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Hydrogen atom emitting a photon

  1. Apr 9, 2014 #1

    STJ

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    1. The problem statement, all variables and given/known data

    Consider the following.
    (a) For a hydrogen atom making a transition from the n = 4 state to the n = 3 state, determine the wavelength of the photon created in the process. (Already solved this, 1.86x10^3 nm)



    (b) Assuming that the atom was initially at rest, determine the recoil speed of the hydrogen atom when it emits this photon.


    2. Relevant equations

    λ=hc/ΔE

    3. The attempt at a solution

    I've done one like this previously, but we were given the energy of the photon colliding with the atom. Found the Kinetic Energy, set it equal to 1/2mv^2 and solved for v. I don't think I can do this for part b. I think this has something to do with momentum perhaps? I'm kind of lost on this one.
     
  2. jcsd
  3. Apr 9, 2014 #2

    patrickmoloney

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    Gold Member

    Momentum of photon = ## \frac{h}{ \lambda} ##

    Conservation of momentum says that this momentum must be in the opposite direction of the hydrogen atom.

    ## p = \frac{h}{\lambda} = \frac{6.63*10^{-34}}{1.83*10^{-6}} = 3.62*10^{-28} kg \cdot ms^{-1} ##

    ## V_{H-atom} = \frac{p}{m} = \frac{3.62*10^{-28}}{1.67*10^{-27}} = 0.22 ms^{-1} ##
     
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