Gen Chem_Ch 6_14th_Radial Distribution (2)

Overview

Dr. Reza Latifi explains how p-orbital nodes and radial distribution change with principal quantum number, using the 4p orbital to demonstrate node counting and radial probability peaks. He compares 2p, 3p, and 4p orbitals, showing that higher-n p orbitals have more radial nodes, extend farther from the nucleus, and have higher energy than lower-n p orbitals.

Key takeaways

Every p orbital has l = 1 and therefore one angular node, a plane that passes through the nucleus.
The radial-node formula is n - 1 - l, so 2p, 3p, and 4p have 0, 1, and 2 radial nodes, respectively.
A 4p orbital has 3 total nodes: 1 angular node and 2 radial nodes.
As n increases across the p orbitals discussed, the radial distribution extends farther from the nucleus and gains additional radial nodes.
Latifi compares 2p and 3p energies, concluding that 2p is lower in energy because it is associated with the lower principal quantum number.

Chapters

0:00 P-Orbital Angular Nodes and the Node-Counting Rule

Latifi reviews the trend that an orbital with a lower principal quantum number, such as 2s rather than 3s, is closer to the nucleus and lower in energy.
For p orbitals, the angular momentum quantum number is l = 1, so every p orbital has one angular node: a plane passing through the nucleus.
The total number of nodes is n - 1, and the radial-node count is n - 1 - l.

2:23 Counting and Sketching the 4p Orbital's Nodes

For 4p, n = 4 and l = 1, giving 3 total nodes: 1 angular node and 2 radial nodes.
Latifi sketches the p-orbital lobes and marks the angular nodal plane plus two radial nodal surfaces.
The sketch divides the orbital into successive regions with alternating signs, and the outermost region has the largest spatial extent.

4:57 Comparing 2p, 3p, and 4p Radial Distributions and Energies

The 2p orbital has no radial nodes, 3p has 1, and 4p has 2; all three retain one angular node.
In a radial probability-versus-distance graph, the 4p distribution has three radial regions, and its outer peak indicates the most probable radius.
Latifi places the characteristic 2p radius closer to the nucleus than the 3p radius and concludes that 2p has lower energy than 3p.
The lecture ends by noting that comparing d and p orbitals within the same period will be addressed in the next lecture.

Transcript excerpt

0:11 [music] >> Hello and welcome back and thank you very much for watching another lecture from general chemistry. Last lecture we went through radial distribution of graphs for 3s orbitals and we compared them with the 2s and we said that whenever we are dealing with orbitals that they are located at different ends, the one with a lower end is going to have a lower energy and it will be more stable. So if you have electrons, you should put it inside the for example the 2s orbital first and then 3s orbital. And so we said as we increase the n, we get more nodes and because of that the orbital will be less, you know, technically unstable because it has higher energy. And also keep this one in your mind that when you increase n, this distance from the nucleus is going to change, it's going to be a bigger number

0:59 and because it's a bigger number, so there will be less attraction force on that orbital and this is the reason, you know, like 2s orbitals will have electrons inside 2s orbital will have lower energy than the 3s orbital. Okay, now let's talk about the p orbitals. In p orbitals, we have l equal 1 and because of that we're going to have angular node because it's equal to l and l is equal to 1. An angular node we show it by a plane and our angular node for any p orbital it will pass the nucleus and this is going to be the angular node. So all p orbitals all or p orbitals regardless of the n that we are talking about it, they are going to have only one angular node and it's going to be here. It is going to be equal to l 1.

This is the start of the transcript. Save this video free for the whole transcript, searchable and time-coded.

Related notes

Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, Dr. Reza Latifi at Oklahoma State University, OSU.