
A = The activity of the source measured in Bequerels
∑ = this sigma sign is equal to a complex value. To gather this number the individual energy of each photon that this radiation source can produce must be known and multiplied by the rate that they are produced. This is due to the fact that a gamma source does not produce a single energy level but instead there is a range of energies produced.
yi = The initial Yield from this source before any decay
Ei = the initial energy of this source before any decay
E = the energy of the photons
i = The value of i on its own refers to the fact that the calculation must use the initial values of μen/ρ.
r^2 = the distance away that the measurement is taken

please could someone check that this is correct. we were not given this formula or taught how to use it so I am struggeling.

 

[daveb]

If you weren't given that formula, where did you get it from? It's far easier to use the gamma constant for Cs-137, especially since they didn't give you the value for μ_en/ρ, which changes depending on photon energy. Your formula should read

X=5.263 x 10^-6A∑(y_iE_i(μ_en/ρ)_i)/r², where the summation is over all photon energies. However, when you use the gamma constant, this summation is already calculated for you.

 

[murdrobe]

We weren't given anything for this calculation, as a group we found an online calculator that said this was the formula for it. Although it'd be fantastic if there is a simpler way, I'm not sure how to do what you suggested either

 

[daveb]

There are numerous sources for the gamma constant (G) for Cs-137. The Rad Health Handbook lists the gamma constant as 3.3 R-cm²/hr-mCi, and the formula would be X = AG/r², so all you need to do is perform some algebra and unit conversions to get the activity.

 

[murdrobe]

this is FAR easier, thank you

 

[murdrobe]

A = xr² / G

so then i need to convert the units for G to bequerels? but what is R in the R-cm2/hr-mCi

does that mean its 3.3 x 100² is equal to the value in milicuries?

100² due to my calculation being at 1m

 

[daveb]

Yes, millicuries to Becquerels, and R (Roentgen) to mGy. 1 rad = 0.877 roentgen