Electrons in Atoms
Chapter 5
Duality of Light
Einstein proved that matter and
energy are related E = mc2
 The smaller matter becomes the
more like energy it behaves.
 We know electrons are very small
therefore behave like energy.
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Duality of Light
During the 1800’s, Chemists and
physicists found light emitted properties of
a wave.
 In 1905, Albert Einstein explained the
photoelectric effect using a particle theory
of light.
 Scientist have accepted a dual theory of
light, either wave or particle.
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Wave Nature of Light
Electromagnetic Radiation: Form of
energy that exhibits wavelike behavior as
it travels through space.
 Visible light is a form of electromagnetic
radiation.
 All electromagnetic radiation travels at
3.00 x 108 m/s
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Wave Nature of Light
Crest
Wave Nature of Light
Wavelength: represented by λ, is the
shortest distance between equivalent
points. Unit for wavelength is meter.
 Frequency: represented by ν Greek letter
nu, is the number of waves that pass a
given point per second. Unit for frequency
is s-1 or 1/s
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Wave Nature of Light
Wave Nature of Light
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Since all electromagnetic radiation travels at
3.00 x 108 m/s, there is a distinct relationship
between frequency and wavelength.
c=λν
c is a constant, 3.00 x 108 m/s, the speed of light
λ is the wavelength of light in meters
ν is the frequency in s-1 or 1/s or Hz which = s-1
or 1/s
Wave Nature of Light
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Microwaves are used to transmit information.
What is the wavelength having a frequency of
3.44 x 109 Hz
We know c = λ ν
We know c = 3.00 x 108 m/s and we know ν =
3.44 x 109 Hz
Solve for λ
λ = c/ ν
λ = 3.00 x 108 m/s/ 3.44 x 109 Hz
λ = .0872m or 8.72 x 10-2 m
Wave Nature of Light
An X ray has a wavelength of 1.15 x 10-10
m. What is the frequency?
 2.61 s-1
 Yellow light has a frequency of 5.09 x 1014
s-1. What is the frequency?
 5.89 x 10-7 m.

Particle Nature of Light
Max Plank did experiments studying a
black box and the heat given off by it.
 Plank determined energy can only be
released or absorbed by atoms in small
specific amounts called quanta.
 He suggested light consisted of photons.
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Particle Nature of Light
Plank proposed the energy of a single
quantum is
E=hν
 E is the energy of a quantum.
 h is Planck’s constant, 6.626 x 10-34 J x s,
J is the symbol of a joule, which is the SI
unit of energy.
 ν is frequency.

Particle Nature of Light
Calculate the energy of a photon with a
frequency of 7.23 x 1014 s-1 .
 We know E = h ν
 We know h = 6.626 x 10-34 J x s
 We know v = 7.23 x 1014 s-1
 E = 6.626 x 10-34 J x s x 7.23 x 1014 s-1
 E = 4.79 x 10-19 J
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Particle Nature of Light
Calculate the energy of a photon with the
frequency of 6.32 x 1020 s-1.
 4.19x 10-13 J
 Calculate the energy of a photon with a
wavelength of 5.98 x 10-7 m.
 3.32 x 10-19 J
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Relationships of Photons
v↑, E↑, λ↓
 v↓, E↓. λ↑
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Atomic Emission Spectra
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Neon lights
Atoms absorb energy and emit light to release energy
Atomic emission spectrum: set of frequencies of the
electromagnetic waves emitted by atoms of the element.
Unique for all different elements.
Electrons as Waves
de Broglie proposed electrons have wave
like nature and the wavelength of the
electron can be calculated
 λ = h/mv
 h = Planck’s constant
 m = mass
 v = velocity
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Bohr Model of the Atom
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Bohr built upon Planck’s and Einstein’s concepts
of quantized energy.
The chemical properties of the element are
determined by the number of electrons in the
outer orbits.
Used spectra from hydrogen atom
Proposed that hydrogen atom has only certain
allowable energy states
Ground State: Lowest allowable energy state
Stated electron moves in only certain circular
orbits.
Bohr Model of the Atom
The smaller the electron’s orbit, the lower
the atom’s energy state. Larger orbit,
higher energy state.
 First orbit closest to the nucleus, n=1,
second, n=2
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Bohr Model of the Atom
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When energy is added to an atom, the electron
moves from the ground state, n=1, to a higher
energy orbit, excited state, n=2
When an electron is in an excited state, it can
drop from the higher energy orbit to a lower
energy orbit.
The atom emits a photon corresponding to the
difference between the corresponding energy
levels.
Bohr Model of the Atom
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1. proposed that while circling the nucleus of
the atom, electrons could only occupy certain
discrete orbits, that is to say energy levels
2. electrons give or take energy only when
they change their energy levels. If they move
up, they take energy if they move down, they
release energy. This energy itself is released
in discrete packets called photons
3. an electron which is not in its native
energy level always has to fall back to its
original, stable level.
Bohr Model of the Atom
Bohr model perfectly explained the
hydrogen atom
 but, failed to explain any of the other
atoms.
 Therefore, the Bohr model of the atom is
not the currently accepted model of the
atom.
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Heisenberg Uncertainty Principle
It is impossible to measure an object
without disturbing the object.
 Heisenberg attempted to determine exact
location of electrons using photons.
 He found since photons and electrons
have relatively the same amount of kinetic
energy, the photon would disturb the
position and velocity of the electron.
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Heisenberg Uncertainty Principle
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It is impossible to know precisely both the
velocity and position of a particle at the
same time
Quantum Mechanical Model of
Atom
Schrödinger created an equation to
accurately determine where an electron is.
 Unlike Bohr model, makes no attempt to
determine orbit of electron.
 States electrons are in noncircular orbitals.
 Orbitals are based on probability of
location of electron.
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Atomic Orbitals
Principal quantum numbers (n): indicate
the relative sizes and energies of atomic
orbitals.
 As n increases, the orbital is further away
from the nucleus and has more energy.
 n has whole number values of 1, 2, 3, etc.
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Atomic Orbitals
Principle energy levels contain energy
sublevels.
 Sublevels are signified by letters s, p, d, or
f.
 The letter determines the shape of the
sublevel.
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S orbital
First found at energy level 1
 Holds 2 electrons
 Spherical
 1s, 2s, 3s,…
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P Orbital
First found at energy level 2
 3 different shapes per energy level
 2 electrons per shape
 “dumb-bell” shaped
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D Orbitals
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First found at energy level 3.
5 different shapes
2 electrons per shape
Complex shapes
F Orbitals
First found at energy level 4
 7 different shapes
 2 electrons per shape
 Very complex
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f Orbital
First Four Principal Energy Levels
Principle
Quantum
Number
Sublevels
Present
Number of
orbitals in each
sublevel
Total number of
electrons in
energy level
1
s
1
2
2
s
p
1
3
8
3
s
p
d
1
3
5
18
4
s
p
d
f
1
3
5
7
32
Quantum Numbers
Principle quantum number = n
 2nd or Azinmuthal quantum number =
describes shape 0, 1, 2, 3 (s, p, d, f)
 Magnetic quantum number = ml
orientation in space, whole numbers -1, 0,
1
 Spin = s, either ½ or – ½, one e- ½ other
e- has – ½.
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n
Azinmuth
numbers
1
Number of
orbitals
Values of ml
S values
Number of
orbitals in
energy
level
0
0
½, - ½
1
2
0
1
0
-1,0,1
½, - ½
4
3
0
1
2
0
-1,0,1
-2,-1,0,1,2
½, - ½
9
4
0
1
2
3
0
-1,0,1
-2,-1,0,1,2
-3,-2,-1,0,1,2,3
½, - ½
16