1. Jun 10, 2013

### sunrah

1. The problem statement, all variables and given/known data
Estimate the minimum proton lifetime from the fact that you haven't yet died from internal radiation. Use the following conditions:
1.) At a dosis of Dmax = 2 Greys per year (Jkg-1 yr-1) you would already be dead.
2.) The human body is made mostly of water.
3.) The total proton mass of mp = 938 MeV/c2 is released during decay

2. Relevant equations
Dosis D = E/m
I am approx 60kg → m = 60kg
3. The attempt at a solution

maximum energy per year = Pmax = Emax / 1yr = Dmax m = 120 Jyr-1

decay frequency is therefore (maximum energy per year) / (total proton mass-energy) = f = 120 Jyr-1 / (1.6x10-19 JeV-1c2 * 938MeVc-2)

f ≈ 1011 yr-1
T ≈ 10-11 yr

order of magnitude should be T ≈ 1033yr.
and also where does the water element come into this I know H2O has a proton number Z = 10 but so, we are given the an energy limit to work this out and we can just divide this by the energy of one decay to get maximum number of decays? thanks

Last edited: Jun 10, 2013
2. Jun 10, 2013

### Basic_Physics

You can estimate the amount of protons in your body if you assume you consist only of water.