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```Chapter 5
Electrons in Atoms
5.1 Models of the Atom
Development of Atomic Models


First "modern" model - John Dalton (1808) ·
J. J. Thomson (1897)
·
·

Ernest Rutherford (1911)
·

Niels Bohr (1913)
·
proposed how electrons were arranged
around the nucleus
proposed in order to explain how light
interacts with atoms
electrons are in fixed energy levels
quantum=
·
·
·
Bohr's Model of the Hydrogen Atom
Four Assumptions:
1. The electron moves around the nucleus in only certain allowed orbits
2. The energy of these quantized orbits is characterized by an integer, n
3. In order to change energies, an electron must move from one energy level
(orbit) to another.
4. Upon changing levels, an electron absorbs or emits energy equal to the
difference in energy
between the two levels.
Physical picture:
1
Quantum Mechanical Model
Determined the allowed energies an electron can have and how likely it is to
find an electron in various locations around the nucleus.
Atomic Orbitals
· a region of space where there is a high probability of finding an electron
For the quantum mechanical model:
Quantum Numbers
 The energy of the electron is expressed in terms of four variables called
quantum numbers.
 These variables can have only certain restricted values in order to solve
the wave equation.
The Four Quantum Numbers:
n
 the principle quantum number
 it describes the main energy level or shell
 it can any positive integer value
 these energy levels are also called "shells"
n=1
n=2
n=3
n=4
2
l
 the angular momentum quantum number
 it describes the sublevels or subshells (each energy sublevel
corresponds to an orbital of different shape depending on where the
electron is likely to be found)
 it can have any integer value from 0 to n-1
Ex. if n = 3, l can be:0,1,2
Other designations:
if l = 0
if l = 1
if l = 2
if l = 4
if l = 3
if n = 1
1sublevel
if n = 2
2 sublevels
if n = 3
3 sublevels
if n = 4
4 sublevels
m
 the magnetic quantum number
 it describes the orientations of the "orbitals"
 it can have any integer value from -l . . . +l
Ex. if l = 3, m =s
 the spin quantum number
 it describes the "spin" of the electron
 it can have only two possible values
The energy of the electron is described in terms of these four quantum
numbers.
3
Electron Arrangement in Atoms
Electron Configurations/Electron Diagrams
Atomic Orbitals
For the quantum mechanical model:
Energy Levels (shells)
Sublevels (subshells)
Orbitals
The Arrangement of Levels, Sublevels, and Orbitals
First Level
Second Level
Third Level
The Arrangement of Electrons
Electrons will be represented as arrows: if s=+½  if s=-½
4
The arrangement of electrons is show by Electron Diagrams
Three rules for placing electrons in an atom:
 Aufbau Principle:
An electron diagram for hydrogen (Z=1)
An electron diagram for helium (Z=2)
An electron diagram for lithium (Z=3)
 Pauli Exclusion Principle:
An electron diagram for nitrogen (Z=7)
 Hund’s Rule:
p. 133 fig. 5.7
A Table:
Energy Level
Number of
Sublevels
Number of
Orbitals
Number of
electrons
5
Shapes of Orbitals
The 1s
The 2s
The 2p’s
The Famous Diagonal Rule
Electron Configurations
 a shorthand method of drawing electron diagrams
6
 list the sublevels and show the number of electrons in each sublevel
Examples:
Element Electron Diagram
Electron Configuration
Must know:
 Diagonal Rule
 The maximum number of electrons in each sublevel
Some Exceptions to the Diagonal Rule
·
5.3 Physics and the Quantum Mechanical Model
Light
Visible light is one form of electromagnetic radiation
 other forms include: radio waves
microwaves
ultraviolet
X-rays
Properties of waves:
Amplitude 7
Wavelength  The symbol used for wavelength is the Greek letter: λ
 Wavelengths of visible light are usually expressed in nanometers (nm):
1m = 1 x 109 nm
 Different colors of visible light have different wavelengths:
ROYGBIV Red Orange Yellow Green
Blue
Indigo
Violet
low
energyhigh
energy
long
wavelengthsshort
wavelengths
low frequencyhigh
frequency
Another property of light is frequency
 defined as the number of wave cycles that pass a given point per unit of time
 represented by the Greek letter: v
Compare two waves:
P.139 fig.5.10
 Waves with shorter λ's have higher v's
 Frequency and wavelength are inversely related.
where c = the speed of the wave
vλ =
c
8
For light, c =
Example:
Calculate the frequency of light which has a wavelength of 588 nm.
Max Planck (1900)
 energy is not continuous, but exists in little units called quanta (singular:
quantum)
 the energy of a quantum of light (a photon) is directly proportional to its
frequency
Ev
E = hv
h is Planck's Constant = 6.6262  10-34 J·s
Example:
Calculate the energy of a single photon of light energy which has a λ = 450
nm.
For one mole of photons:
Atomic Spectra
The spectroscope p.141 fig. 5.12
9
Bohr
 If the electron can have only certain energies, it can have only certain
changes in energy
 Only certain energies (photons, wavelengths) will be emitted by an atom
 This will produce a line spectrum called atomic emission spectrum
In order to predict which lines would be formed, Bohr calculated the energies
of the electron
His simplified equation:
-1312 kJ
n2
If the energies of each level can be calculated, the differences in energies (ΔE)
can be calculated.
Using E = hv, the frequency and wavelength of the light emitted can be
calculated.
Example:
Calculate the λ of light emitted when an electron falls from level 5 to level
2.
10
Explanation of Atomic Spectra
Patterns of Spectral Lines:
Energy Levels to Scale:
E1
E2
E3
E4
E5
E6
=
=
=
=
=
=
-1312 kJ
-328 kJ
-146 kJ
-82 kJ
-52 kJ
-36 kJ
Lyman seriesBalmer seriesPaschen series-
Quantum Mechanics
Historical Development
1900 - Max Planck
 radiant energy (light) has a duel character
 light has both wave and particle properties
1924 - Louis deBroglie
 matter also has both wave and particle properties
 the wave character of matter is important for very small particles
(electrons)
1927 - Werner Heisenberg
 developed a mathematical principle which deals with very small
particles
The Heisenberg Uncertainty Principle
11
"It is impossible to know exactly both the velocity (energy) and the position
of a small particle at the
same time."
Again, this principle is important only for very small particles like the
electron
1926 - Erwin Schrodinger
 used quantum mechanics to develop a model of the hydrogen atom
 developed an equation (the wave equation) which treated the electron as
a wave
The Model:
 also has quantized energy levels
 could solve for the energy exactly, but only approximates the position of
the electron
 the position of the electron is expressed interms of probability diagrams.
Example: the ground state of hydrogen
Homework:
1,2,4,5,7,8,9,10,11,12,14,15,16,17,20,21,29,30,32,33,3
4,35,36,38,39,40,44,45,49,50,51,52,53,54,55,56,57,58,60,61,
62,63,64,68,69,70,71
12
13
14
15
```
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