Quantum physics (quantum theory, quantum mechanics)

1
Quantum physics(quantum theory, quantum
mechanics)

• Part 2

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Summary of 1st lecture

• classical physics explanation of black-body
  radiation failed
• Plancks ad-hoc assumption of energy quanta
• of energy Equantum h?, modifying Wiens
  radiation law, leads to a radiation spectrum
  which agrees with experiment.
• old generally accepted principle of natura non
  facit saltus violated
• Opens path to further developments

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Outline

• Introduction
• photoelectric effect
• observation
• studies
• Einsteins explanation
• cathode rays and electrons
• models of the atom
• Summary

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Cathode rays

• Cathode rays
• During 2nd half of 19th century, many physicists
  do experiments with discharge tubes, i.e.
  evacuated glass tubes with electrodes at ends,
  electric field between them (HV)
• 1869 discharge mediated by rays emitted from
  negative electrode (cathode)
• rays called cathode rays

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Studies of cathode rays

• study of cathode rays by many physicists find
• cathode rays appear to be particles
• cast shadow of opaque body
• deflected by magnetic field
• negative charge
• eventually realized
• cathode rays were
• particles named
• them electrons

6
Photoelectric effect

• 1887 Heinrich Hertz
• In experiments on e.m. waves, unexpected new
  observation when receiver spark gap is shielded
  from light of transmitter spark, the maximum
  spark-length became smaller
• Further investigation showed
• Glass effectively shielded the spark
• Quartz did not
• Use of quartz prism to break up light into
  wavelength components ? find that wavelenght
  which makes little spark more powerful was in the
  UV

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Hertz and p.e. effect

• Hertz conclusion I confine myself at present
  to communicating the results obtained, without
  attempting any theory respecting the manner in
  which the observed phenomena are brought about

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Photoelectric effect further studies

• 1888 Wilhelm Hallwachs (1859-1922) (Dresden)
• Performs experiment to elucidate effect observed
  by Hertz
• Clean circular plate of Zn mounted on insulating
  stand plate connected by wire to gold leaf
  electroscope
• Electroscope charged with negative charge stays
  charged for a while but if Zn plate illuminated
  with UV light, electroscope loses charge quickly
• If electroscope charged with positive charge
• UV light has no influence on speed of charge
  leakage.
• But still no explanation
• Calls effect lichtelektrische Entladung
  (light-electric discharge)

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Hallwachs experiments

• photoelectric discharge
• photoelectric excitation

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Further studies of photoelectric effect

• 1899 J.J. Thomson studies of photoelectric
  effect
• Modifies cathode ray tube make metal surface to
  be exposed to light the cathode in a cathode ray
  tube
• Finds that particles emitted due to light are the
  same as cathode rays (same e/m)

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More studies of p.e. effect

• 1902 Philipp Lenard
• Studies of photoelectric effect
• Measured variation of energy of emitted
  photoelectrons with light intensity
• Use retarding potential to measure energy of
  ejected electrons photo-current stops when
  retarding potential reaches Vstop
• Surprises
• Vstop does not depend on light intensity
• energy of electrons does depend on color
  (frequency) of light

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Explanation of photoelectric effect

• 1905 Albert Einstein (1879-1955) (Bern)
• Gives explanation of observation relating to
  photoelectric effect
• Assume that incoming radiation consists of light
  quanta of energy hf (h Plancks constant,
  ffrequency)
• ? electrons will leave surface of metal with
  energy
• E hf W W work function energy
  necessary to get electron out of the metal
• When cranking up retarding voltage until current
  stops, the highest energy electrons must have had
  energy eVstop on leaving the cathode

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Photoelectric effect

• ? Minimum light frequency for a given metal, that
  for which quantum of energy is equal to work
  function
• Therefore eVstop hf W
• 1906 1916 Robert Millikan (1868-1963) (Chicago)
• Did not accept Einsteins explanation
• Tried to disprove it by precise measurements
• Result confirmation of Einsteins theory,
• measurement of h with 0.5 precision
• 1923 Arthur Compton (1892-1962)(St.Louis)
• Observes scattering of X-rays on electrons

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Cathode rays

• Cathode rays
• During 2nd half of 19th century, many physicists
  do experiments with discharge tubes, i.e.
  evacuated glass tubes with electrodes at ends,
  electric field between them (HV)
• 1869 discharge mediated by rays emitted from
  negative electrode (cathode)
• rays called cathode rays

17
Studies of cathode rays

• study of cathode rays by many physicists find
• cathode rays appear to be particles
• cast shadow of opaque body
• deflected by magnetic field
• negative charge
• eventually realized
• cathode rays were
• particles named
• them electrons

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Electron, contd

• 1897 three experiment measure charge/mass, all
  with improved vacuum
• All measure charge/mass to similar value
• Assuming value for charge that of H ion,
  concludes that charge carrying entity is about
  2000 times smaller than H atom
• Cathode rays part of atom?

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J. J. Thomsons conclusion

• 1897 Joseph John Thomson (1856-1940) (Cambridge)
• Bold conclusion we have in the cathode rays
  matter in a new state, a state in which the
  subdivision of matter is carried very much
  further than in the ordinary gaseous state a
  state in which all matter... is of one and the
  same kind this matter being the substance from
  which all the chemical elements are built up.

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Models of Atom

• J.J. Thomsons model
• Plum pudding or raisin cake model
• atom sphere of positive charge
• (diameter ?10-10 m),
• with electrons embedded in it, evenly
  distributed (like raisins in cake)
• i.e. electrons are part of atom, can be kicked
  out of it atom no longer indivisible!

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WHAT IS INSIDE AN ATOM?

• THOMSON'S MODEL OF ATOM
• (RAISIN CAKE MODEL)
• atom sphere of positive charge (diameter
  ?10-10 m),
• with electrons embedded in it, evenly
  distributed (like raisins in cake)
• Geiger Marsdens SCATTERING EXPERIMENT
• (Geiger, Marsden, 1906 - 1911) (interpreted by
  Rutherford, 1911)
• get particles from radioactive source
• make beam of particles using collimators
  (lead plates with holes in them, holes aligned in
  straight line)
• bombard foils of gold, silver, copper with beam
  
• measure scattering angles of particles with
  scintillating screen (ZnS) .

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Geiger Marsdens scattering experiment

• Geiger, Marsden, 1906 - 1911
• make beam of particles using radioactive
  source
• bombard foils of gold, silver, copper with beam
  
• measure scattering angles of particles.

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Geiger Marsden experiment result

• most particles only slightly deflected (i.e. by
  small angles), but some by large angles - even
  backward
• this did NOT agree with expectations from Thomson
  model (only small angles expected),
• but did agree with that
• expected from scattering
• on small, dense, positively
• charged nucleus

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• Rutherfords scattering experiment
• Results can be explained only if one assumes that
  there is a massive positively charged nucleus in
  the middle of atom
• Rutherfords planetary model
• Electrons orbit a tiny positive nucleus that has
  gt99.9 of the mass

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Rutherford model

• planetary model of atom
• positive charge concentrated in nucleus (lt10-14
  m)
• negative electrons in orbit around nucleus at
  distance ?10-10 m
• electrons bound to nucleus by electromagnetic
  force.

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Rutherfords atom, contd

• problem with Rutherford atom
• according to theory of electromagnetism,
  accelerated electron emits electromagnetic
  radiation
• electron loses energy by radiation ? orbit
  decays,
• atoms would be unstable (lifetime lt 10-10 s)
• ? we would not exist to think about this!!
• This problem later solved by Quantum Mechanics

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Early Models of the Atom

• Plum-pudding model electrons distributed in
  positively charged materials.

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Rutherfords Experiment

• Rutherford examined the scattering of alpha
  particles from thin metal foils.
• Thompsons model predicts relatively small
  deflections of the alpha particles by the atoms
  in the foil.

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Reality Check

• What was observed?
• Strong repulsive forces.
• Many backward scattered alphas.
• Atoms appear to have a heavy positively charged
  core.

v
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The New Atomic Model

• Model that emerged
• Heavy positively charged core ? nucleus
• Electrons orbiting the nucleus
• Size of orbits much larger than nucleus.

But there were still problems.
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Visible Quanta

• Emission ( absorption) Spectra
• Discrete wavelengths (energies)
• Key to understanding atomic structure.

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Bohr Model of Atoms

• Electrons moved around nucleus only in certain
  stable orbits.
• They emitted (absorbed) light only when they
  changed from one orbital to another.
• Orbits have quanta of angular momenta. L nh/2?
• Orbit radius increases with energy rn n2 r1
  (r1 .529 x 10-10 m)

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Emission Spectra
R 1.097 x 107 m-1 n 1, 2, 3, m m1,
m2, m3
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Emission Spectra
Lyman n 1
Balmer n 2
Paschen n 3
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Atomic Energy Levels

• En Z2/n2 E1
• Hydrogen
• En - 13.6 eV/n2

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Capa 6
Determine the wavelength of the fifth Lyman line
(n 6 to n 1 transition).
E1 -13.6 eV E6 -0.378 eV hf E6 - E1 hf
-.378 - -13.6 eV hf 13.22 eV
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Capa 6
Determine the wavelength of the fifth Lyman line
(n 6 to n 1 transition).
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Capa 9
What is the longest wavelength light capable of
ionizing a hydrogen atom in the n 5 state?

• hc/?E
• hc/(0-E5)
• hc/.544 eV1.6x10-19 J/eV
• 1.98x10-25Jm/8.7x10-20 J
• 2.27 x 10-6 m

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deBroglies Atom

• The mystery created by Bohrs model of the atom,
  why were some orbits stable?, was solved by
  deBroglies hypothesis that particles are also
  waves.
• Stable orbits were those for which an integral
  number of wavelengths fit into the diameter of
  the orbit (2?rn n?)
• All other orbits, the waves destructively
  interfered and were not stable.
• Leads naturally to quantized angular momentum (L
  nh/2?)

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Atomic Model

• Electrons moved around nucleus only in certain
  stable orbits.
• Stable orbits are those in which an integral
  number of wavelengths fit into the diameter of
  the orbit (2?rn n?)
• They emitted (absorbed) light only when they
  changed from one orbital to another.
• Orbits have quanta of angular momenta. L nh/2?
• Orbit radius increases with energy rn n2 r1
  (r1 .529 x 10-10 m)

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Atomic Energy Levels

• En Z2/n2 E1
• Hydrogen
• En - 13.6 eV/n2

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Emission Absorption

• Energy is conserved.
• E? ?Eatom ?Ef - ?Ei
• Photon energy hf hc/?
• Absorption ? photon disappears a electron in the
  atom changes from a lower energy level to a
  higher energy level.
• Emission ? an electron in atom goes from higher
  energy level to a lower energy level. This
  change in energy is the energy of the photon.

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Emission Spectra
R 1.097 x 107 m-1 n 1, 2, 3, m n1,
n2, n3
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Quantum Mechanics of the Hydrogen Atom

• En -13.6 eV/n2,
• n 1, 2, 3, (principal quantum number)
• Orbital quantum number
• L 0, 1, 2, n-1,
• Magnetic quantum number -l ? m ? l, (there are
  2l1 possible values of m)
• Spin quantum number ms ?½

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Multi-electron Atoms

• Similar quantum numbers but energies are
  different.
• No two electron can have the same set of quantum
  numbers.
• These two assumptions can be used to motivate
  (partially predict) the periodic table of the
  elements.

46
Predicting the Periodic Table
n 1, L 0, ml 0, ms ½ ? 2 electrons
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Predicting the Periodic Table
Element electrons electrons Highest Energy Level Highest Energy Level Highest Energy Level Highest Energy Level
Tot. Val. n L mL mS
H 1 1 1 0 0 ½
He 2 2 1 0 0 -½
Li 3 1 2 0 0 ½
Be 4 2 2 0 0 -½
B 5 3 2 1 -1 ½
C 6 4 2 1 -1 -½
N 7 5 2 1 0 ½
O 8 6 2 1 0 -½
F 9 7 2 1 1 ½
Ne 10 8 2 1 1 -½
H
He
Li
Be
B
C
N
O
F
Ne
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Predicting the Periodic Table
Element electrons electrons Highest Energy Level Highest Energy Level Highest Energy Level Highest Energy Level
Tot. Val. n L mL mS
Na 11 1 3 0 0 ½
Mg 12 2 3 0 0 -½
Al 13 3 3 1 -1 ½
Si 14 4 3 1 -1 -½
P 15 5 3 1 0 ½
S 16 6 3 1 0 -½
Cl 17 7 3 1 1 ½
Ar 18 8 3 1 1 -½
H
He
Li
Be
B
C
N
O
F
Ne
Na
Mg
Al
Si
P
S
Cl
Ar
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Atomic Energy Levels
n 4, L 1
n 3, L 2
n 4, L 0
n 3, L 0,1
Energy depends on n and on L2
n 2, L 0,1
n 1, L 0
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Predicting the Periodic Table
Element electrons electrons Highest Energy Level Highest Energy Level Highest Energy Level Highest Energy Level
Tot. Val. n L mL mS
Sc 21 3 3 2 -2 ½
Ti 22 4 3 2 -2 -½
V 23 5 3 2 -1 ½
Cr 24 6 3 2 -1 -½
Mn 25 7 3 2 0 ½
Fe 26 8 3 2 0 -½
Co 27 9 3 2 1 ½
Ni 28 10 3 2 1 -½
Cu 29 11 3 2 2 ½
Zn 30 12 3 2 2 -½
H
He
Li
Be
B
C
N
O
F
Ne
Na
Mg
Al
Si
P
S
Cl
Ar
K
Ca
Ga
Ge
As
Se
Br
Kr
Sc
Ti
Mn
Fe
Co
Ni
Cu
Zn
V
Cr
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Heisenberg Uncertainty Principle

• Impossible to know both the position and the
  momentum of a particle precisely.
• A restriction (or measurement) of one, affects
  the other.
• ?x ?p ? h/(2?)
• Similar constraints apply to energy and time.
• ?E ?t ? h/(2?)

EXAMPLE If an electron's position can be
measured to an accuracy of 1.9610-8 m, how
accurately can its momentum be known?
?x ?p ? h/(2?) ? ?p h/(2??x) ?p 6.63x10-34
Js /(2? 1.96x10-8 m) 5.38 x 10-27 N s
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Quantum Mechanics of the Hydrogen Atom

• En -13.6 eV/n2,
• n 1, 2, 3, (principal quantum number)
• Orbital quantum number
• l 0, 1, 2, n-1,
• Angular Momentum, L v l(l1) (h/2?)
• Magnetic quantum number - l ? m ? l, (there are
  2 l 1 possible values of m)
• Spin quantum number ms ?½

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Multi-electron Atoms

• Similar quantum numbers but energies are
  different.
• No two electron can have the same set of quantum
  numbers.
• These two assumptions can be used to motivate
  (partially predict) the periodic table of the
  elements.

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Predicting the Periodic Table
n 1, L 0, ml 0, ms ½ ? 2 electrons
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Predicting the Periodic Table
Element electrons electrons Highest Energy Level Highest Energy Level Highest Energy Level Highest Energy Level
Tot. Val. n L mL mS
H 1 1 1 0 0 ½
He 2 2 1 0 0 -½
Li 3 1 2 0 0 ½
Be 4 2 2 0 0 -½
B 5 3 2 1 -1 ½
C 6 4 2 1 -1 -½
N 7 5 2 1 0 ½
O 8 6 2 1 0 -½
F 9 7 2 1 1 ½
Ne 10 8 2 1 1 -½
H
He
Li
Be
B
C
N
O
F
Ne
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Predicting the Periodic Table
Element electrons electrons Highest Energy Level Highest Energy Level Highest Energy Level Highest Energy Level
Tot. Val. n L mL mS
Na 11 1 3 0 0 ½
Mg 12 2 3 0 0 -½
Al 13 3 3 1 -1 ½
Si 14 4 3 1 -1 -½
P 15 5 3 1 0 ½
S 16 6 3 1 0 -½
Cl 17 7 3 1 1 ½
Ar 18 8 3 1 1 -½
H
He
Li
Be
B
C
N
O
F
Ne
Na
Mg
Al
Si
P
S
Cl
Ar
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Atomic Energy Levels
n 4, L 1
n 3, L 2
n 4, L 0
n 3, L 0,1
Energy depends on n and on L
n 2, L 0,1
n 1, L 0
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Predicting the Periodic Table
Element electrons electrons Highest Energy Level Highest Energy Level Highest Energy Level Highest Energy Level
Tot. Val. n L mL mS
Sc 21 3 3 2 -2 ½
Ti 22 4 3 2 -2 -½
V 23 5 3 2 -1 ½
Cr 24 6 3 2 -1 -½
Mn 25 7 3 2 0 ½
Fe 26 8 3 2 0 -½
Co 27 9 3 2 1 ½
Ni 28 10 3 2 1 -½
Cu 29 11 3 2 2 ½
Zn 30 12 3 2 2 -½
H
He
Li
Be
B
C
N
O
F
Ne
Na
Mg
Al
Si
P
S
Cl
Ar
K
Ca
Ga
Ge
As
Se
Br
Kr
Sc
Ti
Mn
Fe
Co
Ni
Cu
Zn
V
Cr
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• Exclusion Principle
• No two electrons in an atom can occupy the same
  quantum state.
• When there are many electrons in an atom, the
  electrons fill the lowest energy states first
• lowest n
• lowest l
• lowest ml
• lowest ms
• this determines the electronic structure of
  atoms