What is the wavelength of the light?

  1. Calculate the wavelength of the light emitted when an electron in a one-dimensional box of length 5.2nm makes a transition from the n = 7 state to the n = 6 state.
    Express your answer with the appropriate units.

    I calculated in this way:
    E = n^2*h^2/8*m*a^2
    E= (7^2-6^2)*(6.626*10^-34)^2/8*(9.1*10^-31)*(5.2*10^-9)^2
    E= 2.9*10^-20 J

    E = hc/λ
    λ = 6.85*10^-6 m

    But the answer is wrong.

    What is wrong with my calculation?
     
  2. jcsd
  3. Simon Bridge

    Simon Bridge 14,438
    Science Advisor
    Homework Helper
    Gold Member

    How do you know the answer is wrong?

    It can help if you do the algebra first, then use more convenient units:$$\lambda=\frac{8(m_e c^2) L^2}{hc}\frac{1}{n_f^2-n_i^2}$$

    ##hc=1.240\text{eV$\mu$m}##
    ##m_ec^2=511\text{eV}##
    ##L=0.0052\text{$\mu$m}##
    ... give it a go.
    (Don't forget to check my algebra to get that equation.)
     
  4. It is the same calculation as mine.
    I did the exercise on MasteringChemistry. It only said my answer is wrong.
     
  5. Simon Bridge

    Simon Bridge 14,438
    Science Advisor
    Homework Helper
    Gold Member

    But I got a different order of magnitude from you.
    Repeat the calculation ... you have misplaced a decimal point someplace.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook