Conversations with Henry: More Nodes for Nerds

[This post is a continuation-in-part of this one: link]


Henry: So after helium comes lithium with three electrons. That third electron must go into a new and different orbital called the 2s orbital.

Me:  The 2s orbital is like the 1s orbital except it's bigger, right?

Henry:  Not exactly. It's not like those Russian matrushka dolls where the next bigger shell simply encompasses the previous one. The 2s orbital interleaves the 1s orbital so that its electrons can stay closer to the core without getting in the way of the others. Likewise the 3s orbital interleaves the 2s and the 1s. Look at these cross-sections:

original

Me:  Why are you even showing me this stuff?  Trooper York says he hates chemistry.

Henry:  I'm just trying to explain why the toy metals like lithium, sodium, and potassium are so boring -- not the whole of chemistry.

Conversations with Henry: Nodal Theory

Henry: The electrons in hydrogen and helium are easiest to depict -- they stay in simple spherical orbitals surrounding the kernel. There are no nodes.

Me: What are nodes?

Henry: In physics, a node is a point of minimum displacement in a periodic system, for example in a vibrating string:

The first harmonic (fundamental) has no nodes, except for the stationary ends. The second harmonic has one additional node in the middle. Nodes correlate with higher energy-- the more nodes, the higher the energy.

Me: How does this relate to electrons?

Henry: Well look at these pictures of how electrons surround a nucleus: Which shape has more nodes?

Me: An s-orbital has no node, a p-orbital has one node, a d-orbital has two nodes, and an f has three?

Henry: Exactly! And that's how electrons order themselves in atoms. It's almost self-assembly. If there's one thing we've learned about electrons it's that they don't flow uphill.

Me: There's got to be exceptions for every rule.