A radioactive source is distributed homogeneously throughout

A radioactive source is distributed homogeneously throughout a medium, producing RE at a point of interest. What is the absorbed dose there if 10^16 of the total mass present is converted to energy, 60 % of which is given to neutrinos?

Solution

let m kg be the mass present

mass converted to energy = me-16

E = mc² e-16 J

60% of energy is taken away by neutrinos, neutrinos being neutral particles will not interact with matter and this amount of energy is not absorbed in the matter

Energy absorbed = 0.4 mc² e-16 = 0.4*9 = 3.6m J

energy absorbed per kg of matter = 3.6m /m = 3.6 J/kg

            absorbed dose = 3.6 Gy