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X-ray Wavelengths

  1. Jul 25, 2008 #1
    1. The problem statement, all variables and given/known data
    The tube in a medical research X-ray unit uses lead (Z=82) as it's target. Assume the electrons are accelerated through the voltage calculated in part (b). What is the wavelength of the Kα line?

    2. Relevant equations
    KE=-13.6 ev ((Z-1)squared) / (1squared)
    KE=PE=VQ
    E=QV
    λ=hc/E

    3. The attempt at a solution
    KE=-13.6 ev ((Z-1)squared) / (1squared)
    KE =-13.6 ev ((82-1)squared)/ 1 squared)
    KE=89229.6 ev

    KE=PE=QV
    89229.6=(1.602E-19 J/ev)V
    V=89229.6 V

    E=QV
    E=(1.602E-19 C)(89229.6V)
    E=1.429E-14 J

    λ=hc/E
    λ=((6.63E-34 J*s)(3E8 m/s))/(1.429E-14 J)
    λ=1.3856E-11 m = 0.013856 nm

    I'm not sure what's wrong... I correctly solved for KE and V, but I can't seem to solve for λ.
     
  2. jcsd
  3. Jul 25, 2008 #2

    Astronuc

    User Avatar

    Staff: Mentor

    I'm not sure where part b is, but think about the energies.

    The accelerated electron must have enough energy to dislodge a K-electron from the lead atom.

    Then another orbital electron will fall from a higher state to the spot in the K-shell, so the X-ray energy represents a difference in energy levels of atomic electrons. What's the significance of Kα?
     
  4. Jul 26, 2008 #3
    Oh okay I got it now. Thanks!
     
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