physics

Analyze the radial distribution of the H-atom at the 2s state. How are the maxima
situated with respect to the minimum?
Is the “golden ratio” involved?

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  1. The 2s orbital has a probability distribution function that is a function of r only.

    There is a maximum at r = 0 and a zero-probability node at r = 2 ao, where ao is the Bohr radius. There is a secondary spherical-shell 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

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  2. The probability distribution function of that state is

    u^2(r) = [1/(32 pi)]*(1/ao)^3 *[(2 -(r/ao)]^2 *exp(-r/ao)

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