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Section summary

  • 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 , size 12{ left (α right ),} {} beta β , size 12{ left (β right ),} {} and gamma γ size 12{ left (γ right )} {} . The α size 12{α} {} decay equation is
    Z A X N Z 2 A 4 Y N 2 + 2 4 He 2 . size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } rightarrow "" lSub { size 8{Z - 2} } lSup { size 8{A - 4} } Y rSub { size 8{N - 2} } +"" lSub { size 8{2} } lSup { size 8{4} } "He" rSub { size 8{2} } } {}
  • Nuclear decay releases an amount of energy E size 12{E} {} related to the mass destroyed Δ m by
    E = ( Δ m ) c 2 . size 12{E= \( Δm \) c rSup { size 8{2} } } {}
  • There are three forms of beta decay. The β size 12{β rSup { size 8{ - {}} } } {} decay equation is
    Z A X N Z + 1 A Y N 1 + β + ν ¯ e .
  • The β + decay equation is
    Z A X N Z 1 A Y N + 1 + β + + ν e .
  • The electron capture equation is
    Z A X N + e Z 1 A Y N + 1 + ν e .
  • β is an electron, β + size 12{β rSup { size 8{+{}} } } {} is an antielectron or positron, ν e size 12{v rSub { size 8{e} } } {} represents an electron’s neutrino, and ν ¯ e size 12{ {overline {ν rSub { size 8{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 γ decay equation is
    Z A X N * Z A X N + γ 1 + γ 2 + size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } rSup { size 8{*} } rightarrow "" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } +γ rSub { size 8{1} } +γ rSub { size 8{2} } + dotsaxis } {}
    γ size 12{γ} {} is a high-energy photon originating in a nucleus.

Conceptual questions

Star Trek fans have often heard the term “antimatter drive.” Describe how you could use a magnetic field to trap antimatter, such as produced by nuclear decay, and later combine it with matter to produce energy. Be specific about the type of antimatter, the need for vacuum storage, and the fraction of matter converted into energy.

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What conservation law requires an electron’s neutrino to be produced in electron capture? Note that the electron no longer exists after it is captured by the nucleus.

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Neutrinos are experimentally determined to have an extremely small mass. Huge numbers of neutrinos are created in a supernova at the same time as massive amounts of light are first produced. When the 1987A supernova occurred in the Large Magellanic Cloud, visible primarily in the Southern Hemisphere and some 100,000 light-years away from Earth, neutrinos from the explosion were observed at about the same time as the light from the blast. How could the relative arrival times of neutrinos and light be used to place limits on the mass of neutrinos?

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What do the three types of beta decay have in common that is distinctly different from alpha decay?

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Problems&Exercises

In the following eight problems, write the complete decay equation for the given nuclide in the complete Z A X N size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } } {} notation. Refer to the periodic table for values of Z size 12{Z} {} .

β size 12{β rSup { size 8{ - {}} } } {} decay of 3 H size 12{"" lSup { size 8{3} } H} {} (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs.

1 3 H 2 2 3 He 1 + β + ν ¯ e

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β size 12{β rSup { size 8{ - {}} } } {} decay of 40 K size 12{"" lSup { size 8{"40"} } K} {} , a naturally occurring rare isotope of potassium responsible for some of our exposure to background radiation.

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β + size 12{β rSup { size 8{+{}} } } {} decay of 50 Mn size 12{"" lSup { size 8{"50"} } "Mn"} {} .

25 50 M 25 24 50 Cr 26 + β + + ν e size 12{"" lSub { size 8{"25"} } lSup { size 8{"50"} } M rSub { size 8{"25"} } rightarrow "" lSub { size 8{"24"} } lSup { size 8{"50"} } "Cr" rSub { size 8{"20"} } +β rSup { size 8{+{}} } +v rSub { size 8{e} } } {}

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β + size 12{β rSup { size 8{+{}} } } {} decay of 52 Fe size 12{"" lSup { size 8{"52"} } "Fe"} {} .

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Electron capture by 7 Be size 12{"" lSup { size 8{7} } "Be"} {} .

4 7 Be 3 + e 3 7 Li 4 + ν e size 12{"" lSub { size 8{4} } lSup { size 8{7} } "Be" rSub { size 8{3} } +e rSup { size 8{ - {}} } rightarrow "" lSub { size 8{3} } lSup { size 8{7} } "Li" rSub { size 8{4} } +v rSub { size 8{e} } } {}

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Electron capture by 106 In size 12{"" lSup { size 8{"106"} } "In"} {} .

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α size 12{α} {} decay of 210 Po size 12{"" lSup { size 8{"210"} } "Po"} {} , the isotope of polonium in the decay series of 238 U size 12{"" lSup { size 8{"238"} } U} {} that was discovered by the Curies. A favorite isotope in physics labs, since it has a short half-life and decays to a stable nuclide.

84 210 Po 126 82 206 Pb 124 + 2 4 He 2 size 12{"" lSub { size 8{"84"} } lSup { size 8{"210"} } "Pb" rSub { size 8{"126"} } rightarrow "" lSub { size 8{"82"} } lSup { size 8{"206"} } "Pb" rSub { size 8{"124"} } +"" lSub { size 8{2} } lSup { size 8{4} } "He" rSub { size 8{2} } } {}

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α size 12{α} {} decay of 226 Ra size 12{"" lSup { size 8{"226"} } "Ra"} {} , another isotope in the decay series of 238 U size 12{"" lSup { size 8{"238"} } U} {} , first recognized as a new element by the Curies. Poses special problems because its daughter is a radioactive noble gas.

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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