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: Transitional state of electrons.

  1. Apr 3, 2005 #1
    This is how I went about it but I am unsure if it is correct..
    An n=3 to n=1 transition from an electron trapped in a rigid box produces a 240 nm photon. What is the width of the box?

    λ = hc / E:

    E = hc / λ

    E = (1.06E-34 J*s * 3E8m/s) / 240nm

    = 1.33E-19 J

    E = h2 / 8mL2

    L2 = h2 / 8mE
    L = √ h2 / 8mE

    L = √ ((1.06E-34 J*s) 2 / (8*9.11E-31kg*1.33E-19 J))

    = 1.08E-10 m
  2. jcsd
  3. Apr 3, 2005 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    You are missing a factor of 8:

    Allowed values of electron momentum are:

    [tex]p = \frac{hn}{2L}[/tex]

    Since [itex]E = p^2/2m[/itex], the allowed energy values are:

    [tex]E = \frac{n^2h^2}{4L^2}\frac{1}{2m} =n^2\frac{h^2}{8mL^2}[/tex]

    The change in energy between n=3 and n=1 results in the photon (E=hv):

    [tex]\Delta E = (9-1)\frac{h^2}{8mL^2} = \frac{hc}{\lambda}[/tex]

    [tex]L^2 = 8\frac{h\lambda}{8cm}[/tex]

    [tex]L = \sqrt{\frac{h\lambda}{cm}}[/tex]

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook