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Chapter 42: Q9P (page 1307)
Find the disintegration energy Q for the decay of by Kelectron capture (see Problem 54). The needed data are and .
The disintegration energy for the decay of vanadium atom is 600 keV .
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A typical kinetic energy for a nucleon in a middle-mass nucleus may be taken as 5.00MeV. To what effective nuclear temperature does this correspond, based on the assumptions of the collective model of nuclear structure?
Verify the binding energy per nucleon given in Table 42-1 for the plutonium isotope .The mass of the neutral atom is 239.05216u.
Two radioactive materials that alpha decay,and , and one that beta decays, are sufficiently abundant in granite to contribute significantly to the heating of Earth through the decay energy produced. The alpha-decay isotopes give rise to decay chains that stop when stable lead isotopes are formed. The isotopehas single beta decay. (Assume this is the only possible decay of that isotope.) Here is the information:
In the table Qis the totalenergy released in the decay of one parent nucleus to the finalstable endpoint and fis the abundance of the isotope in kilograms per kilogram of granite;means parts per million. (a) Show that these materials produce energy as heat at the rate offor each kilogram of granite. (b) Assuming that there isof granite in a 20-km-thick spherical shell at the surface of Earth, estimate the power of this decay process over all of Earth. Compare this power with the total solar power intercepted by Earth,1.
An electron is emitted from a middle-mass nuclide (A=150, say) with a kinetic energy of 1.0 MeV. (a) What is its de-Broglie wavelength? (b) Calculate the radius of the emitting nucleus. (c) Can such an electron be confined as a standing wave in a “box” of such dimensions? (d) Can you use these numbers to disprove the (abandoned) argument that electrons actually exist in nuclei?
The radionuclidedecays toas described by Eq. 42-24. In a particular decay event, an1.71 MeVelectron is emitted, the maximum possible value. What is the kinetic energy of the recoilingatom in this event? (Hint:For the electron it is necessary to use the relativistic expressions for kinetic energy and linear momentum. Theatom is non-relativistic.)
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