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Homework Help: Radial distribution

  1. Nov 21, 2008 #1
    1. The radial distribution function for the 1s orbital of the hydrogen atom is given by the equation below. Where a = the Bohr radius. What is the most probable distance from the nucleus for an electron in this orbital?

    2. P(r) = 4r^2 (1/a)^3 exp(-2/a)

    3. Setting dP/dr = 0, I know you'll get ((r-r^2)/a) exp(-2r/a) = 0
    so you'd get something like (4/a^3)((2r exp-2r/a) + r^2 (exp-2/a)exp(-2r/a)

    What should I get as the 2nd derative? I know if I set the r = 0 for the 2nd der. i get the minimun. If r = a I get the maximum, so the actual distance would be a, but an explanation through the actual steps would be greatly appreciated.
  2. jcsd
  3. Nov 22, 2008 #2


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    If the second derivative is negative at a specified point, then that point is a [local] maximum.
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