It has been estimated that the Earth contains 109 metric tons ofnatural uranium
ID: 1730156 • Letter: I
Question
It has been estimated that the Earth contains 109 metric tons ofnatural uranium that can be mined economically. Of this total, 0.7%is 235U that can be fissioned to produce energy. Assume 208 MeV perfission; 1 MeV = 1.6x10-13 J; 235 g of U has 6x1023atoms.How many atoms of 235U are there in 109 metric tons of naturaluranium?
What is the energy release possible from the 235U in 109 metrictons of natural uranium?
If all the world’s current power needs (7x1012 W) weresupplied by 235U fission, how long would this supply of uraniumlast?
Explanation / Answer
It has been estimated that the Earth contains 109 metric tons ofnatural uranium that can be mined economically. Of this total, 0.7% is 235U that can be fissioned to produceenergy. Assume 208 MeV per fission; 1 MeV = 1.6x10-13 J; 235 g of U has 6*10^23 atoms. a) How many atoms of 235U are there in 109 metric tons of naturaluranium? mass of 235U = .007*109*1000 kg = 763 Kg number of 235U atoms = (6*10^23)(763)/(.235) = 1.95*10^27 b)What is the energy release possible from the 235U in 109 metrictons of natural uranium? total energy release possible = 1.95*10^27 *208 MeV = 4.05*10^29MeV = 6.5*10^16 J c) If all the world’s current power needs (7x10^12 W) weresupplied by 235U fission, how long would this supply of uraniumlast? time = 6.5*10^16 J / (7*10^12 W) = 9286 s
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