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Linewidth from quality factor

  1. Mar 7, 2016 #1
    1. The problem statement, all variables and given/known data
    Light with wavelength 500 nm is emitted from an electron in an atom behaving as a lightly damped simple harmonic oscillator with Q = 5 x 10^7. Find the linewidth (width to half-power points) in nm.

    2. Relevant equations
    wavelength=c/f
    f=w/2pi
    Q=f/delta f=w/delta w

    3. The attempt at a solution

    So i started by calculating frequency and then angular frequency

    f = 3E8/500E-9 = 6E14hz
    w = 6E14*2pi = 3.77E15 radians/sec

    I did some research and found that Q=resonant frequency/(half-power bandwidth)
    But how do i work out the resonant frequency? The lecturer said it would take us maybe an hour or two to solve this problem so it seems to simple for the frequency i have to be the one required here.
     
    Last edited: Mar 7, 2016
  2. jcsd
  3. Mar 7, 2016 #2
    so you can find the line width as you have the Q-value as well as the frequency!
     
  4. Mar 7, 2016 #3
    Yes but as i said at the bottom of the post, is the frequency i have the resonant frequency because this seems far too simple, the lecturer said it would take an hour or two but it's only taken 5 minutes... And he asks for it in nm but when i try the frequency i have i end up with 25m as the answer so it seems wrong to me.
     
  5. Mar 7, 2016 #4
    Q=f(resonant)/delta f

    => delta f = 6E14/5E7 = 1.2E7 Hz
    lamda=c/f
    =>lamda = 3E8/1.2E7 = 25m

    It just seems far too big when he's asking for it in nm :/
     
  6. Mar 8, 2016 #5

    ehild

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    Calculate the frequencies on the resonant curve which correspond to the half power and convert those frequencies to wavelength.
     
  7. Mar 8, 2016 #6
    When damping is small, the resonant frequency is approximately equal to the natural frequency of the system, which is a frequency of unforced vibrations.
     
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