1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Electron in an infinite well

  1. Nov 18, 2012 #1
    An electron is trapped in an infinite one-dimensional well of width 0.251nm. Initially the electron occupies the n=4 state. Suppose the electron jumps to the ground state with the accompanying emission of a photon. What is the energy of the photon?

    (Time independent)

    What I did was realize that [itex]\psi(x)[/itex] must equal zero at the walls, so I chose [itex]\sin(kL)[/itex] and set it to [itex]n\pi[/itex], then solved for k.

    Putting this value of k into the energy for a free particle (Time-ind Schrodinger), I eventually come to the expression:
    \frac{h^2 n^2}{8mL^2}

    To find the corresponding energy of the emitted photon I plugged in the appropriate values of n and solved for the difference.

    Does that seem right?

    E=\frac{h^2 15}{8m L^2}

    Obviously plugging in appropriate values of m and L afterward.
  2. jcsd
  3. Nov 18, 2012 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    That is certainly the method.
    If this is long answer you want to write it explicitly in the math though.
  4. Nov 18, 2012 #3
    Yeah, I have it officially written out showing steps and whatnot. Just felt lazy with the LaTex so I shortened it. Thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook