Download Chapter 11 Notes

Chapter 11 Notes
Modern Atomic Theory
Introduction
You may recall that one of the ideas of Dalton’s Atomic Theory was that all elements are
composed of indivisible particles called atoms. For about 50 years past the time of John
Dalton (1766-1844) this idea remained. However, around 1900 J. J. Thomson discovered
the presence of electrons - small, light quantities of negative charge. This chapter focuses
on the electron and the arrangement of electrons in atoms.
Models of the Atom
Our description of the atom has evolved over the years. Below is a brief description of
the four basic models that have existed through the years.
1) Thomson Model
This model is sometimes called the plum pudding model. The negative
electrons (the plums) are embedded a positive matrix (the pudding). This
early model does not acknowledge the existence of the nucleus.
2) The Rutherford Model
This model is a direct result of the discovery of the nucleus by Rutherford in 1911. In this model, stationary electrons surround a center of
positive charge.
3) The Bohr Model
In 1913 Niels Bohr proposed a model in which the electrons circled
the nucleus, like the planets orbit the sun. This model is sometimes
called the planetary model. This model also proposed a very insightful
idea: that the electrons could only occupy certain positions around
the nucleus, and the farther out electrons got, the greater the electron’s
energy. An electron could only move to a higher energy level if it
acquired a certain amount (a quantum) of energy.
4) The Quantum Mechanical Model
In 1926, Erwin Schrodinger wrote a mathematical equation to describe
the location and speed of an electron in an atom. This model is based
on probability. This model describes the location in terms of the region
in which one will find an electron 90% of the time.
The Wave-like Nature of the Electron
Every object has a wave-like nature to it. For most common objects, however, the
macroscopic quantities are enormous compared to the wave behavior; hence, we do not
normally associate wave characteristics with common objects. The electron, however, is
sufficiently small (it has very little mass) and so the wave characteristics are much more
pronounced. Here, we will examine the basics of waves.
Basics of Waves
The picture below shows a typical representation of a wave. The wavelength () is the
distance between adjacent points on a wave. It is usually measured in meters. The
frequency () of a wave is how many crests pasts by a certain point per second.
Frequency is usually measured in Hertz (Hz). One Hz is a wave per second, 1/sec, or
sec-1. There is an inverse relationship between frequency and wavelength - when one
goes up the other goes down, and vice versa.
Speed of a Wave
The speed of a wave is given by the product of the frequency and wavelength. If the
wave is an electromagnetic wave, such as light, then the speed of the wave through a
vacuum is a constant of 3.00 X 108 m/s.
c = 
EXAMPLE:
What is the frequency of light that has a wavelength of 580. nm?
(1 nm = 1 nanometer = 1 X 10-9 m)
EXAMPLE:
What is the wavelength of radiation that has a frequency of
6.00 X 1017 Hz?
Energy of a Photon
Einstein though of light as little packets of energy known as “photons”. The energy of a
photon is given by the product of Planck’s constant times the frequency.
E=h
where h = Planck’s constant = 6.63 X 10-34 Jsec
EXAMPLE:
How much energy is in a photon of frequency 6.00 X 1017 Hz?
EXAMPLE:
Consider an atom with the energy levels described in the picture
below. Suppose an electron falls from an excited state (fourth
energy level) back to the ground state (first energy level). What
will be the wavelength of light given off?
Arrangement of Electrons in Atoms
There are four levels of organization to describe the location of an electron in any
particular atom.
1) Principal Energy Level - Describes in very general terms how far away from the
nucleus an electron can be found. It is given the symbol n.
2) Sublevel - There are four different sublevels called s, p, d, and f. The first principal
energy level has only one sublevel, called the “1s”. The second principal
energy level has two sublevels: a “2s” and a “2p”. The third principal
energy level has three sublevels: a “3s”, a “3p” and a “3d”. The fourth
and all subsequent principal energy levels have four sublevels. For n = 4,
there is the 4s, 4p, 4d and 4f. Theoretically, there exists a “5g” in the fifth
principal energy level, but we run out of electrons before we begin filling
it.
3) Orbitals - The s sublevel contains only one orbital, which is spherically shaped. The
p sublevel contains three orbitals, which are shaped like dumbells and are
oriented mutually perpendicular to each other (like the x, y and z axes).
There are five d orbitals, and seven f orbitals. Pictures of some orbitals
can be found on pages 372-374 in the text.
4) Spin -
Each orbital can contain two electrons, one with spin up and the other with
spin down. Two electrons with the same spin will never occupy the same
orbital. (Furthermore, the first electron in an orbital is spin up, according
to the Law of Maximum Multiplicity.)
The table below summarizes our results so far:
Principal Energy
Level
Number of
Sublevels
Types of
Sublevels
Maximum number of
Electrons
n=1
1
1s
2
n=2
2
2s, 2p
8
n=3
3
3s, 3p, 3d
18
n=4
4
4s, 4p, 4d, 4f
32
Rules for Placing Electrons
1) Aufbau Principle - Electrons enter orbitals of lowest energy first.
2) Pauli Exclusion Principle - An orbital can only contain two electrons, and these
electrons must have opposite spin. (Another way of
stating this principle is to say that no two electrons in an
atom can have the same four quantum numbers.)
3) Hund’s Rule - Within a sublevel, electrons enter singly before pairing up.
We will use these rules to place electrons in atoms in some examples
that will follow.
Energy Level Diagram for Sublevels
Below is a diagram which arranges sublevels in order of increasing energy. Each box
represents an orbital. You don’t have to memorize this table. There is an easier way.
That way involves making diagram shown on the bottom right corner.
EXAMPLES: Fill in the orbital diagram, and give the electron configuration
of the following elements:
H
1s
He
1s
2s
Li
1s
2s
Be
1s
2s
B
1s
2s
C
2p
1s
2s
N
2p
1s
2p
2s
O
1s
2s
F
Ar
Ca
V
2p
1s
2s
Ne
2p
2p
1s
3s
3p
2s
2p
3d
1s
4s
4p
4d
3s
3p
3d
2s
2p
4f
1s
4s
4p
4d
3s
3p
3d
2s
2p
1s
4f
Finding the Last Electron in an Atom (The Easy Way)!
EXAMPLE: What is the last electron in the following elements:
(a) V
EXAMPLE:
(b) Ba
(c) Pb
Write the electron configuration (long-hand and shortcut) for the
following elements:
Nickel (Z = 28)
Bromine (Z = 35)
Lead (Z = 82)
Paramagnetism and Diamagnetism in Elements
If an element has unpaired electrons in its electron configuration, that element will be
paramagnetic and will be bent by a magnetic field. An element that has no unpaired
electrons is diamagnetic, and will not be bent in a magnetic field.
Example: Write the electron configuration, and determine if the following
elements are paramagnetic or diamagnetic.
Mg
S
Exceptional Electron Configurations
Some of the elements have electron configurations that deviate from the norm. The
driving force for this deviation is the extra stability offered by filled and half-filled
sublevels. The most well-known exceptions are chromium and copper. The 3d sublevel
steals an electron from the 4s for added stability. Draw the configurations for copper and
chromium below:
EXPECTED CONFIGURATIONS
Cr
Cu
ACTUAL CONFIGURATIONS
Cr
Cu
Configurations of Ions
Atoms gain or lose electrons to form ions. To write the configuration of an anion, just
add an appropriate number of electrons to the configuration. When forming a cation,
remove electrons in the configuration. For transition metals (the d-block), electrons will
be lost from the ns sublevel before losing electrons from the (n-1)d sublevel. The
following examples will demonstrate these procedures.
EXAMPLES: Write the electron configurations of the following ions:
O-2
Al+3
Co+3
Quantum Numbers
Each electron in every atom is assigned a set of four quantum numbers. According to the
Pauli exclusion principle, no two electrons can have the exact quantum numbers. The
rules are stated below.
1) Principal Quantum Number (n) - Just the value of the principal energy level.
2) Angular Momentum Quantum Number (l) - This number is determined from the
type of sublevel. The numbers are
0, 1, 2, and 3 for s, p, d, and f sublevels, respectively.
3) The Magnetic Quantum Number (ml) - This number runs from -l to +l and states
which orbital the electron is in.
4) The Spin Quantum Number (ms) - This is +1/2 for the first electron in an orbital, and
-1/2 for the second electron in an orbital.
EXAMPLES: Write the quantum numbers for each electron
1s1
4d6
1s2
2p1
4d3
2p4
EXAMPLES: Determine the electron for the following sets of quantum numbers.
3, 2, 0, -1/2
EXAMPLE:
2, 1, 1, +1/2
3, 3, 0, +1/2
If the first quantum number is a three, what are the limits on the
second and third quantum numbers?