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Electrons inside a carbon nanotube - Quatum Mechanics

  1. May 14, 2014 #1
    1. The problem statement, all variables and given/known data
    Electrons inside a carbon nanotube can be approximated as a one dimensional "particle in a box". If the nanotube is 3 micrometers long, what is the minimum speed of an electron inside the tube?


    2. Relevant equations



    3. The attempt at a solution

    The minimum occurs as n=1 so therefore

    [itex]K=\frac{h^{2}}{8M_{e^{-}}(3E-6)}= 2.01E-32J[/itex]

    If I use 1/2 mV^2 to find V I get the wrong answer. Why can't I use it and what should I use instead?
     
  2. jcsd
  3. May 14, 2014 #2
    The lowest energy state in a particle in a box is

    [tex]
    E_n = \frac{h^2}{8m_eL^2}
    [/tex]

    If you used the equation as you wrote it, you didn't square your L.

    Then you can use the

    [tex]
    E = \frac{1}{2}mv^2
    [/tex]

    formula to solve for v.
     
  4. May 14, 2014 #3
    Gah it's always something stupid like that. Thanks.
     
  5. May 14, 2014 #4
    No worries! I've done 28328348238 stupid things like that over the years.
     
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