Quantum physics (quantum theory, quantum mechanics) - PowerPoint PPT Presentation

Loading...

PPT – Quantum physics (quantum theory, quantum mechanics) PowerPoint presentation | free to download - id: 4d4934-OGQ1N



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Quantum physics (quantum theory, quantum mechanics)

Description:

(quantum theory, quantum mechanics) Part 2 Summary of 1st lecture classical physics explanation of black-body radiation failed Planck s ad-hoc assumption of ... – PowerPoint PPT presentation

Number of Views:74
Avg rating:3.0/5.0
Slides: 60
Provided by: Horst3
Learn more at: http://www.hep.fsu.edu
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Quantum physics (quantum theory, quantum mechanics)


1
Quantum physics(quantum theory, quantum
mechanics)
  • Part 2

2
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

3
Outline
  • Introduction
  • photoelectric effect
  • observation
  • studies
  • Einsteins explanation
  • cathode rays and electrons
  • models of the atom
  • Summary

4
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

5
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

7
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

8
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)

9
Hallwachs experiments
  • photoelectric discharge
  • photoelectric excitation

10
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)

11
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

12
(No Transcript)
13
(No Transcript)
14
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

15
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

16
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

18
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?

19
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.

20
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!

21
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) .

22
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.

23
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

24
  • 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

25
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.

26
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

27
Early Models of the Atom
  • Plum-pudding model electrons distributed in
    positively charged materials.

28
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.

29
Reality Check
  • What was observed?
  • Strong repulsive forces.
  • Many backward scattered alphas.
  • Atoms appear to have a heavy positively charged
    core.

v
30
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.
31
Visible Quanta
  • Emission ( absorption) Spectra
  • Discrete wavelengths (energies)
  • Key to understanding atomic structure.

32
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)

33
Emission Spectra
R 1.097 x 107 m-1 n 1, 2, 3, m m1,
m2, m3
34
Emission Spectra
Lyman n 1
Balmer n 2
Paschen n 3
35
Atomic Energy Levels
  • En Z2/n2 E1
  • Hydrogen
  • En - 13.6 eV/n2

36
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
37
Capa 6
Determine the wavelength of the fifth Lyman line
(n 6 to n 1 transition).
38
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

39
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?)

40
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)

41
Atomic Energy Levels
  • En Z2/n2 E1
  • Hydrogen
  • En - 13.6 eV/n2

42
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.

43
Emission Spectra
R 1.097 x 107 m-1 n 1, 2, 3, m n1,
n2, n3
44
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

45
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
47
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
48
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
49
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
50
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
51
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
52
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

53
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.

54
Predicting the Periodic Table
n 1, L 0, ml 0, ms ½ ? 2 electrons
55
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
56
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
57
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
58
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
59
  • 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
About PowerShow.com