- #1
rupp
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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.
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.