HRadius

HRadius - How Big is an Atom?: Most Probable and Average...

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How Big is an Atom?: Most Probable and Average Radius r Ψ Ψ 2 P(r) r Ψ 1 s = 1 f8e5 π Z a o 3/2 e -Zr/ao radial probability distribution function: P(r) = o π o 2 π Ψ 2 r 2 sin θ d θ d φ = 4 π r 2 Ψ 2 volume of annular ring = o π o 2 π r 2 sin θ dr d θ d φ = 4 π r 2 dr most probable radius: dP(r) dr = 0 4 π 1 π Z a o 3 d r 2 e -2Zr/ao dr = 0 4 π 1 π Z a o 3 2r – 2r 2 Z a o e -2Zr/ao = 0 1 – r Z
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This document was uploaded on 02/22/2012.

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