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Photon emitted when proton changes state

  1. Mar 4, 2013 #1
    1. The problem statement, all variables and given/known data
    a proton is confined in an infinitely high square well of length 10 fm. If the proton transitions from n=2 to ground state determine the energy and wavelength of the photon emitted


    2. Relevant equations

    [tex] E = \frac{h^2 n^2}{8mL^2} [/tex]
    [tex] E = \frac{hc}{\lambda} \ \ or \ \ \lambda = \frac{hc}{E} [/tex]

    3. The attempt at a solution
    I need some one to tell me if I did this right.
    energy at n = 2
    [tex] E_1 = \frac{(6.626E-34)^2( 2^2) }{8(1.67E-27)(1E-14)^2} [/tex]
    [tex] E_1 = 1.31E-12 [/tex]

    energy at ground state
    [tex] E_0 = \frac { (6.626E-34)^2}{8(1.67E-27)(1E-14)^2 } [/tex]
    [tex] E_0 = 3.286E-13 [/tex]

    energy of photon released
    [tex] E = E_1 - E_0 [/tex]
    [tex] E = 9.859E-13 \ J [/tex]

    wavelength of photon
    [tex] \lambda = \frac{(6.626E-34)(3E8)}{9.859E-13} [/tex]
    [tex] \lambda = 2.016E-13 m = 0.2016 pm [/tex]
    this would be a gamma ray.

    So did I do this question right?
     
  2. jcsd
  3. Mar 5, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    There are some units missing, but a gamma ray is the right order of magnitude for such a photon and the approach looks fine. You can check the calculations with WolframAlpha, for example.
     
  4. Mar 5, 2013 #3
    thanks.
     
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