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Chapter 29 Learning Objectives

Concepts and Skills to Review

  • Rutherford scattering experiment; discovery of the nucleus (Section 27.6)
  • Fundamental forces (Section 2.2)
  • Mass and rest energy (Section 26.7)
  • Exclusion principle (Section 28.7)
  • Exponential functions (Appendix A.3, Section 18.10)
  • Tunneling (Section 28.10)

Summary

  • A particular nuclide is characterized by its atomic number Z (the number of protons) and its nucleon number A (the total number of protons and neutrons). The isotopes of an element have the same atomic number but different numbers of neutrons.
  • The mass density of all nuclei is approximately the same The radius of a nucleus is
     r = r0A1/3(29-4)
     where r0 = 1.2 × 10-15 m = 1.2 fm(29-5)
  • The binding energy EB of a nucleus is the energy that must be supplied to separate a nucleus into individual protons and neutrons. Since the nucleus is a bound system, its total energy is less than the energy of Z protons and N neutrons that are far apart and at rest.
     EB = Δmc2(29-8)
  • In any nuclear reaction, the total electric charge and the total number of nucleons are conserved.
  • An unstable or radioactive nuclide decays by emitting radiation.
    Alpha decay<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58012/image29_10.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (29-10)
    Beta-minus decay<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58012/image29_11.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (29-11)
    Beta-plus decay<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58012/image29_12.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (29-12)
    Gamma decay<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58012/image29a.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>  
  • Each radioactive nuclide has a characteristic decay probability per unit time l. The activity R of a sample with N nuclei is
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58012/image29_18.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (29-18)
    Activity is commonly measured in becquerels (1 Bq = 1 decay per second) or curies (1 Ci = 3.7 × 1010 Bq).
  • The number of remaining nuclei N in radioactive decay (the number that have not decayed) is an exponential function:
    <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58012/image29_20.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> (29-20)
    where the time constant is t = 1/λ. The half-life is the time during which half of the nuclei decay:
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/58012/image29b.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> (29-23)
  • The absorbed dose is the amount of radiation energy absorbed per unit mass of tissue, measured in grays (1 Gy = 1 J/kg) or rads (1 rad = 0.01 Gy).
  • The quality factor (QF) is a relative measure of the biological damage caused by different kinds of radiation. The biologically equivalent dose in rem is
     Biologically equivalent dose (in rem) = Absorbed dose (in rad) × QF(29-29)
  • A large nucleus can release energy by splitting into two smaller, more tightly bound nuclei in the process called fission. The energy released in a fission reaction is enormous—typically around 200 MeV for the split of a single nucleus.
  • Nuclear fusion combines two small nuclei to form a larger nucleus. Fusion typically releases significantly more energy per nucleon than fission.







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