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Infinitel potential well

  1. Jun 8, 2014 #1
    three parts to this one, I cant seem to justify my values, units cancel, but the numbers don't seem right. I think I may have used a wrong equation for part B but I don't know what else to use.

    Problem: An electron is confined to an infinitely deep potential well of width 0.120 nm.
    a.) Calculate its ground state energy, E1
    b.)If the electron makes a transition from the n=3 state to the n=2 state, how much energy is carried away by the emitted photon?
    c.)What is the wavelength of this photon?


    equations:

    a.) [tex]E_1 = \frac{pi^2 (hbar c)^2}{2M_e C^2 a^2}[/tex]

    b.) [tex]E_\gamma = E_3 - E_2[/tex]

    c.) [tex]\lambda = \frac{hc}{E_\lambda}[/tex]


    My attempt:

    a.) using hbar*c = 197 ev*nm and MeC^2 = 511000 ev i get a value of 26.02ev for E1

    b.) using the same equation as above for the n=3 and n=2 states and subtracting I get 130.13ev

    c.) using hc = 1240 ev*nm I get an answer of 9.53 nm which doesn't seem right to me. I feel like the photon should have a larger wavelength.
     
  2. jcsd
  3. Jun 8, 2014 #2

    Simon Bridge

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    Why do you think the photon should have a bigger wavelength?

    Lets see - using ##h= 2\pi \hbar## ;$$E_n=\frac{n^2(h c)^2}{8mc^2a^2}=n^2E_1$$ (when you use LaTeX, put a backslash in front of the symbol name so \hbar renders as ##\hbar## etc.)

    hc=1239.8 eV.nm
    mc^2=511000 eV
    a=0.120nm

    Looks good to me:
    Go through the arithmetic one step at a time, make sure you have squared the correct terms.
     
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