2. SCOPE OF STUDY
7 sub- topics students should learn and understand :
Electrons
J.J. Thompson’s experiment, Milikan experiment
De Broglie Relation
Wave-particle duality; the Principle of Complementarily
Wave nature of matter
Electron diffraction
Planck’s quantum hypothesis
3. introduction
Quantum Physics:
developed early 20th century, in response to shortcomings of
classical physics in describing certain phenomena (blackbody
radiation, photoelectric effect, emission and absorption spectra…)
describes “small” objects (e.g. atoms and their constituents)
QP is “weird and counterintuitive”
“Those who are not shocked when they first come across quantum
theory cannot possibly have understood it” (Niels Bohr)
“Nobody feels perfectly comfortable with it “ (Murray Gell-Mann)
“I can safely say that nobody understands quantum mechanics”
(Richard Feynman)
4. introduction
Quantum physics is basically the recognition that there is less difference
between waves and particles than was thought before.
Key insights:
• light can behave like a particle
• particles (e.g. electrons) are indistinguishable
• particles can behave like waves (or wave packets)
• waves gain or lose energy only in "quantized amounts“
• detection (measurement) of a particle ⇒ wave will
suddenly into a new wave
• quantum mechanical interference – amplitudes add
• QP is intrinsically probabilistic
• what you can measure is what you can know
change
5. electrons
Tiny and very
light particles
Particles
Negative electric
charge
PROPERTIES
PROPERTIES
Mass : 9.11 ×
Has spin creates
10 −31 kilograms.
magnetic field
Wave
6. electrons
Electrons carry one unit of negative elementary charge.
Since an electric or magnetic field exerts a force on electrons, it a ffects their
motion.
In spite of the fact that electric fields are everywhere around us, in every day
life we do not directly observe the motion of electrons.
However, such observations are possible with a device called a cathode-ray
tube (CRT), which is just a technical name for a tube present in most of TV sets
or computer monitors.
8. J.J.THOMSON’S EXPERIMENT
J.J. Thomson was born on December 18, 1856 in Manchester.
The major accomplishment of J.J. Thomson was the discovery of the electron.
An electron is a particle that is smaller than an atom and is negatively charged.
Thomson created the plum pudding model, which was the way he thought the
structure of the atom was made up.
The tiny negatively charged atoms were embedded in a positively charged
cloud.
(J.J. Thomsons Atom Model)
(J.J. Thomsons Atom Model)
10. MILIKAN EXPERIMENT
Millikan made numerous momentous discoveries.
Mainly in the fields of electricity, optics, and molecular physics.
A major success was the accurate determination of the charge carried by an
electron, using the elegant "falling-drop method".
He also proved that this quantity was a constant for all electrons (1910), thus
demonstrating the atomic structure of electricity.
He verified experimentally Einstein's all-important photoelectric equation, and
made the first direct photoelectric determination of Planck's constant.
11. MILIKAN EXPERIMENT
Droplets of oil could electrify themselves owing to friction when they were
atomised.
They could also get the charge by X-raying.
Millikan put some electric potential difference on plates generating electric field
between them.
12. DE BROGLIE RELATION
PHOTON
PHOTON
A particle representing a quantum of light or other
electromagnetic radiation regarded as a particle with
zero rest mass and charge, unit spin, and energy equal
to the product of the frequency of the radiation and
the Planck constant.
14. DE BROGLIE RELATION
In 1923, Frenchman Louis de Broglie proposed the particles of matter also had
wavelengths and could behave as waves, just as photons did.
He stated that under special relativity :
The photon, a particle of energy, had a wavelength associated with it.
The electron, particles of matter, such as electrons also had a wavelength.
15. DE BROGLIE RELATION
Planck’s constant
6.63 x 10-34 J/s
momentum
mass
λ = h/p = h/mv
λ = h/p = h/mv
velocity
wavelenght
de Broglie wavelength
16. DE BROGLIE RELATION
Example: The de Broglie Wavelength of an Electron and a Baseball
Determine the de Broglie wavelength of (a) an electron moving at a speed of
6.0x106 m/s and (b) a baseball (mass = 0.15 kg) moving at a speed of 13 m/s.
Solution :
( 6.63 × 10 J s) = 1.2 × 10
λ = h p=
( 9.1× 10 kg )( 6.0 × 10 m s)
( 6.63 ×10 J s ) = 3.3 ×10
λ=h p=
− 34
− 31
− 10
m
−34
m
6
−34
( 0.15 kg )(13 m s )
17. Wave particle duality
HISTORY
In 1927, Neils Bohr formulated his "principle of complementarity*' which
In 1927, Neils Bohr formulated his "principle of complementarity*' which
brought together the wave like properties of matter and the particle like
brought together the wave like properties of matter and the particle like
properties of light into aa coherent theoretical framework often called
properties of light into
coherent theoretical framework often called
"wave-particle duality" or the "Copenhagen interpretation."
"wave-particle duality" or the "Copenhagen interpretation."
19. Wave particle duality
His starting point was the impossibility to distinguish satisfactorily
between the actual behavior of atomic objects, and their interaction with the
measuring instruments that serve to define the conditions under which the
phenomena appear.
Examine light with one instrument, the argument went, and it undulates
like a wave; select another and it scatters like a particle.
His conclusion was that evidence obtained under different experimental
conditions cannot be comprehended within a single picture, but must be
regarded as complementary in the sense that only the totality of the
phenomenon exhausts the possible information about the objects.
20. Wave particle duality
Wave Particle Duality
Wave Particle Duality
Principle of Complementarity
Principle of Complementarity
A system can exhibit wave-like behavior and particleA system can exhibit wave-like behavior and particlelike behavior, but no experiment could demonstrate both
like behavior, but no experiment could demonstrate both
behaviors simultaneously.
behaviors simultaneously.
21. Wave NATURE OF MATTER
Remember that ::
Remember that
Matter has dual character
Matter has dual character
With every body there is connected some wave.
With every body there is connected some wave.
The lower mass and the lower velocity the body has, the
The lower mass and the lower velocity the body has, the
longer is its wave.
longer is its wave.
Louis De Broglie created the theory of the dual nature of matter.
Louis De Broglie created the theory of the dual nature of matter.
22. Wave NATURE OF MATTER
Just as light sometimes behaves like a particle, matter sometimes
behaves like a wave.
The wavelength of a particle of matter is
.
This wavelength is extraordinarily small.
23. Wave NATURE OF MATTER
Example: Wavelength of a ball.
Calculate the de Broglie wavelength of a 0.20-kg ball moving with a speed
of 15 m/s.
Solution:
λ = h/p = 2.2 x 10-34 m.
24. Wave NATURE OF MATTER
Example : Wavelength of an electron.
Determine the wavelength of an electron that has been accelerated
through a potential difference of 100 V.
Solution:
The kinetic energy of the electron is classical. Its speed is found
from conservation of energy: ½ mv2 = eV, so v = 5.9 x 106 m/s.
The wavelength is then h/p = 1.2 x 10-10 m; roughly the size of an
atom.
26. PLANCK’S QUANTUM
HYPOTHESIS
He suggested that the energy of atomic oscillations within atoms cannot
have an arbitrary value; it is related to the frequency:
The constant h is now called Planck’s constant and n is called aa
The constant h is now called Planck’s constant and n is called
quantum number (discrete number)
quantum number (discrete number)
27. PLANCK’S QUANTUM
HYPOTHESIS
Planck found the value of his constant by fitting blackbody curves
to the formula
where : I (λ , T) = radiation intensity as a function of wavelength at the
temperature, T
k = Boltzman’s constant
c = speed of light
h = Planck’s constant
28. PLANCK’S QUANTUM
HYPOTHESIS
Planck’s proposal was that the energy of an oscillation had to be an
integral multiple of hf. This is called the quantization of energy.
The quantum hypothesis states that the energy of an oscillator can be E
= hf, or 2hf, or 3hf and so on but there cannot be vibrations with
energies between these values.
Energy would not be a continuous quantity.
29. Electron diffraction
DEFINITION
DEFINITION
A collective scattering phenomenon with
A collective scattering phenomenon with
electrons
electrons
being
being
(nearly
(nearly
elastically)
elastically)
scattered by atoms in a regular array
scattered by atoms in a regular array
(crystal).
(crystal).
30. Electron diffraction
This can be understood in analogy to the Huygens principle for the
diffraction of light.
The incoming plane electron wave interacts with the atoms, and
secondary waves are generated which interfere with each other.
This occurs either constructively (reinforcement at certain
scattering angles generating diffracted beams) or destructively
(extinguishing of beams).
As in X-ray diffraction (XRD), the scattering event can be
described as a reflection of the beams at planes of atoms (lattice
planes).
31. Electron diffraction
The Bragg law gives the relation between interplanar distance d and
The Bragg law gives the relation between interplanar distance d and
diffraction angle θ:
diffraction angle θ:
n λ = 2 d sin θ
n λ = 2 d sin θ
32. Electron diffraction
Example :
Assume that the electrons strike perpendicular to the surface of a solid,
and that their energy is low, K = 100 eV, so that they interact only with
the surface layer of atoms. If the smallest angle at which a diffraction
maximum occurs is at 24°, what is the separation d between the atoms on
the surface?
Solution:
The smallest angle will occur when d sin θ = λ. The electrons are not
relativistic, so the wavelength can be found from the kinetic energy: λ =
0.123 nm. Then the spacing is λ/sin θ = 0.30 nm.
33. ~ ~ The end ~ ~
::
PrOBLeMS
onLY eXisT iN
tHe
hUmaN
MinD ::
