Quantum Physics

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Quantum Physics
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Physics History
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Physics History
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Physics History
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Why do the stars shine?why do the elements
exhibit the order thats so apparent in the
periodic table? How do transistors and
microelectronic devices work?why does copper
conduct electricity but glass doesnt?
Why?
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Quantum Physics
Particle Theory of Light
De Broglie Hypothesis
Photo-electric effect
Compoton effect
Hydrogen spectrum
Uncertainty
Wave Function
Schrodinger equation and application
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Key words

• Quantum
• Blackbody
• Radiation
• Plancks hypothesis
• The photoelectric effect
• The particle theory or light
• X-rays
• Diffraction
• Photons
• Electromagnetic

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Key words

• The wave properties of particles
• The uncertainty principle
• The scanning tunneling microscope
• Atomic Spectra
• The Bohr Theory of Hydrogen

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27.1 Blackbody Radiation and Plancks Hypothesis
Ultraviolet Catastrophe
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Plancks Hypothesis
In 1900 Planck developed a formula for blackbody
radiation that was in complete agreement with
experiments at all wavelengths . Planck
hypothesized that black body radiation was
produced by submicroscopic charged oscillators,
which he called resonators. The resonators were
allowed to have only certain discrete energies,
En, given by
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27.2 The Photoelectric Effect and The Particle
Theory of Light
1.The Photoelectric Effect
1) saturated current is proportion to intensity
of light
? is fixed,I is proportion to voltage,but
theres a saturated current which is proportion
to intensity of light
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inverse voltage is applied,Ic0. Va is
called cutoff voltage or stopping voltage
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2) initial kinetic energy is proportion to the
frequency of incident light,has no relation with
the intensity of light
3) theres a cutoff frequency (threshold
frequency) to a metal,only when ?gt?o,
theres a current 4) photo current produce
immediately,delay time is not more than 10-9s?

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2.Einstains theory
1)the hypothesis of Einstian
Light has particle nature
Intensity of light
2) Einstian equation
A work function
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Notes a. the initial kinetic energy is
linearly proportion to the frequency of incident
light
b.
Cutoff frequency
While ?ltA/h?,no photoelectric effect
c. instantaneously effect
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3.the wave-particle duality
1) Light has dual nature
2) the energy, momentum and mass
energy
momentum
M00
Mass
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• Example the experiment result is as
  follows,find h

1.oq 2.op 3. op/oq 4. qs/os
solution3
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Example the cutoff ?o6500Å, the light
with ? 4000Å incident on the metal?
(1)the velocity of photoelectrons??
(2)stopping voltage??
Solution
? 6.5105(m/s) (2)
c ??
h 6.6310-34
Va1.19 (V)
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Exampleincident frequency is fixedwev
experimental curve (solid line),and then with
fixed intensity of light,increase the incident
frequency,the experimental curve is as dot
line,find the correct answer in the following
graphs
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27.3 The Compton Effect
1.scattering
light go through medium and propagate in
different direction?
from classic viewthe scatter wavelength
is same with incident wavelength? but in
graphite experiment,we found a change in
wavelength,this is called compoton scatter?
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2.principle
suppose photos collide with electrons without
loss of energy
Energy conservation h?omoc2 h?
mc2 Momentum conservation
c??
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?0, ?min?o
?180, ?max?o 2?c
Compton wavelength
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The explanation to compton effect
1)photon pass some energy to electrons
2)compton effect is strong when the photon act on
the atom with small number atom
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• 3) meaningphoton theory is correct show the
  duality nature of light
• 4) micro particle obey the conservative law
• 5) photoelectric effect, compton effect

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Example with ?o 0.014Å X ray in compton
experiment, find maxmum kinetic energy in
electrons?
solutionfron energy conservation
???,Emax
in fact ?max?o 2?c ,
1.110-13 J
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Example ?o 0.1Å X ray in
experiment?In the direction of 90,find
wavelength? Kinetic energy and momentum of
electron?
solution ? 90
?? ? ?o ?? 0.10.0240.124Å
3.810-15 J
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From momentum conservation
? 90
8.510-23 (SI)
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example?o 0.03Å X ray in experiment, the
velocity of recoil electron ? 0.6c, find (1)the
rate of the scattering energy of electron to its
rest energy (2)the scattering ?? And scattering
? ?
solution (1)the scattering energy
0.25moc2
? ? 0.0434Å
so ? 63.4
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27.4 Line Spectra and Bohr Model
1.the atomic hydrogen spectrum
2.the empirical formula of Balmer
Rydberg constant
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The line spectrum system
Lyman series
ultraviolet
Balmer series
visible
Baschen
infrared
General form
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Physicist Rutherford
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3.Bohr model
?? hypothesis
1) stationary hypothesis electrons can be in
some certain stable orbits
2) quantum transition
3) quantization of angular momentum
?? to hydrogen atom
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Notes 1.Ground state n1 2.excited
state ngt1 3.n2,the first excited
state
4.ionization
5. explanation of hydrogen spectrum
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Examplefind the energy for hydrogen atom giving
longest wavelength in lyman series? 1)1.5ev
2)3.4ev 3)10.2ev 4)13.6ev
solution3 n2-1
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Examplewith 913A violent light,hydrogen atom
can be ionized,find the wavelength expression of
lyman series
solution4
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Examplewith visible light,can we ionized the
first excited state of hydrogen atom?
Solution
Needed enrgy
no
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Example hydrogen atom in third
excited state,find the number of its line after
transition,name its series?
solution
lyman 3 Balmer 2 Pachen 1
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Physicist De Broglie
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27.5 Wave Nature of Particles
chapter 42 Quantum Mechanics
1. De Broglie wavelength
Particle nature of light
Notes1)
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Notes1)
examplea bullet with m0.01kg,v300m/s
h is so small,the wavelength is so small
Its difficulty to measure,behave in particle
nature
On the atomic scale,however,things are quite
different
Me9.110-31,v106, 0.7nm
This wavelength is of the same magnitude as
interatomic spacing in matter,and in diffraction
experiment the phenomena is evidence.
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2) quantization condition of angular momentum of
Bohr is the showing of de broglie wave
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2. experiment
diffraction by electrons
(Thomoson1927)
slit,double slit diffraction
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? Experiment
Davision and Germer experiment
A
?
?
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example (1)the kinetic energy of
electron Ek100eV(2)momentum of bullet
p6.63106kg.m.s-1, find ??
solutionfor the small kinetic
energy,with classic formula
1.23Å
h 6.6310-34
(2)bullet
1.010-40m
conclusionthe wave nature is only
obvious in microparticle,to macroparticle,you
cant detect the effect
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Examplewith 5104V accelerating
voltage,find the ?
solutionwith relativity effect
??1.24108(m/s)
1010-31 (kg)
mo9.1110-31 (kg)
0.0535Å
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Examplesuppose
,kinetic energy equal to its rest energy,
solution2
Examplethe first bohr radius a,electron move
along n track,
solution
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27.6 Heisenbergs Uncertainty Relation
1.uncertainty relation
It states that measured values cant be
assigned to the position and momentum of a
particle simultaneously with unlimited precision.
Notes 1) represent the intrinsic
uncertainties in the measurement of the x
components of and even with best measure
instruments.
2) small size of plancks constant guarantees
uncertainty relation is important only in atomic
scale
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2.the meaning of uncertainty
1)the result of dual nature 2)give the applied
extent of classic mechanics,if h can be ignored
,the uncertainty relation have no use.
3)the intrinsic of uncertainty is that theres a
uncertain action between observer and the object,
It cant be avoided.
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exampleestimate ?vx in hydrogen atom
solution ?x10-10m(the size of atom),
From ? x?px ? h,
so big,velocity and coordinate cant be
determined at the same time?
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example a bullet m0.1kg , ??x10-6 m/s ,find
?x?
solution ? x?px ? h
so small,we can consider it with classic
view (to macro object)
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example?5000Å,??10-3Å,find ?x
solution
from ? x?px ? h,
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Physicist De Broglie
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27.7 Wave Function, Schrodinger Equation

• 1.Schrodinger equation

2.the statistic explanation of wave function
wave view
particle view Bright fringe ??(x,y,z,t)?2 big,
possibility big Dark fringe ??(x,y,z,t)?2
small , possibility small ? ??(x,y,z,t)?2
is proportion to possibility density in this
point.
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The meaning of wave functionits related to the
probability of finding the particle in various
regions
Character single value, consecutive limited, be
one in whole space
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Notes on Schrodinger equation

• EEkEpp2/2mu non relativity form
• From the Solution of equation, E ? can only
  take special value
• ???2 express possibility density
• Quantum condition can be got in natural way,this
  related with atomic state

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2?the application of Schrodinger equation on
hydrogen atom
1) quantum energy
2) quantum of angular momentum
Angular momentum quantum number
3) if in magnetic field
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examplel1,
Examplen3,the possible value of L. and Lz
Solution 1) 3 2) 5
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4) possibility distribution of electron
Solutionfrom schudigder equation
Possibility density
for example to 1S
electron,possibility density
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27.8 Electron Spin Four Quantum Number
1921,(O.Stern) and (W.Gerlach)
proveexcept the orbital motion,theres a spin
Spin angular momentum
z component of s
Spin magnetic number
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in summarythe status of atom is
determined by four quantum number?
(1)principal quantum numbern1,2,3,?
determine the energy of atom?? (2)angular
quantum number l0,1,2,,(n-1)? determine
the angular momentum? (3)magnetic quantum
number ml0,1,2,,l? determine Lz,thats
space quantum property?
(4)spin magnetic quantum number
determine z component of spin angular
momentum
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Physicist Plank