Textbook Question
The nuclear masses of 7Be, 9Be, and 10Be are 7.0147, 9.0100, and 10.0113 amu, respectively. Which of these nuclei has the largest binding energy per nucleon?
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Ch.21 - Nuclear Chemistry
Chapter 21, Problem 85
The average energy released in the fission of a single uranium-235 nucleus is about 3 * 10^-11 J. If the conversion of this energy to electricity in a nuclear power plant is 40% efficient, what mass of uranium-235 undergoes fission in a year in a plant that produces 1000 megawatts? Recall that a watt is 1 J/s.
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Calculate the total energy produced by the power plant in one year. Start by converting the power output from megawatts to watts, then multiply by the number of seconds in a year to find the total energy in joules.
Determine the total energy required from uranium-235 fission by accounting for the efficiency of the conversion process. Since the efficiency is 40%, divide the total energy produced by the efficiency (expressed as a decimal) to find the energy that must be released by fission.
Calculate the number of uranium-235 nuclei that must undergo fission to produce the required energy. Divide the total energy required by the energy released per fission event (3 * 10^-11 J) to find the number of fission events.
Convert the number of fission events to moles of uranium-235. Use Avogadro's number (6.022 * 10^23 nuclei/mol) to convert from the number of nuclei to moles.
Calculate the mass of uranium-235 that undergoes fission. Multiply the number of moles by the molar mass of uranium-235 (approximately 235 g/mol) to find the mass in grams.
Related Practice
Open Question
A 26.00-g sample of water containing tritium, ³¹H, emits 1.50 * 10³ beta particles per second. Tritium is a weak beta emitter with a half-life of 12.3 years. What fraction of all the hydrogen in the water sample is tritium?
Open Question
The Sun radiates energy into space at the rate of 3.9 * 1026 J/s. (a) Calculate the rate of mass loss from the Sun in kg/s. (b) How does this mass loss arise? (c) It is estimated that the Sun contains 9 * 1056 free protons. How many protons per second are consumed in nuclear reactions in the Sun?
Open Question
Tests on human subjects in Boston in 1965 and 1966, following the era of atomic bomb testing, revealed average quantities of about 2 pCi of plutonium radioactivity in the average person. How many disintegrations per second does this level of activity imply? If each alpha particle deposits 8 * 10^-13 J of energy and if the average person weighs 75 kg, calculate the number of rads and rems of radiation in 1 yr from such a level of plutonium.
Open Question
A 53.8-mg sample of sodium perchlorate contains radioactive chlorine-36 (whose atomic mass is 36.0 amu). If 29.6% of the chlorine atoms in the sample are chlorine-36 and the remainder are naturally occurring nonradioactive chlorine atoms, how many disintegrations per second are produced by this sample? The half-life of chlorine-36 is 3.0 * 105 yr.
Open Question
Calculate the mass of octane, C8H18, that must be burned in air to evolve the same quantity of energy as produced by the fusion of 1.0 g of hydrogen in the following fusion reaction: 4 1^1H → 4 2He + 2 0^1e. Assume that all the products of the combustion of octane are in their gas phases. Use data from Exercise 21.50, Appendix C, and the inside covers of the text. The standard enthalpy of formation of octane is -250.1 kJ/mol.