COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 27, Problem 52QAP
To determine
The number of collisions is required to slow 200 MeV neutron
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•3 @ A thermal neutron (with approximately zero kinetic energy) is
absorbed by a 23U 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.
237U 237.048 723 u
239U 239.054 287 u
238U 238.050 782 u
240U 240.056 585 u
1.008 664 u
•30 Verify that the fusion of 1.0 kg of deuterium by the reaction
?H + ?H - 'He + n
could keep a 100 W lamp burning for 2.5 x 10' y.
(Q = +3.27 MeV)
•49 SSM Generally, more massive nuclides tend to be more un-
stable to alpha decay. For example, the most stable isotope of ura-
nium, 28U, has an alpha decay half-life of 4.5 x 10° y. The most stable
isotope of plutonium is 24Pu with an 8.0 x 10' y half-life, and for
curium we have 248Cm and 3.4 x 10 y. When half of an original sam-
ple of 238U has decayed, what fraction of the original sample of (a) plu-
tonium and (b) curium is left?
Chapter 27 Solutions
COLLEGE PHYSICS
Ch. 27 - Prob. 1QAPCh. 27 - Prob. 2QAPCh. 27 - Prob. 3QAPCh. 27 - Prob. 4QAPCh. 27 - Prob. 5QAPCh. 27 - Prob. 6QAPCh. 27 - Prob. 7QAPCh. 27 - Prob. 8QAPCh. 27 - Prob. 9QAPCh. 27 - Prob. 10QAP
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- If two nuclei are to fuse in a nuclear reaction, they must be moving fast enough so that the repulsive Coulomb force between them does not prevent them for getting within R1014mof one another. At this distance or nearer, the attractive nuclear force can overcome the Coulomb force, and the nuclei are able to fuse. (a) Find a simple formula that can be used to estimate the minimum kinetic energy the nuclei must have if they are to fuse. To keep the calculation simple, assume the two nuclei are identical and moving toward one another with the same speed v. (b) Use this minimum kinetic energy to estimate the minimum temperature a gas of the nuclei must have before a significant number of them will undergo fusion. Calculate this minimum temperature first for hydrogen and then for helium. (Hint: For fusion to occur, the minimum kinetic energy when the nuclei are far apart must be equal to the Coulomb potential energy when they are a distance R apart.)arrow_forwardA nuclear physicist finds 1.0of 236Uin a piece of uranium ore (T1/2=2.348107y) . (a) Use die decay law to determine how much 236Uwould had to have been on Earth when it formed 4.543109yago for 1.0gto be left today, (b) What is unreasonable about this result? (c) How is this unreasonable result resolved?arrow_forwardWhen a nucleus (decays, does the (particle move continuously from inside the nucleus to outside? That is, does it travel each point along an imaginary line from inside to out? Explain.arrow_forward
- The purpose of producing 99Mo (usually by neutron activation of natural molybdenum, as in the preceding problem) is to produce 99mTc. Using the rules, verily that the decay of 99Mo produces 99mTc. (Most 99mTc nuclei produced in this decay are left in a metastable excited state denoted 99mTc.)arrow_forwardThe fact that BE/A is greatest for A near 60 implies that the range at the nuclear force is about the diameter of such nuclides. (a) Calculate the diameter at an A = 60 nucleus. (b) Compare BE/A for 58Ni and 90Sr. The first is one of the most tightly bound nuclides, while the second is larger and less tightly bound.arrow_forwardThe purpose of this problem is to show in three ways that the binding energy at the election in a hydrogen atom is negligible compared with the masses of the proton and electron. (a) Calculate the mass equivalent in u of the 13.6eV binding energy of an electron in a hydrogen atom, and compete this with the mass of the hydrogen atom obtained from Appendix A. (b) Subtract the mass at the proton given in Table 31.2 from the mass at the hydrogen atom given in Appendix A. You will find the difference is equal to the electron’s mass to three digits, implying the binding energy is small in comparison. (c) Take the ratio of the binding energy at the electron (13.6 eV) to the energy equivalent of the electron's mass (0.511 MeV). (d) Discuss how your answers confirm the stated purpose of this problem.arrow_forward
- Integrated Concepts: (a) What temperature gas would have atoms moving fast enough to bring two 3He nuclei into contact? Note that, because both are moving, the average kinetic energy only needs to be half the electric potential energy of these doubly charged nuclei when just in contact with one another. (b) Does this high temperature imply practical difficulties for doing this in controlled fusion?arrow_forwardConstruct Your Own Problem Consider a detector needed to observe the proposed, but extremely rare, decay of an electron. Construct a problem in which you calculate the amount of matter needed in the detector to be able to observe the decay, assuming that it has a signature that is clearly identi?able. Among the things to consider are the estimated half life (long for rare events), and the number of decays per unit time that you wish to observe, as well as the number of electrons in the detector substance.arrow_forwardExplain how an (particle can have a larger range in air than a (particle with the same energy in lead.arrow_forward
- This problem demonstrates that the binding energy of the electron in the ground state of a hydrogen atom is much smaller than the rest mass energies of the proton and electron. Calculate the mass equivalent in u of the 13.6-eV binding energy of an electron in a hydrogen atom, and compare this with the known mass of the hydrogen atom. Subtract the known mass of the proton from the known mass of the hydrogen atom. Take the ratio of the binding energy of the electron (13.6 eV) to the energy equivalent of the electron’s mass (0.511 MeV). Discuss how your answers confirm the stated purpose of this problem.arrow_forwardAnother set of reactions that result in the fusing of hydrogen into helium in the Sun and especially in hotter stars is called the carbon cycle. It is 12C+1H13N+, 13N13C+e++ve, 13C+1H14N+, 14N+1H15O+, 15O15N+e++ve, 15N+1H12C+4He. Write down the overall effect at the carbon cycle (as was done for the protonproton cycle in 2e+41H+4He+2ve+6. Note the number of protons (lH) required and assume that the positrons (e+) annihilate electrons to form more (rays.arrow_forward*•58 Two radioactive materials that alpha decay, 238U and 232Th, and one that beta decays, "K, are sufficiently abundant in granite to contribute significantly to the heating of Earth through the de- cay energy produced. The alpha-decay isotopes give rise to decay chains that stop when stable lead isotopes are formed. The isotope 4"K has a single beta decay. (Assume this is the only possible decay of that isotope.) Here is the information: Stable Decay Half-Life End Parent Mode (y) Point (MeV) (ppm) 238U 232Th 4.47 x 10° 206рЬ 51.7 1.41 x 1010 208Pb 42.7 13 1.28 x 10° 40Ca 1.31 4 In the table Q is the total energy released in the decay of one par- ent nucleus to the final stable end point and f is the abundance of the isotope in kilograms per kilogram of granite; ppm means parts per million. (a) Show that these materials produce energy as heat at the rate of 1.0 x 10-9 W for each kilogram of granite. (b) Assuming that there is 2.7 x 102 kg of granite in a 20-km-thick spherical shell at…arrow_forward
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