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Chapter 11: Q37E (page 519)
As noted in section 11.5, Carbon-11 decays to boron-11. How do the factors involved in nuclear stability argue that such a decay is favorable?
The binding energy for carbon- is lower, and it is favorable for it to decay to boron- .
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Ignoring annihilation energies of the positrons, how much total kinetic energy is released in the six-step carbon cycle? (There is a quick way to answer this, and a much slower way.)
In electron spin resonance, incoming electromagnetic radiation of the proper (resonant) frequency causes the electron’s magnetic moment to go from its lower-energy, or “relaxed,” orientation, aligned with the external field, to its higher-energy anti-aligned state. MRI is analogous. A quantity commonly discussed in MRI is the ratio of the frequency of the incoming radiation to the external magnetic field. Calculate this ratio for hydrogen. Note that the proton gyromagnetic ratio, , is .
According to the semiempirical binding energy formula, what should be binding energy per nucleon of technetium - .
You occupy a one-dimensional world in which beads of mass when isolated-attract each other if and only if in contact. Were the beads to interact solely by this attraction, it would take energy to break the contact. Consequently. We could extract this much energy by sticking two together. However, they also share a repulsive force, no matter what their separation. For which the potential energy is . Whererole="math" localid="1660033271423" is a bead's radius and is centre to centre separation. The closer the beads. The higher is this energy.
(a) For one stationary bead, by how much does the energy differ from?
(b) For two stationary beads in contact, by how much does the energy differ from ?
(c) For three beads in contact (in a line, of course, since this world is one-dimensional). by how much does the energy differ from ?
(d) For four beads in contact, by how much does the energy differ from ?
(e) If you had 12 isolated beads and wished to extract the most energy by sticking them together (in linear groupings), into sets of what number would you group them?
(f) Sets of what number would be suitable fuel for the release of fusion energy? Or fission energy?
Calcium-41 decays by electron capture.
(a) Find for the decay.
(b) Show that calcium-41 cannot decay by emission.
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