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Homework Help: Atomic Hydrogen

  1. Nov 28, 2006 #1
    I spent my Thanksgiving trying to solve my homework and I will need some help:

    1)For fixed electron energy ,the orbital quantum number l is limited to n-1.We can obtain this result from a semiclassical argument using the fact that the larges angular momentum describes circular orbits,where all kinetic energy is in orbital form.For hydrogen-like atoms U(x)=-(Zke^2)/r
    and the energy in circular orbits becomes:

    E=((|L|^2)/2mr^2)-(Zke^2)/r

    Quantize this realtion using the rules of |L|=(l(l+1))^0.5 and E=-((ke^2)Z^2)/(2an^2),together with the Bohr result for the allowed values of r,to show that the largest integer value of l consistent with total energy i s lmax=n-1


    solution:

    ke^2)Z^2)/(2an^2)=((|L|^2)/2mr^2)-(Zke^2)/r and substituting |L|=(l(l+1))^0.5


    ke^2)Z^2)/(2an^2)=(l(l+1))/2mr^2)-(Zke^2)/r

    but i dont know what to do after this

    please can somebody help me
     
  2. jcsd
  3. Nov 28, 2006 #2

    dextercioby

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    You have to substitute for the r versus n dependence as given by Bohr.

    Daniel.
     
  4. Nov 28, 2006 #3
    When I use formula for Bohrs radius

    my equation is :

    n=(l(l+1))^05

    and i dont know how i can from here get

    lmax=n-1
     
  5. Nov 29, 2006 #4

    dextercioby

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    You should have gotten an inequation. See if l_max=n will fit into your equation.

    Daniel.
     
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