Estimate minimum proton lifetime from internal radiation rate

[sunrah]

Homework Statement

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 D_max = 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 m_p = 938 MeV/c² is released during decay

Homework Equations

Dosis D = E/m
I am approx 60kg → m = 60kg

The Attempt at a Solution

maximum energy per year = P_max = E_max / 1yr = D_max 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

 

[Basic_Physics]

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