Why do the number of peaks on a radial dependence probability distribution differ between 3s, 3p and 3d?
The radial dependence probability distribution of the 3s orbital has three peaks, the 3p has twp peaks and the 3d orbital only one peak. Referring to the 2s and the 2p orbital here, and their radial dependence probability distributions, why does the 2s have two peaks, and the 2p distribution only have one bell-shaped peak?
Also with the radial dependence plots, some (like the 2s and 3s) dip and then tend to a limiting value whereas others such as the 2p and 3p have a peak. How can these be predicted?
Number of nodes in the radial distribution function for a hydrogen-like orbital = principal quantum number (n) – angular momentum quantum number (l) -1. Number of radial maxima, or peaks, = number of radial nodes + 1. So number of radial peaks = n-l
Angular quantum numbers are:
s: l=0
p: l=1
d: l=2
f: l=3.
So number of radial peaks are:
3s: 3-0 = 3
3p: 3-1 = 2
3d: 3-2 = 1
2s: 2-0 = 2
2p: 2-1 = 1
See the source website, but note that there is a typo. The site says number of radial maxima = n-1, but it should be n-l.
I’m not sure what you mean by the dips vs. peaks. Radial distribution functions with the same number of peaks look more or less the same, e.g. 2s and 3p have similar radial distribution functions. The functions are shown in the reference.
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