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Homework Help: Determine the most probable radius for a 2s orbital (Hydrogen atom)

  1. Nov 21, 2007 #1
    1. The problem statement, all variables and given/known data

    Determine the most probable radius for a 2s orbital (Hydrogen atom)

    2. Relevant equations

    Wavefunction for a 2s orbital:

    1/(4√2pi*a^(3⁄2) ) (2-r⁄a) e^((-r)⁄(2a)) where, a=bohr radius

    3. The attempt at a solution

    First step:
    find the probability density by squaring the wavefunction and multiplying but the spherical element of Volume

    Second step:
    Set the derivative of the probability density equal to zero to solve for where the slope of the plotted function is equal to zero
  2. jcsd
  3. Nov 21, 2007 #2


    User Avatar
    Science Advisor
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    Gold Member

    So you know all the steps, you simply have to go ahead!

    Are you stuck on something?
  4. Oct 7, 2009 #3
    i am working on the same problem, and i am stuck on one particular part, when i take the derivative and set it equal to zero i end up with a cubic polynomial, like

    (r/a)^3 - 6(r/a)^2 + 8r/a - 4 =0

    not sure it this is correct, and if it is then do i need to use a graphing program to calculate the min and max points (roots) or is there an easier way?

    thanks in advance for any help...
  5. Dec 14, 2010 #4
    Stuck on this problem also!!

    I get to a stage where I get a massive cubic equation...I'm assuming I've gone wrong somewhere...

    Any help? Or any online resources where the problem is worked through...?
  6. Dec 14, 2010 #5
    think i ended up solving it sometime last year.. think the equation factors to something like: (x-4)*(x-2)*(x-2)=0 or something like that.. roots are then 4 & 2.. cant remember exactly but hope this points you in the right direction.... oh x=r/a) of course..
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