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Homework Help: Determining the life time of a excited state.

  1. Jul 10, 2012 #1
    1. The problem statement, all variables and given/known data
    The smallest uncertainty in the frequency of emitted light when excited atoms return to ground state for molecules is estimated to be 8 MHz. Use this information to estimate the lifetime of the excited states.
    I would like to know if I'm thinking correct.

    2. Relevant equations
    Well here, it is a question we can take in general by having an uncertainty of the frequency at f = MHz.
    I took the hydrogen atom in which the energy levels in general can be written as

    [itex]E_n=\frac{-13.6eV}{n^2}[/itex] where I then calculate the difference in energy for instance between state n = 1 and n = 2.

    3. The attempt at a solution
    Can I then apply the energy-time uncertainty principle [itex]\Delta E \Delta t \ge \frac{\hbar}{2}[/itex] ?
    I'm not sure about this, science we have an uncertainty in FREQUENCY which makes me stuck.

    Appreciate for help.
  2. jcsd
  3. Jul 10, 2012 #2


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    Recall the general relation E = hf.
  4. Jul 11, 2012 #3
    Can this be used as the uncertainty in energy in the energy-time uncertainty principle?
    (Im not very sure about this, scince I don't have a solution for this)
  5. Jul 11, 2012 #4
    Need to mention that of course f = 8 MHz
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