1. science
2. physics

Atomic
Physics
and
The REAL Question. . . . . . .
Quantum
What is LIGHT?
Effects
AP Physics B Planck's Quantum Hypothesis
Late 1900, proposed as a mathematical
explanation for "blackbody radiation".
Einstein wrote...... "The energy in a beam of light is not distributed continuously through space, but consists of a finite number of energy quanta, which are localized at points, which cannot be subdivided, and which are absorbed or emitted only as whole units."
The energy of any molecular vibration exists as a
whole number multiple of hf.
E = nhf
where n is a whole number
The "quantum" is a discrete unit with no "inbetween".
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1905 - Albert Einstein (Frank's brother) proposed
a new theory of the nature of light. Ultimately,
light is transmitted as tiny particles, now called
photons, instead of waves.
Energy of a photon: E = hf
h Planck's constant 6.63 x 10­34 J/Hz
f frequency Hz
Q: What is the energy range of photons in the
visible light spectrum, consisting of wavelengths 400
- 700 nm? Express your answer in both Joules and
Electron-Volts.
700 nm
700x10­9 m
4.3x1014 Hz
2.84x10­19 J
1.5 eV
400 nm
400x10­9 m
7.5x1014 Hz
4.98x10­19J
3.1 eV
To convert from Joules to­19eV divide Joules by the
= eV
Joules / 1.6x10
-19 eV/J)
charge
of an
electron
(1.6
Slide
to
reveal conversion
J to eV
­19x 10 from
or eV x 1.6x10 = J
Q: What determines the energy of a photon? Photons also have momentum and the momentum
is related to the wavelength.
Q: What seems strange about this? p=h
l
remember: h = 6.63 x 10-34 J/Hz
from v = f l
l =
hf
p= c
v
f
v is really
"c"
speed of light
3.0 x 108 m/s
The Photoelectric Effect
light energy
producing
current
The PE Effect is the phenomenon that when light
shines on a metal surface, electrons are emitted
from the surface of the metal. Think of a solar cell.
metal
plate
Q: What is the momentum, frequency, and
energy of a 0.20 nm X-ray photon?
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metal
plate
This minimum amount of energy needed to eject
an electron is called the "work function" of the
metal. Different metals have different work
functions.
φ (phi) is the work function
Q: How will we determine the energy of the photons of light?
E = hf, of course!
IF Ephotons φ, electrons are ejected
IF Ephotons φ, electrons are NOT ejected
Maxwell's wave theory of light predicts that if the
intensity (brightness) of the light is increased,
then electrons would be ejected.
That's not really what happens.
LINK
more stuff
The photons of light
from the bulb must
have a certain
minimum amount of
energy to be able to
eject electrons from
the metal's surface.
The photon theory explains that in order to
increase the energy of the incident light, the
frequency of the incident light must be increased.
IF the incident light energy is greater than the
work function, there will be an excess of energy
for the ejected electrons. This excess energy will
be the kinetic energy of the ejected electrons.
KEMAX = E - φ
work function
of the metal
of the photoelectrons
φ = hfo
of the incident
photons
E = hf
Another way of solving this equation:
KEMAX = hf - hfo
energy of the
incident
photons
cutoff
frequency
work
function
of the
metal
Notice: Red light ejects no electrons. Why?
Green light does eject electrons. How does green
light differ from red?
Violet light also ejects electrons. These
photoelectrons have a higher velocity than the
ones from the green light. Why?
LINK to a pretty simple explanation of the
photoelectric effect.
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Simulation: Try to determine the work
function for silver. Once you find the
minimum wavelength that will eject
electrons, calculate the work function.
Then, change the intensity of the source
and see what effect this has on the
photoelectrons.
from handout in class: Click here for applet
A good applet
What effect does increasing the intensity have
on the photoelectrons?
Q1) What minimum frequency of light is needed to eject electrons from a
metal whose work function is 3.10 eV? What is the wavelength of this light?
solution next page
Q1) What minimum frequency of light is needed to eject electrons from a
metal whose work function is 3.10 eV? What is the wavelength of this
light?
Q2) Barium has a work function of 2.48 eV. What is the maximum kinetic
energy of electrons if the metal is illuminated by light of wavelength 390 nm?
What is their speed?
solution 2 pages over
Q3) What is the maximum kinetic energy of electrons ejected from barium
(φ = 2.48 eV) when illuminated by white light λ = 400 to 700 nm?
solution 3 pages over
Q4) Electrons are ejected from a metallic surface with speeds ranging up to
4.6 x 105 m/s when light with a wavelength of 625 nm is used. (a) What is the
work function of the surface? (b) What is the cutoff frequency for this surface?
solution 4 pages over
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Q2) Barium has a work function of 2.48 eV. What is the maximum
kinetic energy of electrons if the metal is illuminated by light of
wavelength 390 nm? What is their speed?
Q4) Electrons are ejected from a metallic surface with speeds ranging up
to 4.6 x 105 m/s when light with a wavelength of 625 nm is used. (a) What
is the work function of the surface? (b) What is the cutoff frequency for
this surface?
Q3) What is the maximum kinetic energy of electrons ejected from
barium (W0 = 2.48 eV) when illuminated by white light λ = 400 to 700
nm?
Graph of KEMAX versus frequency
X­intercept is the cutoff frequency. The slope of the graph is E/f (this is not h),from this you can calculate h by multiplying by q.
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How can we MEASURE the velocity of the electron?
The electron has kinetic energy? Yes
What if we knew how much work was needed to stop the electron? How are work and kinetic energy related? Are work and potential (as in voltage) related? Yes. How?
KEMAX = qV0
Handy equation hidden here
charge
stopping
of an potential
electron
in Volts
If KEMAX is given in eV, then stopping potential has the same value with units of Volts. The Compton Effect aka Compton Scattering
Photons may also collide with things besides metal plates. If a photon collides with a particle, such as an electron, we treat this like a collision between two particles with both momentum and KE being conserved. After the collision, the photon has transferred some energy to the electron. This loss of energy means the photon loses some energy (frequency) and the velocity slows, thus the wavelength increases. This lengthening of the wavelength is called Compton Shift. interactive
The true Compton experiment used X­ray photons because of their tiny wavelengths. The shift would be more noticeable. Compton Scattering
Compton Scattering Summary
Photon collides with a ______________
The photon loses ____________ & ____________
Thus, its _________ becomes ________________
Photon
E = 1000 keV
f=241.5 EHz
λ=0.0124
θ=0.0
Electron
K=0
φ = 0
Photon
E = 583.2 keV
f=140.9 EHz
λ=0.0212
θ=50.6
Electron
K=416.8 keV
φ = 35.58o
Beautiful Conservation of Energy! 6
Atomic Energy Levels
interactive The electrons in an atom can have only certain, specific amounts of energy (energy is quantized).
X ­ RAYS
Produced when electrons are accelerated by a high voltage and strike a metal/glass surface w/in an x­ray tube. X­rays are emitted as a result. Wavelength can be calculated by determining the energy of the accelerating voltage (K = qV), then from energy calculate frequency (E=hf), then use c
c to get wavelength ( λ= )
f
simplified model of an atom showing two energy levels
Q: What is absorbed or emitted?
lowest level for the electron is called ground state
jump up: absorb
fall down: emit
ENERGY
General X­ray characteristics
1. Charge is 0
2. They diffract, proving they are waves.
3. They are a form of E­Mag radiation
The lowest energy level is called the ground state (closest to nucleus). To move "up", the electron must absorb a certain (exact) amount of energy from a photon. This new "excited" state for the electron is unstable and the electron returns to ground state. As it falls, the electron emits a photon of the same energy. These emitted photons produce the emission spectra that we observed in class. interactive see all the elements
Hydrogen Energy Level Diagram
Energy Levels
For this electron to jump up, it must absorb an exact amount of energy for the level it will jump to. Ground State
Once the electron reaches a higher energy level, due to instability, it quickly falls back to its ground state, emitting energy in the form of light as it falls. Eabsorbed = Eemitted
QDOM:How much energy must our electron absorb E
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to jump to the next level? E
4
QDOM: How much energy E3
is emitted (in eV) once the electron falls back to its ground state? 0.00 eV
E = ­0.54 eV
5
E = ­0.85 eV
4
E = ­1.51 eV
3
E2
E = ­3.40 eV
2
E1
E = ­13.6 eV
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QDOM: What is the wave­
length (in nm) of the emitted photon? QDOM: Could you see it? 7
Hydrogen Energy Level Diagram
0.00 eV
E = ­0.54 eV
E = ­0.85 eV
E5
An electron can be excited E4
to any higher state and can fall down to any lower E3
state. Photons of varying wavelengths are emitted with each of these E2
transitions. Q: Why are some gray, others colored? E = ­1.51 eV
E = ­3.40 eV
Q: Why reddish and violet? E1
E = ­13.6 eV
another way of looking at it. . . We saw spectra like this in an activity last month.
Emission Spectrum Lines
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What are the associated energies for each of the visible lines for hydrogen?
Hydrogen Energy Level Diagram
E5
E4
0.00 eV
E = ­0.54 eV
E = ­0.85 eV
E3
E = ­1.51 eV
E2
E = ­3.40 eV
E1
E = ­13.6 eV
What wavelength (nm) of light must an electron absorb to get from E2 to E3?
What if an electron absorbs 13.6 eV of energy, where does it go? The highest energy value represents the ionization Another energy for that atom. The electron absorbing that Answer
much energy would be Under Here
ejected from the atom (thus forming an ion) Practice: de Broglie Wavelength
de Broglie Wavelength
If light, which was considered to be a wave could exhibit particle tendencies/behaviors; could particles exhibit wave­
like behaviors?
h
λ =
p
h
=
mv
Yes, particles moving with a velocity have wavelengths.
Q) Calculate the de Broglie wavelength for a 5 kg bowling ball rolling at 3 m/s. 1) What is the de Broglie wavelength of a proton moving at 1 x 106 m/s?
­13 m
3.97 x 10
2) An electron is accelerated through a potential difference of 54 V. Find the maximum velocity and de Broglie wavelength of the electron. 4.36 x 106 m/s; 1.67 x 10­10 m
3) The kinetic energy of an electron is 13.65 eV. Find the velocity and de Broglie wavelength of the electron. 2.19 x 106 m/s; 3.32 x 10­10 m
4) An electron has a de Broglie wavelength of 400 nm. What is its velocity? 1,818 m/s
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What IS Light?
Is is composed of waves, with wavelength and frequency, etc and exhibits diffraction and interference?
OR
Is it composed of a stream of particle­like photons which can perform the photoelectric effect and Compton scattering?
Actually, .....
Light has a dual nature. At times, it behaves as a wave and at times it behaves as a particle. It can never be both simultaneously. This is the Wave­Particle Duality of Light.
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