Quantum Physics

Problems 967CONCEPTUAL QUESTIONS1. Isotopes of a given element have different physicalproperties, such as mass, but the same chemicalproperties. Why is this?2. If a heavy nucleus that is initially at rest undergoesalpha decay, which has more kinetic energy after thedecay, the alpha particle or the daughter nucleus?3. A student claims that a heavy form of hydrogen decaysby alpha emission. How do you respond?4. Explain the main differences between alpha, beta,and gamma rays.5. In beta decay, the energy of the electron or positronemitted from the nucleus lies somewhere in a relativelylarge range of possibilities. In alpha decay,however, the alpha particle energy can only havediscrete values. Why is there this difference?6. If film is kept in a box, alpha particles from a radioactivesource outside the box cannot expose thefilm, but beta particles can. Explain.7. In positron decay, a proton in the nucleus becomesa neutron, and the positive charge is carried away bythe positron. But a neutron has a larger rest energythan a proton. How is this possible?8. An alpha particle has twice the charge of a beta particle.Why does the former deflect less than the latterwhen passing between electrically charged plates, assumingthey both have the same speed?9. Can carbon-14 dating be used to measure the age ofa stone?10. Pick any beta-decay process and show that the neutrinomust have zero charge.11. Why do heavier elements require more neutrons inorder to maintain stability?12. Suppose it could be shown that the intensity of cosmicrays was much greater 10 000 years ago. Howwould this affect the ages we assign to ancient samplesof once-living matter?13. Compare and contrast a photon and a neutrino.14. Why is carbon dating unable to provide accurate estimatesof very old materials?15. Two samples of the same radioactive nuclide areprepared. Sample A has twice the intial activity ofsample B. How does the half-life of A compare withthe half-life of B ? After each has passed through fivehalf-lives, what is the ratio of their activities?16. (a) Describe what happens to the number of protonsand neutrons in a nucleus when the nucleusundergoes alpha decay. (b) Repeat for beta decay.PROBLEMS1, 2, 3 = straightforward, intermediate, challenging full solution available in Student Solutions Manual/Study Guide coached problem with hints available at www.cp7e.com biomedical applicationTable 29.4 will be useful for many of these problems. A more TABLE 29.4complete list of atomic masses is given in Appendix B.Some Atomic Masses0231. Compare the nuclear radii of the following nuclides:,( 1 n ) 1.008 665 12Mg 22.994 1272 60 197 2391 H 27 Co , 79 Au , 94 Pu127.1 H 1.007 825 13Al 26.981 53823012. What is the order of magnitude of the number of2.014 102 15P 29.978 310440protons in your body? Of the number of neutrons?2He 4.002 602 20Ca 39.962 591742Of the number of electrons?3Li 7.016 003 20Ca 41.958 6229434Be 9.012 174 20 Ca 42.958 7703. Using the result of Example 29.1, find the radius of 10 565 B 10.012 936 26Fe 55.934 940a sphere of nuclear matter that would have a mass 12 64equal to that of the Earth. The Earth has a mass of6 C 12.000 000 30Zn 63.929 1445.98 10 24 kg and average radius of 6.37 10 6 13 64m.6 C 13.003 355 29Cu 63.929 59914 937 N 14.003 074 41Nb 92.906 3774. Consider the hydrogen atom to be a sphere of radiusequal to the Bohr radius, 0.53 10 10 7 N 15.000 108 79Au 196.966 54315 197m, and 15 2028 O 15.003 065 80Hg 201.970 617calculate the approximate value of the ratio of the 17 216nuclear density to the atomic density.8 O 16.999 131 84 Po 216.001 79018 2208 O 17.999 160 Rn 220.011 4015. An alpha particle (Z 2, mass 6.64 10 27 86kg) approachesto within 1.00 10 14 9018 2349 F 18.000 937 Th 234.043 583m of a carbon nucleus(Z 6). What are (a) the maximum Coulomb2023810Ne 19.992 435 92U 238.050 784Element Atomic Mass (u) Element Atomic Mass (u)Section 29.1 Some Properties of Nuclei0( 1 e ) 0.000 5492311Na 22.989 770