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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.
Next
• Bohr’s model
• How a laser works
• X-ray production
• Wave-particle duality
• Quantum Physics
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?
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.
Emission spectral
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.
• Attraction between negative electrons and positived nucleus.
• Rutherford’s proposal
+
- -
--
-
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.
• Energy is emitted as photons with energy
initial finalhf E E
+
--
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
• 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
• 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
• 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
• 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
Total energy of electron n-th orbital
n n n
4e2 2
0
E K U
m e18n h
Energy level diagram
• The possible energies which electrons in the atom can have is depicted in an energy level diagram.
1E
2E
3E4E
• 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
Bohr’s model and the operation of the Laser
Bohr’s model and the operation of the Laser
1E
2E
3E4E
Bohr’s model and the operation of the Laser
Bohr’s model and the operation of the Laser
1E
2E
3E4E
Bohr’s model and the operation of the Laser
1E
2E
3E4E
Bohr’s model and the operation of the Laser
Bohr’s model and the operation of the Laser
1E
2E
3E4E
Bohr’s model and the operation of the Laser
1E
2E
3E4E
Bohr’s model and the operation of the Laser
Bohr’s model and the operation of the Laser
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).
Operation of an X-ray machine
X-ray production on the atomic scale
X-ray production on the atomic scale
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).
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.
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.
De Broglie’s Wave Particle Model
• Similar to photons
photonphoton
hp
• Wavelength of particle is related to its momentum by
partic lepartic le
hp
where
partic le
hmv
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
2 r
• General
n2 r n
• Yields
n n n nn
h hL p r r n
2
partic lepartic le
hp
Wave Phenomenon
• Phenomenon associated with waves include:
1. Interference effects
2. Reflection
3. Refraction
Interference
• Superposition of wave pulse
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.
Electron diffraction pattern
Scanning electron microscope images
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
Quantum Scale
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.
Finding the location of an electron
-
hp
ep m v
Finding the location of an electron
-
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
Schroedinger’s Wave Equation
x
hx p
2
• 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
Schroedinger’s solution to the electron orbitals in the
atom