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Homework Help: Confused on how they derived this

  1. Mar 25, 2006 #1

    Pengwuino

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    The book im using did a simple little algebra and it is showing the quantized energy levels of an electron in a one-dimensional atom of width 0.1nm.

    They did this:

    [tex]
    \begin{array}{l}
    E_n = n^2 \frac{{h^2 }}{{8ml^2 }} \\
    E_n = n^2 \frac{{h^2 c^2 }}{{8mc^2 l^2 }} \\
    E_n = n^2 \frac{{(1239.8eV*nm)^2 }}{{(8)(0.511*10^6 eV)(0.1nm)^2 }} \\
    \end{array}[/tex]

    But where did the c^2 go on top?
     
  2. jcsd
  3. Mar 26, 2006 #2

    Physics Monkey

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    The [tex] c [/tex] has been put with the [tex] h [/tex] to give something with units of [tex] [E][T]\frac{[L]}{[T]} = [E][L] [/tex], and numerically [tex] h c = 1239.8[/tex] eV nm. This is one of those common estimation factors, although I remember it as [tex] \hbar c \sim 200 [/tex] eV nm.
     
    Last edited: Mar 26, 2006
  4. Mar 26, 2006 #3

    Pengwuino

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    Oh ok i get why they did this. They have a conversion at the front of the book for hc = (1239.8eV*nm) that i didn't notice or make the connection to.
     
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