Gen Chem_Ch 6_13th_Radial Distribution Graph

Overview

Dr. Reza Latifi explains how principal quantum number n affects orbital size, node count, and energy, then applies the rules to a 3s orbital. He calculates its two radial nodes, sketches its spherical regions and radial distribution graph, and compares 1s, 2s, and 3s orbitals, including penetration and bonding implications.

Key takeaways

For an orbital with quantum numbers n and l, total nodes are n - 1, angular nodes are l, and radial nodes are n - l - 1.
A 3s orbital has n = 3 and l = 0, so it has two radial nodes and no angular nodes.
The two 3s radial nodes divide the radial distribution into three probability regions; the graph's origin and endpoint are not nodes.
Within the s-orbital sequence discussed, orbital size and energy increase from 1s to 2s to 3s.
Penetration describes electron probability close to the nucleus and can affect orbital stability and energy.

Chapters

0:00 How n and l Determine Orbital Size and Nodes

For s orbitals, l = 0, so the orbital is spherical and has no angular nodes.
Total nodes equal n - 1; increasing n for s orbitals increases radial nodes and orbital size.
The 1s orbital is smaller than 2s and 3s because its principal quantum number is lower.

2:05 Calculating and Graphing the 3s Orbital's Two Radial Nodes

For 3s, n = 3 and l = 0, giving 3 - 1 = 2 total nodes, both radial.
The radial-node formula n - l - 1 also gives 3 - 0 - 1 = 2.
Latifi sketches the s orbital as concentric spherical regions around the nucleus, with alternating signs across the two radial nodes.
The radial distribution graph has three probability regions separated by two zero crossings; its start and end are not radial nodes.

5:37 Comparing 1s, 2s, and 3s Energy, Penetration, and Bonding

Latifi orders the s orbitals by increasing n and energy: 1s, then 2s, then 3s.
Higher-n s orbitals extend farther from the nucleus; the lecture describes bonds formed with 3s orbitals as weaker than comparable 2s bonds.
Penetration refers to probability at distances closer to the nucleus than the main radial-distribution peak, which can increase stability.
The radial-distribution peak indicates the distance at which finding the electron is most probable.

Transcript excerpt

0:11 [music] >> Hello and welcome back and thank you very much for watching another lecture from general chemistry. In this lecture we want to answer this question that's what will happen to the orbital when we increase n. Okay, while n goes up and should we expect any change with shape of the orbital or maybe there are some stuff happening inside the orbital. And overall the shape is not going to change except the size of the orbital it will go up. Okay, as we decrease the n and as we decrease n this center from nucleus gets bigger and bigger and because the distance gets bigger so the shape size of orbital will get bigger. Okay, and that and that's the reason 1s orbital here is the smallest one and the 3s orbital is going to be the biggest one. And we are talking about s orbital here and s orbital it has l equal to zero and

0:59 because l is equal to zero so it's not going to have angular node. Angular node is equal to l and l equal to zero. Remember angular node we show them by plane. So if there is a node then node is going to be radial node and s orbitals yes can have node providing is providing n is bigger than one. If n is bigger than one because we say the total nodes total nodes equal to n minus one so then we say two for example minus one we get one or three minus one we get two nodes. And I want to go through how to you know like study these orbitals and also connect the technically the shapes that you see with probability of finding electron while moving atom to nucleus. And let's practice how to how to get any

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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.