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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View Full DocumentGeneral 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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 Spring '09
 Electron, Nucleus, radial probability, radial wavefunction

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