Electron Clouds and Probability
Goal: To use the study of light to
predict the probable locations of
electrons in atoms
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.
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.
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.
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. 4.14 page 95 ( Text)
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.
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.
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)
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.
Spectroscopy can be used as a
means of identifying elements.
Absorption and emission spectra
are the fingerprints of the
elements.
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.
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
6.626 075 5 x 10-34 joules per
hertz.
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.
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.
The smallest orbit an electron can
occupy is called the ground state
of the electron.
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.
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.
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.
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.
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.
Quantum Theory
Quantum Numbers
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.
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.
The n quantum number can have
values of 1,2,3,…n. Each energy
level, or quantum number, has n
different sublevels.
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.
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.
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. 5.10
p. 121 (text)
When an electron moves, it
generates a magnetic field. The
fourth quantum number, s,
describes the direction of electron
spin around its axis.
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.
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.
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
2
possible in any one level is 2n
where n is the number of the
energy level ( principal quantum
number).
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)
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.
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.
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).
Orbital Filling Diagrams
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?
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.
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.
Electron Dot Diagrams
• Are useful when showing how atoms bond
together.
• Involve the electrons in the outer energy
level.
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.
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.
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.
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.
The Chemistry Department wish
you success in your studies!