Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 109 - General Chemistry - Spring 2015

Lecture Notes 23: 25 March

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A Quantum Picture of the Atom, cont.

Electronic Energy Levels:

We've taken a brief look at the physics underlying atomic structure, focusing on Schrödinger's Equation and the wave picture of electron distribution in atoms.

What we need to explain is the energy distribution of electrons in atoms and how this correlates with atomic properties. First recall the line spectrum of hydrogen and the Bohr model. We are going to keep the concepts of ground state and quantized energy levels from Bohr, after all they worked very well for Hydrogen. But we will need to build a new structure which will give these same predictions but with other factors which explain the details of hydrogen's spectra as well as other atoms. We'll again start by modelling hydrogen.

Quantum Numbers

This is an alternate way of designating the electrons in an atom. Each electron will have a unique set of quantum numbers.

 Quantum Number Symbol Characteristic specified Information provided  Possible values
Principle quantum number n Shell Average distance from nucleus (r) 1, 2, 3, 4, ...
 Angular momentum (Azimuthal) quantum number Subshell Shape of orbital 0 (s), 1 (p), 2 (d), 3 (f), ...n - 1
 Magnetic quantum number  ml Orbital Orientation of orbital - l ... 0 ... +l
Spin quantum number  ms Electron spin  Spin direction ± 1/2

Let's go back and look at the shapes of some orbitals:

1s orbital icon 1s orbital icon
2s orbital icon
3s orbital icon
1s psi squared plot
2s  psi squared plot
3s  psi squared plot
1s nodes orbital icon
2s nodes orbital icon
3s nodes orbital icon

For each shell with n = 2 or greater there is one s orbital and three p orbitals: px, py, and pz:

2p orbital icon
3p orbital icon
2p  nodes orbital icon
3p  nodes orbital icon
2p psi squared plot
3p  psi squared plot
2p orbital set icon
3p orbital set icon

For each shell with n = 3 or greater there is one s orbital, three p orbitals and five d orbitals: dxz, dyz, dxy, dx2- y2, and dz2

3dxy orbital icon
3dxz orbital icon
3dx2-y2 orbital icon
3dz2 orbital icon
3dxy nodes orbital icon
3dxz nodes orbital icon
3dx2-y2 nodes orbital icon
3dz2 nodes orbital icon

Atomic Orbitals Supplement More orbitals and some additional explanations.

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© R A Paselk

Last modified 25 March 2015