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Determine X-ray Wavelength & Frequency

  1. Mar 7, 2013 #1
    Problem:

    Determine the wavelength and frequency of the emitted x-rays when 100-keV electrons strike a target.

    Solution:

    Assuming all kinetic energy of electrons is used to produce the x-rays,

    E_initial=E_final
    K+m_0*c^2=hf+m_0*c^2
    K=hf
    K=hc/λ
    =>λ=hc/K=(6.63x10^-34 Js)(3.00x10^8 m/s)/(1.60x10^-14 J) [because 100 keV =1.60x10^-14 J]

    λ=0.12 Å

    Also since K=hf,

    f=K/h=(1.60x10^-14 J)/(6.63x10^-34 Js)=2.4x10^-19 Hz

    Is this correct?
     
  2. jcsd
  3. Mar 7, 2013 #2

    Redbelly98

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    Homework Helper

    Looks essentially correct. Just recheck the exponent on your frequency (and my apologies if that's just a simple typo on your part)

    I am wondering if this might have been intended as a "reverse photoelectric effect" problem. But since the work function is negligible compared to 100 keV, you come up with the same K≈hf to work with.

    A few tips for working problems like this:

    It goes easier if you can get used to working in eV rather than always converting to joules.

    A useful constant to remember, for going between wavelength and photon energy, is [itex]hc=1240 \text{ eV-nm}[/itex]

    It's a good habit to think about whether your answer to any problem makes sense. For example, we (hopefully) know that visible light has a frequency way higher than 1 Hz, and x-rays have frequencies way higher than visible light. Again, my apologies if the 10^-19 was simply a typo.
     
  4. Mar 7, 2013 #3
    Oh yes, that is a typo! Should be x10^19~My apologies, but I'm happy you caught it.

    Thanks for the tips, and I'll certainly put in time to commit the value for hc to memory.
     
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