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Homework Help: One dimensional box

  1. Apr 18, 2010 #1
    1. The problem statement, all variables and given/known data

    consider butadiene [itex] H_2 C = CH-CH=cH_2 [/itex] and assume for simplicity that [itex] \pi [/itex] electrons move on a straight line (one -dimensional box) whose length l can be estimated as equal to two [itex] C=C [/itex] bond lengths (2*1.35 angstrom) , plus one [itex] C-C [/itex] lengths. Butadiene has four [itex] \pi [/itex] that fill the [itex] n=1 [/itex] & [itex] n=2 [/itex]. the transition observed in a UV/VIS spectrum thus corresponds to the exitationof ane electron from the [itex] n = 3 [/itex] state. Experimentally one finds that this corresponds to the absorption of light with a wavelengths of 217 nm. Compute and compare the lenghts of the 0ne-D box suggested by the sum of the bond length and by the energy of the transition.

    2. Relevant equations

    not sure

    3. The attempt at a solution

    not sure
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 18, 2010 #2
    Well what are the energy levels of a 1D well with length L?
     
  4. Apr 19, 2010 #3
    [tex] E = \frac {n^2 h^2}{8 m l^2} [/tex]
    is that what im to use?
    If it is may be energy is calculated from [itex] E = hv[/itex]
    and the information given then equate that to the energy difference calculated between n=3 and n= 2 ,
    if im headed in the correct direction
     
  5. Apr 19, 2010 #4
    Yes. You will want to find the L that gives that energy difference, and you will want to use the L given to you to find what energy difference that gets.
     
  6. Apr 20, 2010 #5
    thanks, nickjer.
    regards.
     
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