Posted by sweety on .
Analyze the radial distribution of the Hatom at the 2s state. How are the maxima
situated with respect to the minimum?
Is the “golden ratio” involved?

physics 
drwls,
The 2s orbital has a probability distribution function that is a function of r only.
There is a maximum at r = 0 and a zeroprobability node at r = 2 ao, where ao is the Bohr radius. There is a secondary sphericalshell relative maximum at r = 4 ao. In don't see where the "golden ratio" (1.618) is involved.
The probability distribution function of that state is
u^2(r) = [1/(32 pi)]*(1/ao)^3 *[(2 (r/ao)]^2 *exp(r/ao)
See if you can find a golden ratio in the min and max locations 
physics (correction) 
drwls,
The probability distribution function of that state is
u^2(r) = [1/(32 pi)]*(1/ao)^3 *[(2 (r/ao)]^2 *exp(r/ao)