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Radial distribution

  • Thread starter rupp
  • Start date
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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.
 

Answers and Replies

Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,598
6
If the second derivative is negative at a specified point, then that point is a [local] maximum.
 

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