In my notes for a module on atomic and molecular physics it has this statement:(adsbygoogle = window.adsbygoogle || []).push({});

"For a given n the probability density of finding e- near the nucleus decreases as l increases, because the centrifugal barrier pushes the e- out. So the low-l orbitals are called penetrating."

I just want to clear a few things up to make sure I understand this correctly.

In a text book I found a good set of graphs comparing different combinations of n and l:

http://img.photobucket.com/albums/v319/Adwodon/IMG.jpg

Taking the n=3 set as the example, it appears to me that for l=0 the average distance is actually further from the nucleus than l=1,2.

However there are 2 other peaks which seem to be roughly the same distance as the most probable distance for n=1,2 (I don't know if this is just coincidental?)

So would I be totally wrong if I thought of these as sets of orbits (ie n=3 l=0 has 3 sets) and that low-l orbitals can 'penetrate' into sets of orbits which are closer to the nucleus (which are of a similar orbits to lower energy orbitals). As l increases the electron can no longer "penetrate" into lower sets due to increased angular momentum / centrifugal barrier(?), and the most probable position of the individual sets moves closer to the nucleus.

For example (distances are made up and represent the location of the peaks):

n=3 l=0 has

Set 1 @ r=1 , Set 2 @ r=5, Set 3 @ r= 15

at n=3 l=1, set one is now inaccessible and set 2 /3 have moved closer:

Set 2 @ r=4.5, Set 3 @ r= 14

and for n=3 l=2 both set 1/2 are inaccessible

Set 3 @ r=12

Although I cant say I really know why the average position would move closer to the nucleus as the angular momentum is increased?

Ultimately im just trying to put it into a form I can understand rather than have to learn by rote so unless my thinking is completely self defeating I don't mind if it doesn't give a totally accurate picture.

Also please correct me if i'm using incorrect terminology, this is all fairly new to me and ive always been slow when it comes to buzzwords.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Radial probability density / quantum numbers.

**Physics Forums | Science Articles, Homework Help, Discussion**