Saving a young man's life

Finally lets have fun with Physics!!!

 

    Lets say a wonderful young man weighting 80 Kg is diagnosed with an early stage cancer, goes into the doctors office and receives 1.0 mSv of the radioactive isotope 137^Cs. Where 137^Cs radiates .66 Mev gamma ray photons. Lets find out how many gamma rays are taken in by the young man.

 

Note:

Radiation type     RBE

X rays                     1

Gamma rays           1

Beta particles           1-2

Neutrons                5-20

Alpha particles        20

 

Step one: Lets state what we know

 

The RBE for Gamma rays is = 1

 

Dose equivalent (Sv) = 1 mSv x .001 because its in millisievert mSv

 

.66 Mev = energy of each proton taken in by the man

 

Dose equivalent (Sv) = absorbed dose (Gy) x RBE  so lets rearrange the equation to solve for absorbed dose (Gy)

 

Absorbed dose (Gy) = dose equivalent (Sv) / RBE

 

Absorbed dose (Gy) = .001 Gy = .001 J/kg

 

So what this means is that for a whole body exposure of a 80 Kg man the energy ejected from the radioactive isotope is .001 J/Kg x 80 Kg = .08 J

 

Understanding that .08 J are absorbed by the body of the man, now we need find the number of protons in the .08 J.

 

By solving for joules we get N = .08 J / ((6.6 x 10^5 eV/photon)(1.6 x 10^-19 J/eV))

 

We get that N = 7.57 x 10^11 photons

 

Conclusive analysis; we found that the exposure for the young man is 7.57 x 10^11 photos to the .08 J which is a very small amount. We can cure his cancer and not hurt him at the same time.                                                                                                  


Photo from: healthfavo.com