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Chemistry Chapter 4
Arrangement of Electrons in Atoms
The 1998 Nobel Prize in
Physics was awarded "for
the discovery of a new
form of quantum fluid with
fractionally charged
excitations." At the left
is a computer graphic of
this kind of state.
The Puzzle of the Atom
Protons and electrons are attracted to each
other because of opposite charges
Electrically charged particles moving in a
curved path give off energy
Despite these facts, atoms don’t collapse into
the nucleus of the atom but instead
“magically” fill up an e- cloud.
Wave-Particle Duality
JJ Thomson won the Nobel prize for describing the
electron as a particle.
His son, George Thomson won the Nobel prize for
describing the wave-like nature of the electron.
electron is
a particle!
electron is
an energy
Confused??? You’ve Got Company!
“No familiar conceptions can be
woven around the electron;
something unknown is doing we
don’t know what.”
Physicist Sir Arthur Eddington
The Nature of the Physical World
The Wave-like Electron
The electron propagates
through space as an energy
wave. To understand the
atom, one must understand
the behavior of
electromagnetic waves.
Louis deBroglie
Electromagnetic radiation propagates
through space as a wave moving at the
speed of light.
C = speed of light, a constant (3.00 x 108 m/s)
ƒ = frequency, in units of hertz (hz, sec-1)
 = wavelength, in meters
Types of electromagnetic radiation:
Maxwell Planck
The energy (E ) of
electromagnetic radiation
is directly proportional to
the frequency (ƒ) of the
E = h ƒ
E = Energy, in units of Joules (kg·m2/s2)
h = Planck’s constant (6.626 x 10-34 J·s)
ƒ = frequency, in units of hertz (hz, sec-1)
Low Frequency
High Frequency
Wavelength Table
Spectroscopic analysis of the visible spectrum…
…produces all of the colors in a continuous spectrum
Spectroscopic analysis of the hydrogen
…produces a “bright line” spectrum
Electron transitions
involve jumps of
definite amounts of
This produces bands
of light with definite
The Bohr Model of the Atom
I pictured
electrons orbiting
the nucleus much
like planets
orbiting the sun.
Neils Bohr
But I was
wrong! They’re
more like bees
around a hive.
An orbital is a region within an atom where there
is a probability of finding an electron. This is a
probability diagram for the s orbital in the first
energy level…
Orbital shapes are defined as the surface that
contains 90% of the total electron probability.
Schrodinger Wave Equation
V 
8  m dx
 E
Equation for probability of a
single electron being found
along a single axis (x-axis)
Erwin Schrodinger
Heisenberg Uncertainty Principle
“One cannot simultaneously
determine both the position
and momentum of an electron.”
You can find out where the
electron is, but not where it
is going.
You can find out where the
electron is going, but not
where it is!
The address of the e- determined.
The Address of the e- comes from the probability of
its location in an orbital. Through energy
calculations and wave equations the address can
be simplified via the following:
1) Bohr diagrams (e- dot diagrams)
2) e- configuration notation
3) e- orbital notation
4) Quantum numbers
The s orbital has a spherical shape centered around
the origin of the three axes in space.
s orbital shape
Sizes of s orbitals
Orbitals of the same shape (s, for instance) grow
larger as n increases…
Nodes are regions of low probability within an
P orbital shape
There are three dumbbell-shaped p orbitals in
each energy level above n = 1, each assigned to
its own axis (x, y and z) in space.
Things get a bit more
complicated with the five d
d orbital shapes
orbitals that are found in
the d sublevels beginning
with n = 3. To remember
the shapes, think of “double
…and a “dumbell
with a donut”!
Shape of f orbitals
Quantum Numbers
To determine the location of an electron
scientists have invented a system to organize
each electron found in an atom. The system is
based upon the unique energy of each of the
atom’s electrons.
Each electron in an atom has a unique set of 4
quantum numbers which describe it.
 Principal quantum number
 Angular momentum quantum number
 Magnetic quantum number
 Spin quantum number
Pauli Exclusion Principle
No two electrons in an atom
can have the same four
quantum numbers.
e two electrons or objects
can exist in the same
place at the same time.
Principal Quantum Number
Generally symbolized by n, it denotes the shell
(energy level) in which the electron is located.
Number of electrons
that can fit in a shell:
Angular Momentum Quantum
The angular momentum quantum number, generally
symbolized by l, denotes the orbital (subshell) in
which the electron is located.
Magnetic Quantum Number
The magnetic quantum number, generally
symbolized by m, denotes the orientation of the
electron’s orbital with respect to the three axes in
Spin Quantum Number (s)
Spin quantum number denotes the behavior
(direction of spin) of an electron within a magnetic
Possibilities for electron spin:
1st e- 
2nd e-, 
Assigning the Numbers
 The three quantum numbers (n, l, and m) are integers.
 The principal quantum number (n) cannot be zero.
n must be 1, 2, 3, etc.
 The angular momentum quantum number (l) can be any
integer between 0 and n - 1.
Ex. For n = 3, l can be either 0, 1, or 2.
 The magnetic quantum number (m) can be any integer
between -l and +l.
Ex. For l = 2, m can be either -2, -1, 0, +1, or +2.