Download Quantum Physics at a glance

Quantum Physics at a glance
Quantum Physics ­ deals with the study of light and particles at atomic and smaller levels.
Planck’s Hypothesis ­
(blackbody radiation)
(ultraviolet catastrophe)
Quantized Energy
Einstein
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Light as photon packets
Revised from wave theory:
where amplitude = energy and intensity
⇒Frequency Determines energy
high energy
low energy
⇒# of photons determines intensity
High Intesity
Low Intensity
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Photoelectric Effect ­ most basic
let
vio
en
gre
red
photoemissive metal (ex: sodium)
Increased light intensity (more incoming photons)
= more emitted electrons (photoelectrons)
*but not more energetic emissions, just more of them
Classical Physics (wave nature) vs. Quantum Physics (particle nature)
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Determining if electrons are emitted (photoelectrons)
en
gre
red
Frequency too low, Sufficient frequency (energy) to cause emission
no matter how intense no emission
Threshold Frequency (fo) ­ also called cutoff frequency
Frequency needed is dependent on the type of material and how easily electrons are removed
φ Work Function
Element
Work Function (eV)
Aluminium
4.3
Gold
5.1
Sodium
2.7
When incoming energy (E) > work function, where does the extra energy go?
FORMULAS
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Photoelectric Effect Experiment
1) Video ­ you tube anything
2) Diagrams ­ next page
3) Java Applet ­ need to download it and have java installed to run it. Can be a little tricky.
http://phet.colorado.edu/simulations/sims.php?sim=Photoelectric_Effect
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Diagrams
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Applet 1)
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STOPPING POTENTIAL
NEW FORMULA
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Applet 2) Java
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Graphs
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The Compton Effect ­ more proof of light acting like a particle
(proof easier to understand)
RECALL
photoelectric ­ emission of electrons when a photoemission surface absorbs EM waves in the range of visible­UV light
Increase the EM wave energy (Xrays)
Momentum
XRAYS 'reverse photoelectric'
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Pair Production ­ more proof of light acting like a particle
Photoelectic
­ uses EM visible and UV
Compton
­ uses EM Xrays
Pair Production
­ uses EM Gamma radiation
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Quantum Physics
1.) How do we know that light behaves like a wave?
2.) What equation describes the energy of a light photon?
3.) What is the work function
14 Hz?
4.) What is the energy in eV of one quantum (photon) of yellow light w/ a frequency of 6 x 10
5.) 1 quantum of light has an energy of 5 x 10­19 J. What is the color of this light photon?
6.) Radiation has a λ=940 μm. (a) what is the frequency of this radiation (b) What type of EM wave is this rad iation (c) How much energy is in 1 quantum of this energy (d) What is the momentum of one photon of this radiation
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7.) Tungsten metal has a work function of 4.6 eV. If light of wavelength = 1x10
electrons ejected?
m shines on tungsten, are ­7
8.) A magnesium surface has a work function of 3.68 eV. Electromagnetic waves with a 215 nm wavelength strike the surface and eject photoelectrons. Calculate the energy of the photoelectrons in Joules and in electron volts. 9.) A metal has a threshold frequency of 5.6x 10 14 Hz. If 8.6 x10 14 Hz frequency light illuminates the metal, what is the maximum kinetic energy of the ejected photoelectrons? 10.) When light falls on a photoelectric surface, the stopping potential that prevents the electrons from flowing across a photocell is 3.5 V. What is the maximum speed of the photoelectrons? 11.) Does a red light or green light photon have more energy?
12.) The energy of a photon varies inversely with the
(a) frequency (b) momentum
(c) speed
(d) wavelength
13.) An X ray photon hits an electron at rest. During the interaction, the momentum of the photon
(a) decreases (b) increases
(c) remains the same
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AP SAMPLE PROBLEMS
B2004B6. An incident gamma ray photon of wavelength 1.400 x 10­14 m is scattered off a stationary nucleus. The shift in wavelength of the photon is measured for various scattering angles, and the results are plotted on the graph shown below.
(a) On the graph, sketch a best­fit curve to the data.
In one of the trials, the photon is scattered at an angle of 120° with its original direction.
(b) Calculate the wavelength of this photon after it is scattered off the nucleus.
(c) Calculate the momentum of this scattered photon.
(d) Calculate the energy that this scattering event imparts to the recoiling nucleus.
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2002B7. A photon of wavelength 2.0 x 10 ­11 m strikes a free electron of mass me that is initially at rest, as shown above left. After the collision, the photon is shifted in wavelength by an amount ∆λ = 2h/mec, and reversed in direction, as shown above right.
(a) Determine the energy in joules of the incident photon
.
(b) .
(c) (d) Determine the magnitude of the momentum of the incident photon
Indicate below whether the photon wavelength is increased or decreased by the interaction.
Increased
Decreased
Explain your reasoning.
Determine the magnitude of the momentum acquired by the electron.
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2000B5. A sodium photoelectric surface with work function 2.3 eV is illuminated by electromagnetic radiation and emits electrons. The electrons travel toward a negatively charged cathode and complete the circuit shown above. The potential difference supplied by the power supply is increased, and when it reaches 4.5 V, no electrons reach the cathode. a. For the electrons emitted from the sodium surface, calculate the following. i. The maximum kinetic energy ii. The speed at this maximum kinetic energy b.Calculate the wavelength of the radiation that is incident on the sodium surface. c.Calculate the minimum frequency of light that will cause photoemission from this sodium surface. 17
Atomic Spectra ­ Observed experimental result that needed to be explained in atom models
Two Types, absorption spectra and emission spectra
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EMISSION SPECTRA PRODUCTION
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ABSORPTION SPECTRA PRODUCTION
SODIUM
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Models of The Atom ­ Handout
1st Model ­ Thomson “plum pudding” model (J.J. Thomson)
2nd Model ­ Ernest Rutherford ­ Planetary Model
Also, atom size estimated at 1 angstrom 10­10 , nucleus size estimate at 1 fermi 10­15
3rd Model ­ Neils Bohr Model ­ Revisions of the Rutherford Model
Bohr orbit explained: Matter Waves ­ Louis deBroglie (pronounced “dah­broy”) ­ deBroglie proposed that all matter (electrons) have wave­like properties The matter wavelength can be found by using p = h / λ, which gives a very small and unnoticeable wavelength for everyday sized matter
Matter Wave evidence ­ Davisson­Germer experiment.
4th Model (Todays Current View, Quantum Mechanics Model) ­ Erwin Schrödinger ­ Electron Cloud Model
Pauli exclusion principle ­ explains the order in which atoms fill energy levels. (ex: 2 in the first “s” shell, 2 in the next “s” shell, 6 in the 1st “p” shell …) 21
Bohr Model
­ explains spectral lines though quantized energy level jumps
http://www.colorado.edu/physics/2000/quantumzone/lines2.html
Bohr’s Energy Levels ­ Handout
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A
A
B
γ
UV light, not visible
B
Key Components
­ absorb light, electrons gain energy, jump to higher energy levels
­ emit light, electrons give off energy, move to lower energy levels
­ exact amounts
­ ionization
­ finding E or f or λ absorbed or emitted
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energy levels handout problems
1.) The lowest energy state of an atom is called its
(a) ground state(b) ionized state
(c) initial energy(d) final energy state
2.) Which electron transition in the hydrogen atom results in the emission of a photon with the greatest energy?
(a) n=2 to n=1
(b) n=3 to n=2
(c) n=4 to n=2
(d) n=5 to n=3
3.) What is the minimum energy required to ionize a hydrogen atom in the n=3 state?
(a) 13.6 eV
(b) 12.09 eV
(c) 5.52 eV
(d) 1.51 eV
4.) Which photon energy could be absorbed by a hydrogen atom that is in the n=2 state?
(a) 0.66 eV
(b) 1.51 eV
(c) 1.89 eV
(d) 2.40 eV
5.) Hydrogen atoms undergo a transition from the n=3 energy level to the ground state. What is the total number of different photon energies that may be emitted by these atoms
6.) An electron in a mercury atom jumps from level a to level g by absorbing a single photon. What is the energy of the photon in Joules?
7.) As an atom absorbs a photon of energy, one of its electrons will (a) exchange energy levels with another of its electrons (b) undergo a transition to a higher energy level (c) undergo a transition to a lower energy level (d) increase its charge
8.) Which transition between the energy levels of mercury causes the emission of a photon of highest frequency? (a) e to d
(b) e to c
(c) c to b
(d) b to a
9.) As an atom goes from the ground state to an excited state, the energy of the atom (a) decreases (b) increases (c) remains the same
10.) It is possible for an excited hydrogen atom to return to the ground state by the emission of a single photon. Regardless of the initial excited state, this electron transition produces a spectral line in which region of the EM spectrum
(a) ultraviolet (b) infrared
(c) visible light (d) radio waves
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11.) Determine the frequency of the photon emitted when an excited hydrogen atom changes from energy level n=3 to n=2
12.) An electron in a mercury atom changes from energy level b to level e. This energy­level change occurs as the atom (1) absorbs a 2.03 eV photon (2) absorbs a 5.74 eV photon (3) emits a 2.03 eV photon (4) emits a 5.74 eV photon
13.) A hydrogen atom emits a 2.55 electronvolt photon as its electron changes from one energy level to another.
(a) determine the energy level change for the electron
(b) Express the energy of the emitted photon in joules
(c) determine the frequency of the emitted photon
14.) A photon with 14.5 eV of electronvolts of energy collides with a mercury atom in its ground state.
(a) express the energy of the incident photons in joules
(b) determine the frequency of the incident photon
(c) In what region of the electromagnetic spectrum is the frequency of the incident photon (1) gamma
(2) infrared (3) visible (4) ultraviolet
(d) If the photon collision ionizes the atom, what is the maximum energy that the electron removed from the atom can have? (1) 0.00 eV (2) 4.12 eV
(3) 10.38 eV (4) 14.60 eV
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AP QUESTIONS
B2003B7. An experiment is performed on a sample of atoms known to have a ground state of −5.0 eV. The gas is illuminated with “white light” (400 ­ 700 nm). A spectrometer capable of analyzing radiation in this range is used to measure the radiation. The sample is observed to absorb light at only 400 nm. After the “white light” is turned off, the sample is observed to emit visible radiation of 400 nm and 600 nm.
(a) In the space below, determine the values of the energy levels and on the following scale sketch an energy level diagram showing the energy values in eV’s and the relative positions of:
i. the ground state
ii. the energy level to which the system was first excited
iii. one other energy level that the experiment suggests may exist
(b) What is the wavelength of any other radiation, if any, that might have been emitted in the experiment?
Why was it not observed?
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1993B6. In the x­ray tube shown above, a potential difference of 70,000 volts is applied across the two electrodes. Electrons emitted from the cathode are accelerated to the anode, where x­rays are produced.
a. Determine the maximum frequency of the x­rays produced by the tube.
b. Determine the maximum momentum of the x­ray photons produced by the tube.
An x­ray photon of the maximum energy produced by this tube leaves the tube and collides elastically with an electron at rest. As a result, the electron recoils and the x­ray is scattered, as shown above. The frequency of the scattered x­ray photon is 1.64 x 1019 hertz. c. Determine the kinetic energy of the recoiled electron.
d. Determine the magnitude of the momentum of the recoiled electron.
e. Determine the deBroglie wavelength of the electron
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