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Atomic Physics

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Chapter 28 Atomic Physics Plum Pudding Model of the Atom J. J. Thomson s Plum Pudding model of the atom: Electrons embedded throughout the a volume of ... – PowerPoint PPT presentation

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Title: Atomic Physics


1
Chapter 28
  • Atomic Physics

2
Plum Pudding Model of the Atom
  • J. J. Thomsons Plum Pudding model of the atom
  • Electrons embedded throughout the a volume of
    positive charge
  • A change from Newtons model of the atom as a
    tiny, hard, indestructible sphere

3
Scattering Experiments
  • The source was a naturally radioactive material
    that produced alpha particles
  • Most of the alpha particles passed though the
    foil
  • A few deflected from their original paths
  • Some even reversed their direction of travel

4
Planetary Model of the Atom
  • Based on results of thin foil scattering
    experiments, Rutherfords Planetary model of the
    atom
  • Positive charge is concentrated in the center of
    the atom, called the nucleus
  • Electrons orbit the nucleus like planets orbit
    the sun

5
Difficulties with the Rutherford Model
  • Atoms emit certain discrete characteristic
    frequencies of electromagnetic radiation but the
    Rutherford model is unable to explain this
    phenomena
  • Rutherfords electrons are undergoing a
    centripetal acceleration and so should radiate
    electromagnetic waves of the same frequency
  • The radius should steadily decrease as this
    radiation is given off
  • The electron should eventually spiral into the
    nucleus, but it doesnt

6
Emission Spectra
  • A gas at low pressure and a voltage applied to it
    emits light characteristic of the gas
  • When the emitted light is analyzed with a
    spectrometer, a series of discrete bright lines
    emission spectrum is observed
  • Each line has a different wavelength and color

7
Emission Spectrum of Hydrogen
  • The wavelengths of hydrogens spectral lines can
    be found from
  • RH 1.097 373 2 x 107 m-1 is the Rydberg
    constant and n is an integer, n 1, 2, 3,
  • The spectral lines correspond to different values
    of n
  • n 3, ? 656.3 nm
  • n 4, ? 486.1 nm

8
Absorption Spectra
  • An element can also absorb light at specific
    wavelengths
  • An absorption spectrum can be obtained by passing
    a continuous radiation spectrum through a vapor
    of the gas
  • Such spectrum consists of a series of dark lines
    superimposed on the otherwise continuous spectrum
  • The dark lines of the absorption spectrum
    coincide with the bright lines of the emission
    spectrum

9
Chapter 28Problem 6
  • In a Rutherford scattering experiment, an
    a-particle (charge 2e) heads directly toward a
    gold nucleus (charge 79e). The a-particle had
    a kinetic energy of 5.0 MeV when very far (r ? 8)
    from the nucleus. Assuming the gold nucleus to be
    fixed in space, determine the distance of closest
    approach.

10
The Bohr Theory of Hydrogen
  • In 1913 Bohr provided an explanation of atomic
    spectra that includes some features of the
    currently accepted theory
  • His model was an attempt to explain why the atom
    was stable and included both classical and
    non-classical ideas

11
The Bohr Theory of Hydrogen
  • The electron moves in circular orbits around the
    proton under the influence of the Coulomb force
    of attraction, which produces the centripetal
    acceleration
  • Only certain electron orbits are stable
  • In these orbits electrons do not emit energy in
    the form of electromagnetic radiation
  • Therefore, the energy of the atom
  • remains constant and classical
  • mechanics can be used to describe
  • the electrons motion

12
The Bohr Theory of Hydrogen
  • Radiation is emitted when the electrons jump
    (not in a classical sense) from a more energetic
    initial state to a lower state
  • The frequency emitted in the jump is related to
    the change in the atoms energy Ei Ef h ƒ
  • The size of the allowed electron orbits is
    determined by a quantization condition imposed on
    the electrons orbital angular momentum
  • me v r n h where n 1, 2, 3, h h / 2 p

13
Radii and Energy of Orbits
14
Radii and Energy of Orbits
15
Radii and Energy of Orbits
  • The radii of the Bohr orbits are quantized
  • When n 1, the orbit has the smallest radius,
    called the Bohr radius, ao 0.0529 nm
  • A general expression for the radius of any orbit
    in a hydrogen atom is rn n2 ao

16
Radii and Energy of Orbits
  • The lowest energy state (n 1) is called the
    ground state, with energy of 13.6 eV
  • The next energy level (n 2) has an energy of
    3.40 eV
  • The energies can be compiled in an energy level
    diagram with the energy of any orbit of En -
    13.6 eV / n2

17
Energy Level Diagram
18
Energy Level Diagram
  • The value of RH from Bohrs analysis is in
    excellent agreement with the experimental value
    of the Rydberg constant
  • A more generalized equation can be
  • used to find the wavelengths of any
  • spectral lines

19
Energy Level Diagram
  • The uppermost level corresponds to E 0 and n ?
    ?
  • The ionization energy energy needed to
    completely remove the electron from the atom
  • The ionization energy for hydrogen
  • is 13.6 eV

20
Chapter 28Problem 18
  • A particle of charge q and mass m, moving with a
    constant speed v, perpendicular to a constant
    magnetic field, B, follows a circular path. If in
    this case the angular momentum about the center
    of this circle is quantized so that mvr 2nh,
    show that the expression for the allowed radii
    for the particle are written in the corner, where
    n 1, 2, 3, . . .

21
Chapter 28Problem 24
  • Two hydrogen atoms collide head-on and end up
    with zero kinetic energy. Each then emits a
    121.6-nm photon (n 2 to n 1 transition). At
    what speed were the atoms moving before the
    collision?

22
Modifications of the Bohr Theory Elliptical
Orbits
  • Sommerfeld extended the results to include
    elliptical orbits
  • Retained the principal quantum number, n, which
    determines the energy of the allowed states
  • Added the orbital quantum number, l, ranging from
    0 to n-1 in integer steps
  • All states with the same principle quantum
  • number are said to form a shell, whereas the
  • states with given values of n and l are said
  • to form a subshell

23
Modifications of the Bohr Theory Elliptical
Orbits
24
Modifications of the Bohr Theory Zeeman Effect
  • Another modification was needed to account for
    the Zeeman effect splitting of spectral lines in
    a strong magnetic field, indicating that the
    energy of an electron is slightly modified when
    the atom is immersed in a magnetic field
  • A new quantum number, m l, called the orbital
    magnetic quantum number, had to be introduced
  • m l can vary from - l to l in integer steps

25
Quantum Number Summary
  • The values of n can range from 1 to ? in integer
    steps
  • The values of l can range from 0 to n-1 in
    integer steps
  • The values of m l can range from -l to l in
    integer steps

26
Modifications of the Bohr Theory Fine Structure
  • High resolution spectrometers show that spectral
    lines are, in fact, two very closely spaced
    lines, even in the absence of a magnetic field
  • This splitting is called fine structure
  • Another quantum number, ms, called the spin
    magnetic quantum number, was introduced to
    explain the fine structure

27
Spin Magnetic Quantum Number
  • It is convenient to think of the electron as
    spinning on its axis (the electron is not
    physically spinning)
  • There are two directions for the spin spin up,
    ms ½ spin down, ms - ½
  • There is a slight energy difference between the
    two spins and this accounts for the doublet in
    some lines
  • A classical description of electron spin is
    incorrect the electron cannot be located
    precisely in space, thus it cannot be considered
    to be a spinning solid object

28
de Broglie Waves in the Hydrogen Atom
  • One of Bohrs postulates was the angular momentum
    of the electron is quantized, but there was no
    explanation why the restriction occurred
  • de Broglie assumed that the electron orbit would
    be stable only if it contained an integral number
    of electron wavelengths

29
de Broglie Waves in the Hydrogen Atom
  • This was the first convincing argument that the
    wave nature of matter was at the heart of the
    behavior of atomic systems
  • By applying wave theory to the electrons in an
    atom, de Broglie was able to explain the
    appearance of integers in Bohrs equations as a
    natural consequence of standing wave patterns

30
Quantum Mechanics and the Hydrogen Atom
  • Schrödingers wave equation was subsequently
    applied to hydrogen and other atomic systems -
    one of the first great achievements of quantum
    mechanics
  • The quantum numbers and the restrictions placed
    on their values arise directly from the
    mathematics and not from any assumptions made to
    make the theory agree with experiments

31
Electron Clouds
  • The graph shows the solution to the wave equation
    for hydrogen in the ground state
  • The curve peaks at the Bohr radius
  • The electron is not confined to a particular
    orbital distance from the nucleus
  • The probability of finding the electron at the
    Bohr radius is a maximum

32
Electron Clouds
  • The wave function for hydrogen in the ground
    state is symmetric
  • The electron can be found in a spherical region
    surrounding the nucleus
  • The result is interpreted by viewing the electron
    as a cloud surrounding the nucleus
  • The densest regions of the cloud represent the
    highest probability for finding the electron

33
The Pauli Exclusion Principle
  • No two electrons in an atom or in the same
    location can ever have the same set of values of
    the quantum numbers n, l, m l, and ms
  • This explains the electronic structure of complex
    atoms as a succession of filled energy levels
    with different quantum numbers

34
Filling Shells
  • As a general rule, the order that electrons fill
    an atoms subshell is
  • 1) Once one subshell is filled, the next electron
    goes into the vacant subshell that is lowest in
    energy
  • 2) Otherwise, the electron would radiate energy
    until it reached the subshell with the lowest
    energy
  • 3) A subshell is filled when it holds 2(2l1)
    electrons

35
Filling Shells
36
The Periodic Table
  • The outermost electrons are primarily responsible
    for the chemical properties of the atom
  • Mendeleev arranged the elements according to
    their atomic masses and chemical similarities
  • The electronic configuration of the elements is
    explained by quantum numbers and Paulis
    Exclusion Principle

37
The Periodic Table
38
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39
Chapter 28Problem 28
  • (a) Construct an energy level diagram for the He
    ion, for which Z 2. (b) What is the ionization
    energy for He?

40
Explanation of Characteristic X-Rays
  • The details of atomic structure can be used to
    explain characteristic x-rays
  • A bombarding electron collides with an electron
    in the target metal that is in an inner shell
  • If there is sufficient energy, the electron is
    removed from the target atom

41
Explanation of Characteristic X-Rays
  • The vacancy created by the lost electron is
    filled by an electron falling to the vacancy from
    a higher energy level
  • The transition is accompanied by the emission of
    a photon whose energy is equal to the difference
    between the two levels

42
Energy Bands in Solids
  • In solids, the discrete energy levels of isolated
    atoms broaden into allowed energy bands separated
    by forbidden gaps
  • The separation and the electron population of the
    highest bands determine whether the solid is a
    conductor, an insulator, or a semiconductor

43
Energy Bands in Solids
  • Sodium example
  • Blue represents energy bands occupied by the
    sodium electrons when the atoms are in their
    ground states, gold represents energy bands that
    are empty, and white represents energy gaps
  • Electrons can have any energy within the allowed
    bands and cannot have energies in the gaps

44
Energy Level Definitions
  • The valence band is the highest filled band
  • The conduction band is the next higher empty band
  • The energy gap has an energy, Eg, equal to the
    difference in energy between the top of the
    valence band and the bottom of the conduction band

45
Conductors
  • When a voltage is applied to a conductor, the
    electrons accelerate and gain energy
  • In quantum terms, electron energies increase if
    there are a high number of unoccupied energy
    levels for the electron to jump to
  • For example, it takes very little
  • energy for electrons to jump
  • from the partially filled to one of
  • the nearby empty states

46
Insulators
  • The valence band is completely full of electrons
  • A large band gap separates the valence and
    conduction bands
  • A large amount of energy is needed for an
    electron to be able to jump from the valence to
    the conduction band
  • The minimum required energy is Eg

47
Semiconductors
  • A semiconductor has a small energy gap
  • Thermally excited electrons have enough energy to
    cross the band gap
  • The resistivity of semiconductors decreases with
    increases in temperature
  • The light-color area in the valence band
    represents holes empty states in the valence
    band created by electrons that have jumped to the
    conduction band

48
Semiconductors
  • Some electrons in the valence band move to fill
    the holes and therefore also carry current
  • The valence electrons that fill the holes leave
    behind other holes
  • It is common to view the conduction process in
    the valence band as a flow of positive holes
    toward the negative electrode applied to the
    semiconductor

49
Semiconductors
  • An external voltage is supplied
  • Electrons move toward the positive electrode
  • Holes move toward the negative electrode
  • There is a symmetrical current process in a
    semiconductor

50
Doping in Semiconductors
  • Doping is the adding of impurities to a
    semiconductor (generally about 1 impurity atom
    per 107 semiconductor atoms)
  • Doping results in both the band structure and the
    resistivity being changed

51
n-type Semiconductors
  • Donor atoms are doping materials that contain one
    more electron than the semiconductor material
  • This creates an essentially free electron with an
    energy level in the energy gap, just below the
    conduction band
  • Only a small amount of thermal energy is needed
    to cause this electron to move into the
    conduction band

52
p-type Semiconductors
  • Acceptor atoms are doping materials that contain
    one less electron than the semiconductor material
  • A hole is left where the missing electron would
    be
  • The energy level of the hole lies in the energy
    gap, just above the valence band
  • An electron from the valence band has enough
    thermal energy to fill this impurity level,
    leaving behind a hole in the valence band

53
A p-n Junction
  • A p-n junction is formed when a p-type
    semiconductor is joined to an n-type
  • Three distinct regions exist a p region, an n
    region, and a depletion region
  • Mobile donor electrons from the n side nearest
    the junction diffuse to the p side, leaving
    behind immobile positive ions

54
A p-n Junction
  • At the same time, holes from the p side nearest
    the junction diffuse to the n side and leave
    behind a region of fixed negative ions
  • The resulting depletion region is depleted of
    mobile charge carriers
  • There is also an electric field in this region
    that sweeps out mobile charge carriers to keep
    the region truly depleted

55
Diode Action
  • The p-n junction has the ability to pass current
    in only one direction
  • When the p-side is connected to a positive
    terminal, the device is forward biased and
    current flows
  • When the n-side is connected to the positive
    terminal, the device is reverse biased and a
    very small reverse current results

56
  • Answers to Even Numbered Problems
  • Chapter 28
  • Problem 34
  • 4
  • 7

57
Answers to Even Numbered Problems Chapter 28
Problem 36 Use the lecture notes
58
Answers to Even Numbered Problems Chapter 28
Problem 44 137
59
  • Answers to Even Numbered Problems
  • Chapter 28
  • Problem 52
  • 135 eV
  • 10 times the magnitude of the ground state
    energy of hydrogen
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