Atomic Structure and Periodicity

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= mathematical operator

E = total energy of the atom

A specific wave function is often called an orbital.

This equation is based on operators – not simple algebra. This is a mathematical concept you will not have dealt with yet.

Slide 24

Heisenberg Uncertainty Principle

x = position

mv = momentum

h = Planck’s constant

The more accurately we know a particle’s position, the less accurately we can know its momentum. Both the position and momentum of a particle can not be determined precisely at a given time. The uncertainty principle implies that we cannot know the exact motion of the electron as it moves around the nucleus.

Slide 25

Radial Probability Distribution

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Quantum Numbers (QN)

When we solve the Schrodinger equation, we find many wave functions (orbitals) that satisfy it. Each of these orbitals is characterized by a series of numbers called quantum numbers, which describe various properties of the orbital.

1. Principal QN (n = 1, 2, 3, . . .) - related to size and energy of the orbital.

2. Angular Momentum QN (l = 0 to n  1) - relates to shape of the orbital. l = 0 is called s; l = 1 is called p; l = 2 is called d; l = 3 is called f.

3. Magnetic QN (ml = l to l including 0) - relates to orientation of the orbital in space relative to other orbitals.

4. Electron Spin QN (ms = +1/2, 1/2) - relates to the spin states of the electrons.

Slide 27

Example: For principal quantum level n = 5, determine the number of allowed subshells (different values of l), and give the designation of each.

For n = 5, the allowed values of l run from 0 to 4 (n – 1 = 5 – 1). Thus the subshells and their designations are

l = 0 l = 1 l = 2 l = 3 l = 4

5s 5p 5d 5f 5g

Slide 28

Orbital Shapes and Energies

Two types of representations for the hydrogen 1s, 2s and 3s orbitals are shown below. The s orbitals are spherical shape.

Two Representations of the Hydrogen 1s, 2s, and 3s Orbitals

Slide 29

Representation of p orbitals

The p orbitals are not spherical like s orbital but have two loves separated by a node at the nucleus. The p orbitals are labeled according the axis of the xyz coordinate system.

The Boundary Surface Representations of All Three 2p Orbitals

Slide 30

Representation d orbitals