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SOLUTIONS TO EXERCISE 16
(a) Water weighs 1000 kg/m^3. One mole of water weighs 0.018 kg, and contains 6 * 10^23 water molecules. Each water molecule contains one oxygen atom (which has 8 protons) and two hydrogen atoms (one proton each) – a total of 10 protons per molecule. Thus, 1000 m^3 of water contains (1000 m^3 * 1000 kg/m^3) ------------------------ * (6 * 10^23 molecules/mole) * (10 protons/molecule) (0.018 kg/mole) = 3.3 * 10^32 protons. If the half-life of a proton is 10^31 years, then each year there should be an average of (3.3 * 10^32)/(10^31) = 33 proton decays per year. (b) If after seven years, no proton decays have occurred in these 1000 m^3 of water, then there have been (3.3 * 10^32 protons) * (7 years) = 2.3 * 10^33 "proton years." If no single decay has occurred in that time, then it could be that protons never decay. However, it's possible that a decay could occur tomorrow; in that case, the half life would probably be about 2.3 * 10^33 proton years ------------------------ = 2.3 * 10^33 years. 1 proton |