physics
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?

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 
The probability distribution function of that state is
u^2(r) = [1/(32 pi)]*(1/ao)^3 *[(2 (r/ao)]^2 *exp(r/ao)