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Electromagnetic Radiation
• All electromagnetic
radiation travels at the
same velocity: the
speed of light (c), 3.00
 108 m/s.
• Therefore,
c = 
Blackbody Radiation
All objects emit electromagnetic
radiation which depends on their
temperature: thermal radiation.
A blackbody absorbs all
electromagnetic radiation (light)
that falls on it.
Because no light is reflected or transmitted, the object appears black when it
is cold. However, black bodies emit a temperature- dependent spectrum
termed blackbody radiation. For example, the temperature of the above
Pāhoehoe lava flow can be estimated by observing its color.
Planck’s Quantum Hypothesis
The wave nature of light could not explain the way an object
glows depending on its temperature: its spectrum.
In 1900, Max Planck explained it by assuming that atoms
only emit radiation in quantum amounts.
These days, this assumption is regarded as the birth of quantum physics and the greatest intellectual
accomplishment of Planck's career.
Planck’s Postulate
E = hf
where h is Planck’s constant (6.63 x 10-34 J-s) and
f is the frequency of the light
Planck’s Quantum Hypothesis
According to Planck's hypothesis, since only
certain frequencies of light
were emitted at varying temperatures, the amount of energy put into a
substance triggered that substance to release a very specific type of light.
In other words, if we think of this like a person walking up a flight of stairs,
the person cannot reach a certain height unless first raising his or her legs to
the height of the specific steps.
Planck’s Quantum Hypothesis
Planck didn't believe this was a real...
it just worked.
It was like working from the answers in the book…
you see that it works, but you have no idea why.
Atoms only having steps of energy? This didn't make sense.
Why couldn't they have any energy?
Planck thought a "real" solution would eventually be found...but this one worked
for some reason. Which brings us to our next mystery...
The Nature of Energy
• Einstein used this
assumption to explain the
photoelectric effect.
• He concluded that energy
is proportional to
frequency:
E = h
where h is Planck’s
constant, 6.63  10−34 J-s.
The Photoelectric Effect
When light strikes a metal, electrons sometimes fly off
causing an electric current.
Classical physics couldn't explain some specific features about how the
effect works. So Einstein used Planck's idea to solve it.
The Photon
If atoms can only emit light in packets of specific sizes; maybe light itself travels as packets of energy given
by Planck's formula.
evacuated
chamber
Radiant
energy
metal
surface
E = hf
e-
where h is Planck’s constant
(6.63 x 10-34 J-s)
voltage
source
He called these tiny packets of energy or light photons.
Current
indicator
Photon Theory of Light
This particle theory of light assumes that an electron absorbs a single photon
and made specific predictions that proved true.
For instance, the kinetic energy of escaping electrons vs. frequency of light
shown below:
KEmax of electrons
This shows clear agreement with the photon
theory, and not with wave theory.
This shows that light is made of particles
(photons) and therefore light is not a wave.
Frequency of light f
Wave-Particle Duality
Earlier we proved that light is a
wave.
Now we've proven that light is
a particle.
So which is it?
Wave-Particle Duality
Particle? Wave?
This question has no answer;
we must accept the dual wave-particle nature of light.
While we cannot imagine something that is both a wave and a particle at the
same time; that turns out to be the case for light.
Wave-Particle Duality
Check out this animation
about the Wave-Particle Duality
Like that?
Here's one more to watch
Electron Microscopy
Wave–particle duality is exploited in electron microscopy, where
the small wavelengths associated with the electron can be used
to view objects much smaller than what is visible using visible
light.
11
The ratio of energy to frequency for a given photon gives
A
its amplitude.
B
its velocity.
C
Planck's constant.
D
its work function.
E = hf
c = λf
h = 6.63 x 10-34 J-s
c = 3.00 x 108 m/s
12
What is a photon?
A
an electron in an excited state
B
a small packet of electromagnetic energy that has particle-like properties
C
one form of a nucleon, one of the particles that makes up the nucleus
D
an electron that has been made electrically neutral
13
The energy of a photon depends on
A
its amplitude.
B
its velocity.
C
D
its frequency.
none of the given answers
14
The photoelectric effect can be explained assuming
A
that light has a wave nature.
B
that light has a particle nature.
C
that light has a wave nature and a particle nature.
D
none of the above
15
The energy of a photon that has a frequency 110 GHz is
A
1.1 × 10-20 J
B
1.4 × 10-22 J
C
D
7.3 × 10-23 J
E = hf
c = λf
h = 6.63 x 10-34 J-s
c = 3.00 x 108 m/s
1.3 × 10-25 J
16
The frequency of a photon that has an energy of 3.7 x 10-18 J is
A
B
C
5.6 × 1015 Hz
D
5.4 × 10-8 J
2.5 × 1015 J
E
E = hf
c = λf
h = 6.63 x 10-34 J-s
c = 3.00 x 108 m/s
1.8 × 10-16 Hz
2.5 × 10-15 J
17
The energy of a photon that has a wavelength of 12.3 nm is
E = hf
c = λf
h = 6.63 x 10-34 J-s
c = 3.00 x 108 m/s
A
B
1.51 × 10-17 J
C
D
1.99 × 10-25 J
E
1.61 × 10-17 J
4.42 × 10-23 J
2.72 × 10-50 J
18
If the wavelength of a photon is halved, by what factor does its energy
change?
A
4
B
2
C
1/4
D
1/2
E = hf
c = λf
h = 6.63 x 10-34 J-s
c = 3.00 x 108 m/s
Energy, Mass, and Momentum
of a Photon
Clearly, a photon must travel at the speed of light, (since it is light)
Special Relativity tells us two things from this:
The mass of a photon is zero.
The momentum of a photon depends on its wavelength.
The Wave Nature of Matter
• Louis de Broglie posited that if light can
have material properties, matter should
exhibit wave properties.
• He demonstrated that the relationship
between mass and wavelength was
h
 = mv
Matter as a wave?
Taking all of this into account, in 1924, French physicist
Louis de Broglie asked:
"If light can behave like a wave or a particle, can matter
also behave like a wave?"
He found that amazingly, it does!
Wave Nature of Matter
Electron wavelengths are often about 10-10 m, about the size of an atom, so the wave character of
electrons is important.
In fact, the two-slit experiment that showed that light was a wave, has been replicated with
electrons with the same result...electrons are particles and waves.
Wave Nature of Matter
Electrons fired one at a time towards two slits show the same
interference pattern when they land on a distant screen.
The "electron wave" must go through both slits at the same
time...which is something we can't imagine a single particle
doing...but it does.
Click here for a video with more explanation of all
this!
The most amazing experiment ever!
These photos show electrons being fired one at a time
through two slits.
Each exposure was made after a slightly longer time.
The same pattern emerges as was found by light.
Each individual electron must behave like a wave and
pass through both slits. But each electron must be a
particle when it strikes the film, or it wouldn't make one
dot on the film, it would be spread out.
This one picture shows that matter
acts like both a wave and a particle.
19
Assuming both balls are moving with a speed of 10 m/s, which ball has a
longer de'Broglie wavelength?
A
The tennis ball
B
The bowling ball
C
Both balls have the same wavelength
bowling ball
D
It's impossible to tell
E
I don't know the answer
tennis ball
20
Assuming both balls are not moving (ignoring molecular movement),
which ball has a longer de' Broglie wavelength?
A
The tennis ball
B
The bowling ball
C
Both balls have the same wavelength
D
It's impossible to tell
E
I don't know the answer
bowling ball
tennis ball
21
Which option correctly ranks the objects below in order of increasing de'
Broglie wavelength, if each object is traveling at a speed of 10 m/s?
golfball
tennis ball
baseball
basketball
bowling ball
A
golfball, tennis ball, baseball, basketball, bowling ball
B
baseball, tennisball, golfball, basketball, bowling ball
C
basketball, baseball,tennis ball, bowling ball, golf ball
D
bowling ball, basketball, baseball, tennis ball, golfball
E
tennis ball, bowling ball, basketball, golfball, baseball
22
What is the wavelength of a 0.25 kg ball traveling at 20 m/s?
=
h = 6.63 x 10-34 J-s
h
l=
mv
23
What is the wavelength of a 80 kg person running 4.0 m/s?
=
h
l=
mv
h = 6.63 x 10-34 J-s
24
What is the wavelength of the matter wave associated with an electron (me = 9.1
x 10-31kg) moving with a speed of 2.5 × 107 m/s?
=
h = 6.63 x 10-34 J-s
h
l=
mv
25
What is the wavelength of the matter wave associated with an electron (me = 9.1
x 10-31kg) moving with a speed of 1.5 × 106 m/s?
=
h = 6.63 x 10-34 J-s
h
l=
mv
Atomic Spectra
Small amount of gas heated in a discharge tube emits light only at
characteristic frequencies.
+
Cathode
-
_
_
_
+
_
Anode
+
_
High Voltage
try and think about
listening to hydrogen
Atomic Spectra
An atomic spectrum is a line spectrum – only certain frequencies appear. If
white light passes through such a gas, it absorbs at those same frequencies.
Atomic Spectra
Why don't atoms radiate, or absorb, all frequencies of light?
Why do they radiate light at only very specific
frequencies, and not at others?
Atomic Spectra:
Key to the Structure of the Atom
A portion of the complete spectrum of hydrogen is shown here. The lines
cannot be explained by the Rutherford theory.
infrared
ultraviolet
Lyman
Balmer
Paschen
The Bohr Atom
Bohr proposed that electrons could orbit the nucleus, like planets orbit the
sun...but only in certain specific orbits.
He then said that in these orbits, they wouldn't radiate energy, as would be
expected normally of an accelerating charge. These stable orbits would
somehow violate that rule.
Each orbit would correspond to a different energy level for the electron.
Bohr's Model
n represents the energy level where n=1
is the lowest naturally occupied level or "ground state"
n=1
+
The Bohr Atom
These possible energy states for atomic electrons were quantized – only
certain values were possible. The spectrum could be explained as transitions
from one level to another.
Electrons would only radiate when they moved between orbits, not when they stayed in one orbit.
e-
e-
upper
upper
lower
lower
Absorption
Absorption of electromagnetic radiation is the way by which the energy
of a photon is taken up by matter, typically the electrons of an atom.
The electromagnetic energy is transformed to other forms of energy for
example, to heat.
Electromagnetic Radiation Absorption
Emission
Emission is the process by which a higher energy quantum mechanical state of a particle becomes converted
to a lower one through the emission of a photon, resulting in the production of light.
When the electrons in the atom are excited, for example by being heated, the additional energy pushes the
electrons to higher energy orbitals. When the electrons fall back down and leave the excited state, energy is
re-emitted in the form of a photon.
Electrons Produce Light!!
• Electrons (e-) move within
atoms
– (e-) movement is caused by
energy
– (e-) move in different orbits
Photons
• A particle form of light or
electromagnetic radiation
A photon walks into a hotel and checks in. "Do you want a hand
with your luggage?" asks the receptionist. "No thanks", replies
the photon, " I’m travelling light".
Excited state
1. Electrons jump to a
higher orbit
2. Caused by atoms
absorbing energy
Ground state
• Electron falls
back to lower
level (ground
state)
• Energy is
released as
electromagnetic
radiation (E.R)
(photon)
Transition of n
3→2
4→2
5→2
6→2
7-2
Wavelength (nm)
650
500
450
425
400
color
red
blue
green
violet
UV
Quantum or jump
•
when an e_ jumps orbits it transports to the
next orbit!!!
A photon can be released as any
electromagnetic energy
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Spectral lines summed up
1. e- are in fixed orbits
2. e- can get excited, and jump to a higher
orbit, if they absorb the appropriate
energy
3. e- will fall back to lower level (ground
state) and release a photon of similar
energy (visible light)
5 points of the Bohrs Model
– 1. elements produce spectral lines also known
as energy levels
2. Energy levels are
represented by letters
– 3. Energy
levels get larger the
farther away they are from the
nucleus
–4. larger the energy level more
electrons they can hold
–5 Each energy level can only hold
so many electrons
The Nature of Energy
• Therefore, if one knows the
wavelength of light, one
can calculate the energy in
one photon, or packet, of
that light:
c = 
E = h
The Nature of Energy
• One does not observe
a continuous
spectrum, as one gets
from a white light
source.
• Only a line spectrum of
discrete wavelengths
is observed.
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
1. Electrons in an atom can only
occupy certain orbits
(corresponding to certain
energies).
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
2. Electrons in permitted orbits
have specific, “allowed”
energies; these energies will
not be radiated from the atom.
The Nature of Energy
•
Niels Bohr adopted
Planck’s assumption and
explained these
phenomena in this way:
3. Energy is only absorbed or
emitted in such a way as to
move an electron from one
“allowed” energy state to
another; the energy is
defined by
E = h
Line Spectra of Hydrogen
• Balmer, Rydberg, and Ritz deduced an empirical
formula that predicted the observed wavelengths of
lines in the hydrogen emission spectrum:
1
 1
 RH  2  2 

n k 
1
–
–
–
–
RH = Rydberg constant = 1.0973732  107 m–1
n, k are integers
k > n (always)
Understanding this equation theoretically was a hot topic in
the early 20th Century
The Nature of Energy
The energy absorbed or emitted
from the process of electron
promotion or demotion can be
calculated by the equation:
E = −RH ( 1nf2 -
1
ni2
)
where RH is the Rydberg
constant, 2.18  10−18 J, and ni
and nf are the initial and final
energy levels of the electron.