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**Electron Clouds and Probability**

Goal: To use the study of light to predict the probable locations of electrons in atoms

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Objectives Explain how the bright-line spectrum of hydrogen demonstrates the quantized nature of energy through an understanding of electromagnetic radiation. Predict the positions of electrons in an atom, using the concepts of quantum numbers and orbitals. Draw and write electron configurations of atoms.

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According to the planetary model of the atom, formulated by Rutherford and Bohr, the hydrogen atom should be similar to a solar system consisting of a sun and one planet.

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Atoms have a tendency to absorb some of the energy that results from exposure to light or some other energy source. Such atoms are said to be excited.

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Spectroscopy is the study of substances that are exposed to some sort of exciting energy. A spectrum is a pattern of radiant energy studied in spectroscopy. See Fig page 95 ( Text)

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Electromagnetic energy is energy that consists of variation in electric and magnetic fields taking place in a regular, repeating fashion. Its forms are: visible light, radio, infra red (IR), ultra violet (UV), and x-ray.

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The number of wave peaks that occur in a unit of time is called the frequency of the wave. Frequency is represented by the Greek letter nu (v) and is measured in units of Hertz (Hz). A hertz is one peak, or cycle, per second.

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Another important characteristic of waves is the distance between peaks known as the wavelength and is represented by the Greek letter lambda. It is usually measured in meters, cm, or nm. ( - Greek lambda)

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These characteristics of waves are related by the statement c = ν Where c is the speed of light and is given by 3.00 x 108 m/s.

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**Spectroscopy can be used as a means of identifying elements**

Spectroscopy can be used as a means of identifying elements. Absorption and emission spectra are the fingerprints of the elements.

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**Niels Bohr used the quantum theory to explain the hydrogen spectrum**

Niels Bohr used the quantum theory to explain the hydrogen spectrum. The quantum theory is a theory of energy emission that was stated by Max Planck, a German physicist.

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Planck’s idea was that one quantum of energy (light) was related to the frequency by the equation E=hv, where h is a constant. The constant is known as Planck’s constant. Its value is x joules per hertz.

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**Bohr’s idea was that---**

Orbits of the electron surrounding the nucleus must have a definite diameter. Electrons could only occupy certain orbits. The hydrogen atom was an electron circling a nucleus.

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Very Important!!!!! For our purposes for the rest of this course, we will visualize electrons as clouds and their positions as probable positions. We will avoid the illustration of atoms using Bohr models.

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**The smallest orbit an electron can occupy is called the ground state of the electron.**

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**In summary, the relationship between electromagnetic energy and an electron are as follows:**

An electromagnetic wave of a certain frequency has only one possible wavelength, given by lambda=c/v. It has only one possible amount of energy, given by e=hv. Since both c and h are constants, if frequency, wavelength, or energy is known we can calculate the other two.

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Recall from chapter 4 that the atom has a small, dense, positively –charged nucleus surrounded by an electron cloud. Chemists and physicists usually have to deal with the location of electrons in terms of the chances, or probability, of finding the electron at a particular location.

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**Let’s begin chapter 5 by discarding two misconceptions that many students have--**

Energy levels are like planetary orbits around the sun. Energy levels are equally spaced.

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**Waves can act as particles, and particles can act as waves**

Waves can act as particles, and particles can act as waves. Like light, electrons also have properties of both waves and particles. The whole idea of the two-sided nature of waves and particles is referred to as the wave-particle duality of nature.

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Werner Heisenberg, a German scientist, pointed out that it is impossible to know both the exact position and the exact momentum of an object at the same time. This statement is known as the Heisenberg uncertainty principle.

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Quantum Theory Quantum Numbers

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To completely describe an electron in an atom, four quantum numbers are needed and are identified by the letters n, l, m, and s. Let’s begin with a discussion of the principal quantum number, n.

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The principal quantum number, n, is used to describe the energy of the electron. The energy of an electron is determined by its average distance from the nucleus.

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**The n quantum number can have values of 1,2,3,…n**

The n quantum number can have values of 1,2,3,…n. Each energy level, or quantum number, has n different sublevels.

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**Each sublevel is described by the second quantum number l**

Each sublevel is described by the second quantum number l. The numerical values for l are the integers from 0 to (n-1). The values for l are usually designated by letters, s for l=0, p for l=1, d for l=2, and f for l=3.

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The third quantum number, m (magnetic quantum number), is used to describe each orbital within a sublevel. The values for m are integers from –l to +l.

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**Since m can have any value from +l to –l, its values are –1, 0, an +1**

Since m can have any value from +l to –l, its values are –1, 0, an +1. Thus there are three orbitals in the p sublevel, one located along each of the three perpendicular axes. See fig p. 121 (text)

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**When an electron moves, it generates a magnetic field**

When an electron moves, it generates a magnetic field. The fourth quantum number, s, describes the direction of electron spin around its axis.

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**There are two values for s, that is, +1/2 and –1/2**

There are two values for s, that is, +1/2 and –1/2. These values can be thought of as describing clockwise and counterclockwise rotation around its axis.

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According to the Pauli Exclusion Principle no two electrons can have the same set of quantum numbers. Thus, only two electrons, having opposite spins can occupy an orbital.

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As a result, each sublevel can hold a maximum of twice as many electrons as the number of orbitals in the sublevel. The greatest number of electrons possible in any one level is 2n2 where n is the number of the energy level ( principal quantum number).

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**Students need to study and understand the following illustrations:**

Figure 5.7 page 119 ( text) Figure 5.8 page 119 ( text) Figure 5.9 page 120 ( text)

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The electron configuration of an atom is used to describe the electron distribution in the sublevels. Each sublevel symbol is written following a coefficient that represents the energy level containing the sublevel.

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Each sublevel symbol has a superscript on the right giving the number of electrons in the sublevel. For example, the electron configuration of the boron atom ( atomic number 5) is written 1s2 2s2 2p1.

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There is a rule of thumb that will give a correct configuration for most atoms in the ground state. This rule of thumb is the arrow diagram and is shown in Fig 5.13 (text).

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**Orbital Filling Diagrams**

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The electron configuration gives the number of electrons in each sublevel but does not show how the orbitals of a sublevel are occupied by the electrons. How do we figure this out?

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Hund’s Rule predicts that one electron enters each orbital of a sublevel before any orbital is doubly occupied. Let’s look at the element nitrogen.

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**The electron configuration for nitrogen is 1s2 2s2 2p3**

The electron configuration for nitrogen is 1s2 2s2 2p3. Nitrogen has three electrons in the 2p sublevel, and each of these electrons occupies a separate orbital. In the orbital filling diagram each box (or circle) stands for an orbital. Arrows are used to indicate the direction of electron spin.

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**Electron Dot Diagrams Are useful when showing how atoms bond together.**

Involve the electrons in the outer energy level.

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In electron dot diagrams, the outer energy level electrons, those with the largest value of n, are represented by dots placed around the letter symbol of the element.

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**When writing electron dot diagrams for an element use the following rules:**

Write the orbital filling diagram for the outer energy level of the element using the arrow diagram. Draw dots on the sides of the element’s symbol to represent only the outer electrons. Show them as paired or unpaired based on the orbital diagram.

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You are now able to describe the electron configurations of the atoms of the elements. Your next study will be of a system of arranging elements based on their electronic structure– the periodic table.

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For the test covering the previous material on Electron Clouds and Probability you will need to read the pages designated in chapter 4 of your topic outline as well as chapter 5.It is strongly advised that you read all of chapter 5 so that this presentation will be most meaningful.

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**The Chemistry Department wish you success in your studies!**

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Quantum Theory and the Electronic Structure of Atoms Chapter 7 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Quantum Theory and the Electronic Structure of Atoms Chapter 7 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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