Applying uncertainty principle to decaying states

  1. 1. The problem statement, all variables and given/known data

    I quote from my text, "The decay of excited states in atoms and nuclei often leave the system in another, albeit lower-energy, excited state. (a) One example is the decay between two excited states of the nucleus of ^48Ti. The upper state has a lifetime of 1.4 ps, the lower state 3.0 ps. What is the fractional uncertainty deltaE/E in the energy of 1.3117-MeV gamma rays connecting the two states? (b) Aother example is the H_alpha line of the hydrogen Balmer series. In this case the lifetime of both states is about the same, 10-8 s. What is the uncertainty in the energy of the H_alpha photon?"

    2. Relevant equations

    delta_E*delta_t is greater than or equal to h-bar/2

    3. The attempt at a solution

    Those lifetimes they give are of each state, not of photon itself. I thought about trying to find the energy of each state, by using the above version of the uncertainty principle, and then subtracting to get the energy difference, which should be the energy of the photon. However, I keep getting the wrong answer. Any ideas? The book contains no examples of this type of problem.
    My book, which has been wrong in the past, says the answers are: (a) 5.310-10 eV (b) 1.3210-7 eV
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
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