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1. A pure radioactive substance TI, which has mass number 207 and atomic number 81, emits beta particles of which the average energy is 1.5MeV. The half-life of the isotope is 135 days. Assuming that 207g of the radioactive substance contains 6 x 10^23 atoms, calculatea) the total energy available from the beta... 顯示更多 1. A pure radioactive substance TI, which has mass number 207 and atomic number 81, emits beta particles of which the average energy is 1.5MeV. The half-life of the isotope is 135 days. Assuming that 207g of the radioactive substance contains 6 x 10^23 atoms, calculate a) the total energy available from the beta particles emitted from 1 mole of the isotope, b) the initial rateat which beta particles are emitted from 1 mole of freshly prepares isotope, c the nitial power available from the beta particles emiting at the rate calculated in part b). (e = -1.6 x 10^-19C) 2. A pure radioactive sample contains initially 2 X 10^20 atoms. The half- life of the sample is 30 years. If 4.5MeV of energy is produced in the decay of each atom, calculate a) the total energy produced in a period of 30 years, b) the initial rate of production of energy. (1MeV = 1.6 X 10^-13J)

最佳解答:

1a) 1.5 x 106 x 1.6 x 10-19 x 6 x 1023 = 1.44 x 1011 J b) Decay constant k = (ln 2)/135 day-1 Hence initial rate = 6 x 1023 x (ln 2)/135 = 3.08 x 1021 day-1 c) Converting the initial rate to unit of s-1, Rate = 3.08 x 1021/86400 = 3.57 x 1016 s-1 Hence initial power = 1.5 x 106 x 1.6 x 10-19 x 3.57 x 1016 = 8557 W 2a) After 30 years, half of the atoms have been decayed, i.e. 1 x 1020. So total energy produced = 4.5 x 106 x 1.6 x 10-19 x 1020 = 7.2 x 107 J b) Rate constant = (ln 2)/30 year-1 Initial rate = 1020 x (ln 2)/30 = 2.31 x 1018 year-1= 7.33 x 1010 s-1So initial rate of production of energy is:4.5 x 106 x 1.6 x 10-19 x 7.33 x 1010 = 0.053 W

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