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Homework Help: Excited state lifetime

  1. Dec 11, 2008 #1
    1. The problem statement, all variables and given/known data
    the nucleus of 227Th decays to 223Ra and [tex]\alpha[/tex]. the daughter nucleus is left in a short lived excited state and decays down to the ground state with the emission of an 80 keV gamma ray. the natural line width of this gamma ray is .6 keV. what is the lifetime of the excited state of the 223Ra nucleus?

    2. Relevant equations
    [tex]\Delta[/tex]E [tex]\Delta[/tex]t = [tex]\hbar[/tex]/2 where [tex]\Delta[/tex]t is the lifetime [tex]\tau[/tex]

    3. The attempt at a solution
    can i just solve for [tex]\Delta[/tex]t as the lifetime of the excited state? letting [tex]\Delta[/tex]E = 80 keV? Im not sure what to do with the line width, it's not in my book anywhere.
  2. jcsd
  3. Dec 12, 2008 #2

    Tom Mattson

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    Staff Emeritus
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    The 80 keV photon isn't the thing that determines the lifetime of the state. Check this out and see if it doesn't clear things up.

    http://www.mwit.ac.th/~Physicslab/hbase/quantum/parlif.html [Broken]
    Last edited by a moderator: May 3, 2017
  4. Dec 12, 2008 #3
    so the .6 keV is our uncertainty energy?
    so [tex]\Delta[/tex]t =hbar/2E
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