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TRANSCRIPT
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Rutherford’s Model of the Atom
• Most of the atom is empty space.
• Most of the atom’s mass and + charge is located at the center of the atom.
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Next
• Bohr’s model
• How a laser works
• X-ray production
• Wave-particle duality
• Quantum Physics
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Exercise
• A radiostation broadcasts at 89.3 MHz with a radiated power of 43.0 kW.
a) What is the magnitude of the momentum of each photon?
b) How many photons does the radiostation emit each second?
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Exercise
For a certain cathode material in a photoelectric-effect experiment you measure a stopping potential of 1.0V for light for wavelength 600nm, 2.0 V for 400 nm, and 300nm for 300nm. Determine the work function for this material and the value of Planck’s constant.
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Emission spectral
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Things to consider
1. Unique spectral lines for each element.
2. Each spectral line has a particular frequency => particular photon energy
3. Heavy positively charge nucleus in the center of the atom arounded by electrons.
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• Attraction between negative electrons and positived nucleus.
• Rutherford’s proposal
+
- -
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Bohr’s model
• Electrons move around the nucleus at stable orbits without emitting radiation.
• Electron in one of these stable orbit has a definite energy.
• Energy is radiated only when electrons make transitions from high energy orbit to a low energy orbit.
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• Energy is emitted as photons with energy
initial finalhf E E
+
--
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Quantifying the energy spectrum
• Bohr postulate that the angular momentum of an electron revolving around a nucleus is quantized in units of h/2
n e n n
hL m v r n
2
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• Newton’s 2nd law yields
2 2n
e20 n n
1 e vF m
4 r r
2 2
n 0 2e
n hr
m e
2
n0
1 ev
2nh
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• The smallest radius is obtained by setting n = 1, is called the bohr radius.
2
0 0 2e
ha
m e
2n 0r n a
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• Kinetic energy of moving electrons
n
2n e
1K m v
2
2
n0
1 ev
2nh
0
4e
2 2 2
m e18n h
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• Potential energy of electron bound to + nucleus
2
n0 n
1 eU
4 r
2 2
n 0 2e
n hr
m e
4e2 2
0
m e14n h
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Total energy of electron n-th orbital
n n n
4e2 2
0
E K U
m e18n h
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Energy level diagram
• The possible energies which electrons in the atom can have is depicted in an energy level diagram.
1E
2E
3E4E
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• In 1958, Charles Townes and Arthur Schawlow theorized about a visible laser, an invention that would use infrared and/or visible spectrum light.
• Light Amplification by Stimulated Emission of Radiation- (LASER).
• Properties of Lasers– Produce monochromatic light of extremely high
intensity.
Bohr’s model and the operation of the Laser
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Bohr’s model and the operation of the Laser
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Bohr’s model and the operation of the Laser
1E
2E
3E4E
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Bohr’s model and the operation of the Laser
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Bohr’s model and the operation of the Laser
1E
2E
3E4E
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Bohr’s model and the operation of the Laser
1E
2E
3E4E
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Bohr’s model and the operation of the Laser
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Bohr’s model and the operation of the Laser
1E
2E
3E4E
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Bohr’s model and the operation of the Laser
1E
2E
3E4E
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Bohr’s model and the operation of the Laser
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Bohr’s model and the operation of the Laser
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X-ray production
• Properties of x-rays.– High penetration => High energy =>High
frequency.
• X-rays are produced when acelerated electrons strike a heavy metalic target (W).
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Operation of an X-ray machine
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X-ray production on the atomic scale
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X-ray production on the atomic scale
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ALLAN MACLEOD CORMACK : 1924-1998
• Lecturer in Physics, University of Cape Town, 1950 - 1957
• Nobel Prize for Physiology and Medicine, 1979
• Development of the CAT scanner (Computer Aided Tomography).
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SIR AARON KLUG
• MSc student in Physics, University of Cape Town, 1946? - 1948
• Nobel Prize for Chemistry 1982
• Probing the properties of macromolecules (DNA) with x-rays.
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Wave-Particle Duality
• In the Bohr model, electrons orbit the atomic nucleus in stable orbits.
• What makes an orbit stable?
• Louis de Broglie proposed that subatomic particles, such as electron, could exhibit some wave behaviour.
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De Broglie’s Wave Particle Model
• Similar to photons
photonphoton
hp
• Wavelength of particle is related to its momentum by
partic lepartic le
hp
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where
partic le
hmv
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Bohr’s model with wavy electrons
• An electron orbit is stable if an integer number of de Broglie standing wave can fit into it.
+r
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2 r
• General
n2 r n
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• Yields
n n n nn
h hL p r r n
2
partic lepartic le
hp
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Wave Phenomenon
• Phenomenon associated with waves include:
1. Interference effects
2. Reflection
3. Refraction
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Interference
• Superposition of wave pulse
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Davidson-Germer experiment
• Aim: to test if particle (electrons) exhibit properties of waves i.e. Inteference.
• Young’s experiment to find interference pattern due to particle wave interaction.
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Electron diffraction pattern
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Scanning electron microscope images
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Theory of Quantum mechanics
• Understanding the nature of the particle waves.
• Heisenbergs uncertainty principle
• Schroedinger’s equation.
• Spin-off of quantum theory in the today’s world
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Quantum Scale
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Heisenbergs Uncertainty Principle
• On the scale on life size object a system is not influenced by measurements on a system (Deterministic system).
• On the atomic scale a measurement on a system will influence on it.
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Finding the location of an electron
-
hp
ep m v
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Finding the location of an electron
-
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The Uncertainty Principle
• Act of measurement influences the electron’s state– Neither the position nor the momentum of a
particle can be determined with arbitrary great precision
x
hx p
2
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Schroedinger’s Wave Equation
x
hx p
2
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• Heisenberg Uncertainty + de Broglie waves = Schroedinger’s probabily waves function
2 2
2
d (x)V(x) (x) E (x)
2m dx
(x) A(cos kx i sinkx)
(x) Probability of finding a partic le at location x
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Schroedinger’s solution to the electron orbitals in the
atom