1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If the second derivative is negative at a specified point, then that point is a [local] maximum.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?