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Radial Probabilities Radial Probability: probability of finding the electron at a distance between r and r + dr from the nucleus. In general, ψ nlm (r, θ , φ ) = Radial Part x Angular Part R nl (r) x φ lm ( θ , φ ) Radial Probability = Radial Probability Density x Volume Thus to get the Radial Probability we must specify the Radial Probability Density and the Volume Radial Probability Density = R nl 2 (r) : Square of the Radial Wavefunction The required volume is determined by the volume of the SPHERICAL SHELL enclosed between a sphere of radius (r+dr) and a sphere of radius r (see figure). 4 π r 2 R n 2 l(r) is called a Radial Probability DISTRIBUTION. Thus the figure below and a similar one in your text are plots of Radial Probability Distributions.

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General result: Area under curve between r 1 and r 1 +dr = Probability of finding e - between r 1 and r 1 + dr. Important points to note about the (4 π )r 2 R 2 vs. r plots: i)
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