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College Physics 2e

Section Summary

College Physics 2eSection Summary

31.1 Nuclear Radioactivity

  • Some nuclei are radioactive—they spontaneously decay destroying some part of their mass and emitting energetic rays, a process called nuclear radioactivity.
  • Nuclear radiation, like x rays, is ionizing radiation, because energy sufficient to ionize matter is emitted in each decay.
  • The range (or distance traveled in a material) of ionizing radiation is directly related to the charge of the emitted particle and its energy, with greater-charge and lower-energy particles having the shortest ranges.
  • Radiation detectors are based directly or indirectly upon the ionization created by radiation, as are the effects of radiation on living and inert materials.

31.2 Radiation Detection and Detectors

  • Radiation detectors are based directly or indirectly upon the ionization created by radiation, as are the effects of radiation on living and inert materials.

31.3 Substructure of the Nucleus

  • Two particles, both called nucleons, are found inside nuclei. The two types of nucleons are protons and neutrons; they are very similar, except that the proton is positively charged while the neutron is neutral. Some of their characteristics are given in Table 31.2 and compared with those of the electron. A mass unit convenient to atomic and nuclear processes is the unified atomic mass unit (u), defined to be
    1 u = 1.6605 × 10 27 kg = 931.46 MeV / c 2 . 1 u = 1.6605 × 10 27 kg = 931.46 MeV / c 2 .
  • A nuclide is a specific combination of protons and neutrons, denoted by
    ZAXN or simplyAX,ZAXN or simplyAX,
    ZZ is the number of protons or atomic number, X is the symbol for the element, NN is the number of neutrons, and AA is the mass number or the total number of protons and neutrons,
  • Nuclides having the same ZZ but different NN are isotopes of the same element.
  • The radius of a nucleus, rr, is approximately
    where r0=1.2 fmr0=1.2 fm. Nuclear volumes are proportional to AA. There are two nuclear forces, the weak and the strong. Systematics in nuclear stability seen on the chart of the nuclides indicate that there are shell closures in nuclei for values of ZZ and NN equal to the magic numbers, which correspond to highly stable nuclei.

31.4 Nuclear Decay and Conservation Laws

  • When a parent nucleus decays, it produces a daughter nucleus following rules and conservation laws. There are three major types of nuclear decay, called alpha α,α, beta β,β, and gamma γγ. The αα decay equation is
  • Nuclear decay releases an amount of energy EE related to the mass destroyed ΔmΔm by
  • There are three forms of beta decay. The ββdecay equation is
  • The β+β+ decay equation is
  • The electron capture equation is
  • ββ is an electron, β+β+ is an antielectron or positron, νeνe represents an electron’s neutrino, and ν¯eν¯e is an electron’s antineutrino. In addition to all previously known conservation laws, two new ones arise— conservation of electron family number and conservation of the total number of nucleons. The γγ decay equation is
    Z A X N * Z A X N + γ 1 + γ 2 + Z A X N * Z A X N + γ 1 + γ 2 +
    γγ is a high-energy photon originating in a nucleus.

31.5 Half-Life and Activity

  • Half-life t1/2t1/2 is the time in which there is a 50% chance that a nucleus will decay. The number of nuclei NN as a function of time is
    where N0N0 is the number present at t=0t=0, and λλ is the decay constant, related to the half-life by
  • One of the applications of radioactive decay is radioactive dating, in which the age of a material is determined by the amount of radioactive decay that occurs. The rate of decay is called the activity RR:
    R= Δ N Δ t .R= Δ N Δ t .
  • The SI unit for RR is the becquerel (Bq), defined by
    1 Bq=1 decay/s. 1 Bq=1 decay/s.
  • RR is also expressed in terms of curies (Ci), where
    1Ci=3.70×1010 Bq.1Ci=3.70×1010 Bq.
  • The activity RR of a source is related to NN and t1/2t1/2 by
  • Since NN has an exponential behavior as in the equation N=N0eλtN=N0eλt, the activity also has an exponential behavior, given by
    where R0R0 is the activity at t=0t=0.

31.6 Binding Energy

  • The binding energy (BE) of a nucleus is the energy needed to separate it into individual protons and neutrons. In terms of atomic masses,
    where m1Hm1H is the mass of a hydrogen atom, mAXmAX is the atomic mass of the nuclide, and mnmn is the mass of a neutron. Patterns in the binding energy per nucleon, BE/ABE/A, reveal details of the nuclear force. The larger the BE/ABE/A, the more stable the nucleus.

31.7 Tunneling

  • Tunneling is a quantum mechanical process of potential energy barrier penetration. The concept was first applied to explain αα decay, but tunneling is found to occur in other quantum mechanical systems.
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