Pd Pd 1. Let's consider a toy model of nuclear fission. Suppose an nucleus of Uranium-235 (92 protons, molar weight of 235 g/mole) "splits" into two "daughter" nuclei of Palladium (46 protons each) - this is not how it really happens, but it's a very simple model that actually gives fairly accurate results. The radius of the original U-235 nucleus is about 7.4 x 10-15 m. (a) If the Pd nuclei each have half the volume of the U nucleus, which is reasonable, and they are "touching" right after the split, how far apart are their centerst (b) Using conservation of energy, what will be the sum of the kinetic energies of the Pd nuclei when they are far apart from each other? (c) That's energy of one atom undergoing fission, so what, then, is the energy released by the fission of 1 kg of U-235? Express this in Joules and also in kilotons of TNT, where 1 kt = 4.2x1012 J. (The Hiroshima bomb yielded about 15 kt) (d) How many kwh (kilowatt-hours) of energy is this, (1 kwh = 3.6x10° J), and (if you found a way to slowly convert this energy into electricity) how much would this much energy cost customers at 10 cents per kWh?
Pd Pd 1. Let's consider a toy model of nuclear fission. Suppose an nucleus of Uranium-235 (92 protons, molar weight of 235 g/mole) "splits" into two "daughter" nuclei of Palladium (46 protons each) - this is not how it really happens, but it's a very simple model that actually gives fairly accurate results. The radius of the original U-235 nucleus is about 7.4 x 10-15 m. (a) If the Pd nuclei each have half the volume of the U nucleus, which is reasonable, and they are "touching" right after the split, how far apart are their centerst (b) Using conservation of energy, what will be the sum of the kinetic energies of the Pd nuclei when they are far apart from each other? (c) That's energy of one atom undergoing fission, so what, then, is the energy released by the fission of 1 kg of U-235? Express this in Joules and also in kilotons of TNT, where 1 kt = 4.2x1012 J. (The Hiroshima bomb yielded about 15 kt) (d) How many kwh (kilowatt-hours) of energy is this, (1 kwh = 3.6x10° J), and (if you found a way to slowly convert this energy into electricity) how much would this much energy cost customers at 10 cents per kWh?
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Pd
1. Let's consider a toy model of nuclear fission. Suppose an nucleus of Uranium-235 (92 protons, molar
weight of 235 g/mole) "splits" into two "daughter" nuclei of Palladium (46 protons each) – this is not
how it really happens, but it's a very simple model that actually gives fairly accurate results. The
radius of the original U-235 nucleus is about 7.4 x 10-15 m.
(a) If the Pd nuclei each have half the volume of the U nucleus, which is reasonable, and they are
"touching" right after the split, how far apart are their centers?
(b) Using conservation of energy, what will be the sum of the kinetic energies of the Pd nuclei
when they are far apart from each other?
(c) That's energy of one atom undergoing fission, so what, then, is the energy released by the
fission of 1 kg of U-235? Express this in Joules and also in kilotons of TNT, where 1 kt = 4.2x1012
J. (The Hiroshima bomb yielded about 15 kt)
(d) How many kwh (kilowatt-hours) of energy is this, (1 kwh = 3.6x10° J), and (if you found a way to
slowly convert this energy into electricity) how much would this much energy cost customers
at 10 cents per kWh?
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