David Halliday, Robert Resnick
ISBN #9781119460138
11th Edition
4,175 Questions
Homework Questions
This section provides an in-depth exploration of how energy is produced on a nuclear scale via both fission and fusion processes. It explains that while fission of heavy nuclei releases immense energy by altering the arrangement of nucleons and reducing mass through binding energy differences, fusion combines light nuclei, overcoming a significant Coulomb barrier with the aid of high temperatures and quantum tunneling. The text also covers how these processes are harnessed in reactors, the challenges in achieving controlled fusion, and even insights drawn from natural reactors and stellar processes, ultimately highlighting the transformative role of nuclear reactions in energy production and astrophysics.
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CONCEPT
DEFINITION
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The isotope ${ }^{235} \mathrm{U}$ decays by alpha emission with a half-life of $7.0 \times 10^{8} \mathrm{y} .$ It also decays (rarely) by spontaneous fission, and if the alpha decay did not occur, its half-life due to spontaneous fission alone would be $3.0 \times 10^{17} \mathrm{y}$. (a) At what rate do spontaneous fission decays occur in $1.0 \mathrm{~g}$ of ${ }^{235} \mathrm{U}$ ? (b) How many ${ }^{235} \mathrm{U}$ alpha-decay events are there for every spontaneous fission event?
The nuclide ${ }^{238} \mathrm{~Np}$ requires $4.2 \mathrm{MeV}$ for fission. To remove a neutron from this nuclide requires an energy expenditure of $5.0 \mathrm{MeV} .$ Is ${ }^{237} \mathrm{~Np}$ fissionable by thermal neutrons?
A thermal neutron (with approximately zero kinetic energy) is absorbed by a ${ }^{238} \mathrm{U}$ nucleus. How much energy is transferred from mass energy to the resulting oscillation of the nucleus? Here are some atomic masses and the neutron mass. $$ \begin{array}{cccc} { }^{237} \mathrm{U} & 237.048723 \mathrm{u} & { }^{238} \mathrm{U} & 238.050782 \mathrm{u} \\ { }^{239} \mathrm{U} & 239.054287 \mathrm{u} & { }^{240} \mathrm{U} & 240.056585 \mathrm{u} \\ \mathrm{n} & 1.008664 \mathrm{u} & & \end{array} $$
The fission properties of the plutonium isotope ${ }^{239} \mathrm{Pu}$ are very similar to those of ${ }^{235} \mathrm{U}$. The average energy released per fission is $180 \mathrm{MeV} .$ How much energy, in $\mathrm{MeV},$ is released if all the atoms in $1.00 \mathrm{~kg}$ of pure ${ }^{239} \mathrm{Pu}$ undergo fission?
During the Cold War, the Premier of the Soviet Union threatened the United States with 2.0 megaton ${ }^{239} \mathrm{Pu}$ warheads. (Each would have yielded the equivalent of an explosion of 2.0 megatons of TNT, where 1 megaton of TNT releases $2.6 \times 10^{28} \mathrm{MeV}$ of energy.) If the plutonium that actually fissioned had been $8.00 \%$ of the total mass of the plutonium in such a warhead, what was that total mass?