1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Calculate natural line width of the transition

  1. Nov 26, 2011 #1
    1. The problem statement, all variables and given/known data
    A lifetime of the first excited state for some atom is τ, calculate natural line width for that line.

    3. The attempt at a solution
    Well, I could use energy-time uncertainty relation


    then ΔE*τ=h , now I can use a relation E=hc/λ

    to obitain Δλ=c*τ , which is natural line width.

    Now let's say τ=17ms (something like the lifetime of the Fe xiv)
    then Δλ=3*10^8*17*10^-3=50*10^5m , this can not be true,
    what am I doing wrong ?
  2. jcsd
  3. Nov 28, 2011 #2
    Can someone give me any kind of answer, some thoughts, anything ?

    If I take the example from hyperphysics:


    where they have calculated for some transition in Iron-57 that the natural line width is

    now using the relation for energy E=hc/λ to obitain λ, this gives me:

    λ=hc/E ≈ 4*10^(-15)[eVs]*3*10^8[m/s] /(10^-8[eV]) =120m

    so this is the natural line width expressed in meters,
    as I understand this is the Full width at half maximum for this line, but this does not make sense to me. I think FWHM should be some fraction of 10^-10m, since they are talking about gamma ray there.

    In my first post, in question is some green (green coronal line from sun) and I think that the FWHM (natural line width of a line) should be fraction of a nanometer.

    I know that my reasoning is somewhere wrong but I just don't see where.
  4. Nov 28, 2011 #3


    User Avatar

    On that site you can see the formulae for the Natural linewidth, Gamma.
    Why don't you use that one?

    EDIT: are you sure about the lifetime of the Fe xiv? milliseconds? I don't know it, just asking...
  5. Nov 28, 2011 #4
    I can use that formula but this will also give me a result which I don't understand.
    Let's say I use that formula and plug in just order of magnitude for my values, then

    gamma≈hbar/τ ≈ 10^-16/10^-3 = 10^-13eV

    gamma is in energy (FWHM in energy), but I want that in nanometers, therefore using
    λ=hc/E = hc/(gamma)

    I have λ≈10^-15*10^8/(10^-13) = 10^6 m
    But this can't be natural line width (FWHM) of this green line.
    And for lifetime value τ of this green coronal line, there are several scientific papers
    which also give this value τ in ms , for example this paper
    page 838 just at the top
    "The lifetime of the Fe xiv line we infer from the six data
    sets is 16:69 ±0:10 ms."

    If this ms means millisecond, then τ is ok,
    I'm messing up somewhere else, the λ I calculated is probably something else and not natural line width. But how then to calculate natural line width in meters if you have a lifetime τ given ?
    Last edited: Nov 28, 2011
  6. Nov 28, 2011 #5
    Can someone at least give me an answer to any of these two questions:

    1.) How do you find a natural line width (expressed in meters) ?
    2.) What are typical natural line widths (atomic transitions , lasers etc ... in meters) ?

    I would be grateful :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook