Atomic Structure and the
Periodic Table
The electronic structure of an atom
determines its characteristics
Studying atoms by analyzing light
emissions/
absorbtions
Spectroscopy: analysis of light
emitted or absorbed from a
sample
Instrument used =
spectrometer
Light passes through a slit to
become a narrow beam
Beam is separated into
different colors using a prism
(or other device)
Individual colors are recorded
as spectral lines
Electromagnetic radiation
Light energy
A wave of
electric
and
magnetic
fields
Speed = 3.0 x 10
8
m/s
Wavelength (
)
=
distance
between adjacent peaks
Unit =
any length unit
Frequency (
)
=
number of
cycles per second
Unit =
hertz (Hz)
Relationship between properties of
EM waves
Wavelength x frequency = speed of light
∙
v
= c
Calculate the frequency of light that has a wavelength of 6.0 x 10
7
m.
Calculate the wavelength of light that has a frequency of 3.7 x 10
14
s

1
Visible Light
Wavelengths from 700
nm (
red
) to 400 nm
(
violet
)
No other wavelengths are
visible to humans
Quanta and Photons
Quanta: discrete
amounts
Energy is quantized
–
restricted to discrete
values
Only quantum mechanics
can explain electron
behavior
Analogy: Water flow
Another analogy for quanta
A person walking
up steps
–
his
potential energy
increases in a
quantized
manner
Photons
Packets of
electromagnetic energy
Travel in
waves
Brighter light = more
photons
passing a point
per second
Higher
energy
photons
have a higher frequency
of radiation
Planck
constant
h
= 6.63 x 10

34
J
s
E =
h
v
The energy of a photon is directly
p
roportional to its frequency
In a laboratory, the energy of a photon of blue
light with a frequency of 6.4 x 10
14
Hz was
measured to have an energy of 4.2 x 10
19
J.
Use Planck’s constant to show this:
E = (6.63 x 10

34
J∙s) x (
6.4 x
10
14
1/s) =
4.2 x 10
19
J
Deriving Planck’s constant
Evidence for photons
Photoelectric effect
–
the
ejection of
electrons
from
a
metal
when exposed to
EM radiation
Each substance has its
own “threshold”
frequency
of light needed
to eject electrons
Determining the energy of a photon
Use Planck’s constant!
What is the energy of a
photon of radiation with
a frequency of 5.2 x 10
14
waves per second?
E =
h
v
Another problem involving photon
energy
What is the energy of a
photon of radiation
with a wavelength of
486 nm?
Louis de Broglie
–
proposed that matter and
radiation have properties of both waves and
particles (Nobel Prize 1929)
Calculate the wavelength
of a hydrogen atom
moving at 7.00 x 10
2
cm/sec
=
h
m
m
= mass
= velocity
h
=
Planck’s constant
Hydrogen spectral lines
Balmer
series:
n
1
= 2 and
n
2
= 3,
4
, …
Lyman series (UV lines):
n
1
=
1
and
n
2
= 2, 3, …
Atomic Spectra and Energy Levels
Observe the hydrogen
gas tube, use the prism to
see the frequencies of EM
radiation emitted
Johann
Balmer
–
noticed
that the lines in the visible
region of hydrogen’s
spectrum fit this
expression:
v
= (3.29 x 10
15
Hz) x
1

1
4
n
2
n
= 3, 4, …
Rydberg equation: works for all lines
in hydrogen’s spectrum
v
= R
H
x
1

1
n
1
2
n
2
2
R
H
= 3.29 x 10
15
s

1
Rydberg Constant
Energy associated with electrons in
each principal energy level
Energy of an
electron in a
hydrogen atom

2.178 x 10

18
joule
n
2
E =
n
= principal quantum number
Differences in Energy Levels of the
hydrogen atom
Use the Rydberg Equation
OR
Use the expression for each
energy level’s energy in the following equation:
E =
E
final
–
E
initial
Assumed e

move in circular orbits
about the nucleus
Only certain orbits of definite
energies are permitted
An electron in a specific orbit has a
specific energy that keeps it from
spiraling into the nucleus
Energy is emitted or absorbed ONLY
as the electron changes from one
energy level to another
–
this energy
is emitted or absorbed as a photon
Niels
Bohr’s contribution
When an e

makes a transition from one energy level
to another, the difference in energy is carried away by
a
photon
Different excited hydrogen atoms undergo different
energy transitions and contribute to different spectral
lines
Summary of spectral lines
The Uncertainty Principle
–
Werner
Heisenberg
The dual nature of matter
limits how precisely we
can simultaneously
measure location and
momentum of small
particles
It is IMPOSSIBLE to know
both the location and
momentum at the same
time
Atomic Orbitals
–
more than just
principal energy levels
Erwin Schrodinger
(Austrian)
Calculated the shape of
the wave associated with
any particle
Schrodinger equation
–
found mathematical
expressions for the shapes
of the waves, called
wavefunctions
(psi)
Born’s
contribution
Max Born (German)
The probability of
finding the electron
in space is
proportional to
2
Called the “probability
density” or “electron density”
Atomic Orbital
–
the
wavefunction
for an electron in an atom
s
–
high probability of e

being near or at nucleus
ELECTRON IS NEVER AT
THE NUCLEUS IN THE
FOLLOWING ORBITALS:
p
–
2 lobes separated by a
nodal plane
d
–
clover
shaped
f
–
flower
shaped
More about orbitals
Each orbital can
hold
2
electrons
Orbitals in the
same subshell
have equal
energies
Quantum numbers
–
like an
“address” for an electron
n = principal quantum
number
As n increases
*
orbitals become
larger
e
lectron is
farther from
nucleus
more often
h
igher in
energy
l
ess tightly bound to nucleus
l
= angular momentum quantum
number
Values:
0 to
n
–
1
Defines the shape of the orbital
Quantum numbers
Value of
l
0
1
2
3
Letter
used
s
p
d
f
m
l
=
the magnetic quantum number
Orientation of orbital in space
(i.e.
p
x
p
y
or
p
z
)
Values: between
–
l
and
l
, including 0
Quantum numbers
Example: for
d
orbitals, m can be

2,

1, 0, 1, or 2
For p orbitals, m can be

1, 0, or 1
m
s
= the spin number
When looking at line spectra, scientists
noticed that each line was really a
closely

spaced pair of lines!
Why? Each electron has a SPIN
–
it
behaves as if it were a tiny sphere
spinning upon its own axis
Spin
c
an be + ½ or

1/2
Each represents the direction of the
magnetic field the electron creates
Quantum numbers
n = 4, l = 1, m
l
=

1,
m
s
= +1/2
Describe the electron that has the
following quantum numbers:
Principal level 4
4p orbital
p
x
orbital
s
pin up
Are these sets of quantum numbers
valid?
3, 2, 0,

1/2
2, 2, 0, 1/2
YES!
Level 3
3d orbital
3d
xz
Spin down
NO!
Level 2
2
d orbital
–
does
n
ot exist!
Electron configuration: rules
1.
Aufbau
principle
–
electrons fill
lowest
energy
levels first
2.
Pauli exclusion principle
–
only 2 electrons may
occupy each
orbital, must
have opposite spins
3.
Hund’s
rule
–
the lowest
energy is attained when
the number of electrons
with the same spin is
maximized
(because electrons
repel
each other)
Energy level specifics
s and d orbitals are close
in energy
Example
4s
electrons have slightly
lower energy than
3d
electrons
The
s
electrons can
penetrate to get closer to
the nucleus, giving them
slightly lower energy
4s
3d
Noble Gas Configuration
A shorter electron
configuration
Write the symbol for the
noble gas BEFORE the
element in brackets
Write the remainder of
the configuration
Examples:
Cl
Cs
Special rules
One
electron can move
from an
s orbital
to the
d
orbital
that is closest in
energy
Only happens to create
half or whole

filled d
orbitals
Examples: Cr, Cu
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