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DEVIL PHYSICSTHE BADDEST CLASS ON
CAMPUSIB PHYSICS
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TSOKOS LESSON 6-5:QUANTUM THEORY AND THE UNCERTAINTY PRINCIPLE
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Introductory VideoQuantum Mechanics
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IB Assessment Statements
Topic 13.1, Quantum Physics: Atomic Spectra and Atomic Energy States
13.1.8. Outline a laboratory procedure for producing and observing atomic spectra.
13.1.9. Explain how atomic spectra provide evidence for the quantization of energy in atoms.
13.1.10. Calculate wavelengths of spectral lines from energy level differences and vice versa.
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IB Assessment Statements
Topic 13.1, Quantum Physics: Atomic Spectra and Atomic Energy States
13.1.11. Explain the origin of atomic energy levels in terms of the “electron in a box” model.
13.1.12. Outline the Schrödinger model of the hydrogen atom.
13.1.13. Outline the Heisenberg uncertainty principle with regard to position-momentum and time-energy.
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Objectives
Describe emission and absorption spectra and understand their significance for atomic structure
Explain the origin of atomic energy levels in terms of the ‘electron in a box’ model
Describe the hydrogen atom according to Schrödinger
Do calculations involving wavelengths of spectral lines and energy level differences
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Objectives
Outline the Heisenberg Uncertainty Principle in terms of position-momentum and time-energy
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Atomic Spectra
The spectrum of light emitted by a material is called the emission spectrum.
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Atomic Spectra
When hydrogen gas is heated to a high temperature, it gives off light
When it is analyzed through a spectrometer, the light is split into its component wavelengths
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Atomic Spectra• Different
gases will have emission lines at different wavelengths• Wavelength
s emitted are unique to each gas
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Atomic SpectraMercury
• This is called the emission spectrum of the gas• By identifying the
wavelengths of light emitted, we can identify the material
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Atomic SpectraHelium
• A similar phenomenon occurs when we pass white light through a gas• On a spectrometer,
white light would show a continuous band of all colors
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Atomic SpectraArgon
• When passed through a gas, dark bands appear at the same frequencies as on the emission spectrum• This is called the
absorption spectrum of the gas
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Atomic Spectra - Absorbtion
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Atomic SpectraNeon
• By trial and error, Johann Balmer found that wavelengths in hydrogen followed the formula,
,...5,4,3
1411
2
nn
R
• But nobody could figure out why• But it did show
the frequencies were not random
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Atomic Spectra
Conservation of energy tells us that the emitted energy will be equal to the difference in atomic energy before and after the emission
Since the emitted light consists of photons of a specific wavelength, the energy will be discrete values following the formula,
hchfE
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Electron In A Box
de Broglie Wavelength
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Electron In A Box
Amplitude is zero at ends of the box Since electron can’t lose energy, the
wave in the box is a standing wave with fixed nodes at x = 0 and x = L
nL2
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Electron In A Box
Lhnp
hp
nL
2
2
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Electron In A Box
2
22
2
8
2
2
mLhnE
mpE
Lhnp
k
k
•The result is that electron energy is always a multiple of a discrete or quantized value•The same principle applies for electrons surrounding a nucleus
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Schrödinger Theory
Wave Function, Ψ(x,t)
Schrodinger equation for hydrogen
Separate equations for electrons in every type of atom
Result is that the energy of an electron in a specific atom is quantized
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Schrödinger Theory
Schrodinger’s Theory applied to the electron in a box model yields the following data for a hydrogen atom
Energy is discrete or quantized to one of the energy levels given by n = 1, 2, 3
eVn
E
hkmeC
nCE
2
2
242
2
6.13
2
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Schrödinger Theory
Energy levels of emitted photons correspond to energy level changes of electrons
Each time an electron drops in energy level, a photon is released with that energy
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Schrödinger Theory
Since E = hf, the photon will have a discrete frequency according to its energy
Knowing the energy level change of the electron, we can compute the frequency and vice versa
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Schrödinger TheoryMax Born Interpretation | Ψ(x,t)|2 will give the probability
that an electron will be near position x at time t
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Schrödinger Theory Schrodinger’s Theory also predicts the
probability that a transition will occur (| Ψ(x,t)|2)
Explains why some spectral lines are brighter
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Heisenberg Uncertainty Principle Applied to position
and momentum: Basis is the wave-
particle duality Can’t clearly explain
behavior based on wave theory or classical mechanics
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Heisenberg Uncertainty Principle It is not possible to
simultaneously determine the position and momentum of something with indefinite precision
4hpx
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Heisenberg Uncertainty Principle
Making momentum accurate makes position inaccurate and vice versa As Δp approaches 0, Δx
approaches infinity As Δx approaches 0, Δp
approaches infinity
4hpx
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Heisenberg Uncertainty Principle Think of aiming a
beam of electrons through a thin slit
Like polarization, we limit wave passage through the slit to a vertical plane
However, the wave will diffract which changes the horizontal position
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Heisenberg Uncertainty Principle Even though vertical
position is fairly certain, change in horizontal position means a change in momentum because of the change in the horizontal component of the velocity
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Heisenberg Uncertainty Principle Applied to energy and
time: The same principle
can be applied to energy versus time
4htE
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Putting It All Together
Unique emission and absorption spectra show that electrons exist at discrete energy levels
The frequency/wavelength of emitted / absorbed light is a function of the electron’s energy level
Since each element has unique electron energy levels, the light it emits/absorbs is unique to that element
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Putting It All Together
Schrödinger developed a wave function, Ψ(x,t), to describe electron position vs. time in hydrogen
Wave functions different for each element
Born gave us the probability of finding an electron at a given point at a given time as |Ψ(x,t)|2
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Putting It All Together
But Heisenberg showed that trying to find the electron is difficult
4hpx
4htE
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Σary Review
Can you describe emission and absorption spectra and understand their significance for atomic structure?
Can you explain the origin of atomic energy levels in terms of the ‘electron in a box’ model?
Can you describe the hydrogen atom according to Schrödinger?
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Σary Review
Can you do calculations involving wavelengths of spectral lines and energy level differences?
Can you outline the Heisenberg Uncertainty Principle in terms of position-momentum and time-energy?
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IB Assessment Statements
Topic 13.1, Quantum Physics: Atomic Spectra and Atomic Energy States
13.1.8. Outline a laboratory procedure for producing and observing atomic spectra.
13.1.9. Explain how atomic spectra provide evidence for the quantization of energy in atoms.
13.1.10. Calculate wavelengths of spectral lines from energy level differences and vice versa.
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IB Assessment Statements
Topic 13.1, Quantum Physics: Atomic Spectra and Atomic Energy States
13.1.11. Explain the origin of atomic energy levels in terms of the “electron in a box” model.
13.1.12. Outline the Schrödinger model of the hydrogen atom.
13.1.13. Outline the Heisenberg uncertainty principle with regard to position-momentum and time-energy.
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QUESTIONS?
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Homework
#1-15