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Chapter 7: Atomic Structure

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Chemistry-140 Lecture 17 Chapter 7: Atomic Structure Chapter Highlights electromagnetic radiation photons & Planck s constant Bohr model of the atom – PowerPoint PPT presentation

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Title: Chapter 7: Atomic Structure


1
Chemistry-140 Lecture 17
  • Chapter 7 Atomic Structure
  • Chapter Highlights
  • electromagnetic radiation
  • photons Plancks constant
  • Bohr model of the atom
  • Rydberg equation
  • quantum mechanics
  • orbitals
  • Heisenberg uncertainty principle
  • quantum numbers

2
Chemistry-140 Lecture 17
  • Electronic Structure Electromagnetic Radiation
  • Electronic structure of an atom detailed
    description of the arrangement of electrons in
    the atom
  • Electromagnetic radiation electrical and
    magnetic waves traveling at 2.9979 x 108 m/s
    (speed of light, c). Includes visible light,
    radio waves, microwaves, infrared
    (heat),ultraviolet, X-ray, and g-ray radiation.

3
Chemistry-140 Lecture 17
  • Electromagnetic Radiation
  • Wavelength, l distance between two successive
    peaks or troughs of a wave. Units are length
    (m).
  • Frequency, n number of complete waveforms that
    pass through a point in one second. Units of
    s-1, /s, or hertz (Hz).
  • Relationship
  • speed of light (wavelength) x (frequency)

c ln
4
Chemistry-140 Lecture 17
5
Chemistry-140 Lecture 17
  • Electromagnetic Radiation

Question Yellow light of a sodium vapour
lamp has a wavelength of 589 nm. What is the
frequency of this light?
6
Chemistry-140 Lecture 17
Answer Since we know
then n

c ln
5.09 x 1014 s-1
7
Chemistry-140 Lecture 17
  • Quantum Effects Photons
  • Max Planck proposed that radiation is not
    continuous, but rather consists of small pieces
    known as quanta (a quantum).
  • Frequencies, n, of these quanta were
    whole-number multiples of a fundamental
    frequency.
  • Energies E hn, 2hn, 3hn,...
  • where h Planck's constant
  • h 6.626 x 10-34 J-s.
  • and

E hn
8
Chemistry-140 Lecture 17
  • Quantum Effects Photons

Question A laser emits light energy in short
pulses with frequency 4.69 x 1014 Hz and deposits
1.3 x 10-2 J for each pulse. How many quanta of
energy does each pulse deposit ?
9
Chemistry-140 Lecture 17
Answer Step 1 Determine the energy of one
quantum (photon). E hn
(6.63 x 10-34 J-s) (4.69 x 1014 s-1)
3.11 x 10-19 J
10
Chemistry-140 Lecture 17
Step 2 Determine how many quanta are in a
laser pulse. Number

4.18 x 1016 quanta
11
Chemistry-140 Lecture 17
  • Photoelectric Effect
  • Photoelectric effect metallic surfaces produce
    electricity (electrons are ejected) when exposed
    to light.
  • There is a minimum frequency below which
  • no electricity is produced.
  • Above the minimum frequency
  • i) number of electrons ejected depends only on
    light intensity,
  • ii) energy of the ejected electrons depends only
    on the frequency of the light.

12
Chemistry-140 Lecture 17
13
Chemistry-140 Lecture 17
  • Photoelectric Effect

The packet of energy sufficient to eject an
electron is called a photon. The kinetic energy
EK of the electrons is given by EB
binding energy EP photon energy hn
EK EP - EB
14
Chemistry-140 Lecture 17
  • Photoelectric Effect

Question Potassium metal must absorb
radiation with a minimum frequency of 5.57 x 1014
Hz before it can emit electrons from its surface
via the photoelectric effect. If K(s) is
irradiated with light of wavelength 510 nm, what
is the maximum possible velocity of an emitted
electron?
15
Chemistry-140 Lecture 17
Answer Step 1 Convert threshold frequency to
binding energy. Eb hn
(6.63 x 10-34 J-s) (5.57 x 1014 s-1)
3.69 x 10-19 J
16
Chemistry-140 Lecture 17
Step 2 Determine the photon energy of 510 nm
light. EP

3.90 x 10-19 J
17
Chemistry-140 Lecture 17
Step 3 Determine the kinetic energy of the
emitted electrons EK EP -
EB (3.90 x 10-19 J) - (3.69 x 10-19
J)
2.10 x 10-20 J
18
Chemistry-140 Lecture 17
Step 4 Calculate the velocity of the emitted
electrons EK mv2 2.10 x
10-20 J v

2.15 x 105 m/s
19
Chemistry-140 Lecture 17
  • Bohrs Model of the Hydrogen Atom
  • A spectrum is produced when radiation from a
    source is separated into its component
    wavelengths.
  • Bohr used Planck's quantum theory to interpret
    the line spectrum of hydrogen.
  • Bohr's model of the hydrogen atom described a
    nucleus surrounded orbits of fixed (quantized)
    radius,
  • numbered n 1, 2, 3,...

20
Chemistry-140 Lecture 17
21
Chemistry-140 Lecture 17
22
Chemistry-140 Lecture 17
  • Bohrs Model of the Hydrogen Atom
  • Bohr concluded
  • the energy of the electron in an orbit of
    hydrogen is quantized
  • the energy difference between two orbits must
    also be quantized
  • The frequency of a line in the spectrum
    corresponds to the energy difference between two
    orbits

DE hn
23
Chemistry-140 Lecture 17
  • Bohrs Model of the Hydrogen Atom
  • The energy of a Bohr orbit (and an electron in
    it) is given by
  • where RH is the Rydberg constant 2.179 x
    10-18 J

24
Chemistry-140 Lecture 17
Transitions in the Bohr Hydrogen Atom
25
Chemistry-140 Lecture 17
  • Transitions and the Rydberg Equation
  • An electron in the lowest energy orbit, n 1, is
    in the ground state
  • An electron in any orbit other than n 1, is in
    an
  • excited state
  • The energy of a line is the difference in the
    energies of the two orbits involved in the
    transition
  • DE Efinal - Einitial

26
Chemistry-140 Lecture 17
  • Transitions in the Bohr Hydrogen Atom
  • The radius of a Bohr orbit is given by
  • r n2(5.30 x 10-11 m)
  • The ionization energy of hydrogen is the energy
    required to remove the electron from the atom,
    that is
  • the energy of the n 1 to n transition

27
Chemistry-140 Lecture 17
  • Transitions in the Bohr Hydrogen Atom

Question (similar to example 7.4) Calculate
the wavelength of light that corresponds to the
transition of the electron from the n 4 to the
n 2 state of the hydrogen atom. Is the light
absorbed or emitted by the atom?
28
Chemistry-140 Lecture 17
Answer Step 1 Use the Rydberg equation with
ni 4 and nf 2. n


-6.17 x 1014 s-1
29
Chemistry-140 Lecture 17
Step 2 Convert to wavelength of
light l

4.86 x 10-7 m
c ln
486 nm
30
Chemistry-140 Lecture 18
  • Chapter 7 Atomic Structure
  • Chapter Highlights
  • electromagnetic radiation
  • photons Plancks constant
  • Bohr model of the atom
  • Rydberg equation
  • quantum mechanics
  • Heisenberg uncertainty principle
  • orbitals
  • quantum numbers

31
Chemistry-140 Lecture 18
  • Bohrs Model of the Hydrogen Atom
  • The energy of a Bohr orbit (and an electron in
    it) is given by
  • where RH is the Rydberg constant 2.179 x
    10-18 J

32
Chemistry-140 Lecture 18
  • Transitions and the Rydberg Equation
  • An electron in the lowest energy orbit, n 1, is
    in the ground state
  • An electron in any orbit other than n 1, is in
    an
  • excited state
  • The energy of a line is the difference in the
    energies of the two orbits involved in the
    transition
  • DE Efinal - Einitial

33
Chemistry-140 Lecture 18
Transitions in the Bohr Hydrogen Atom
34
Chemistry-140 Lecture 18
  • Transitions in the Bohr Hydrogen Atom
  • The radius of a Bohr orbit is given by
  • r n2(5.30 x 10-11 m)
  • The ionization energy of hydrogen is the energy
    required to remove the electron from the atom,
    that is
  • the energy of the n 1 to n transition

35
Chemistry-140 Lecture 18
  • Transitions in the Bohr Hydrogen Atom

Question Calculate the wavelength of light
that corresponds to the transition of the
electron from the n 4 to the n 2 state of the
hydrogen atom. Is the light absorbed or emitted
by the atom?
36
Chemistry-140 Lecture 18
Answer Step 1 Use the Rydberg equation with
ni 4 and nf 2. n


-6.17 x 1014 s-1
37
Chemistry-140 Lecture 18
Step 2 Convert to wavelength of
light l

4.86 x 10-7 m
c ln
486 nm
38
Chemistry-140 Lecture 18
  • Dual Nature of the Electron
  • De Broglie proposed that particles may behave as
    if they were waves. Similar to the idea that
    light may behave as if it was a particle. Matter
    wave is the term used by de Broglie where
  • where momentum mv, (m is mass v is
    velocity)

39
Chemistry-140 Lecture 18
  • Dual Nature of the Electron

Question What is the characteristic
wavelength of an electron with velocity 5.97 x
106 m/s ? (mass of an electron is 9.11 x 10-28 g)
40
Chemistry-140 Lecture 18
Answer Use de Broglie's equation for matter
waves.
1.22 x 10-10 m
0.122 nm
41
Chemistry-140 Lecture 18
  • Quantum Mechanics
  • Heisenberg Uncertainty Principle Werner
    Heisenberg proposed the uncertainty principle,
    which states that it is impossible for us to
    know, simultaneously, both the exact momentum of
    an electron and its exact location in space

42
Chemistry-140 Lecture 18
  • Quantum Mechanics
  • Schrödinger Wave Equation Erwin Schrödinger
    proposed a mathematical model of the atom using
    measured energies and known forces rather than a
    preconceived "picture" of the atom's structure.
    This is called quantum mechanics or wave
    mechanics.

43
Chemistry-140 Lecture 18
  • Wave Functions Probability
  • Solutions to the wave equation are called wave
    functions, symbolized y. Wave functions cannot
    describe the exact position of an electron only
    the probability of finding it in a given location.
  • The probability of finding the electron in a
    given location is the electron density and is
    given by the square of the wave function for that
    location, y2.

44
Chemistry-140 Lecture 18
  • The Wave Equation Orbitals
  • Solutions to the wave equation are called
    orbitals..

45
Chemistry-140 Lecture 19
  • Chapter 7 Atomic Structure
  • Chapter Highlights
  • electromagnetic radiation
  • photons Plancks constant
  • Bohr model of the atom
  • Rydberg equation
  • quantum mechanics
  • Heisenberg uncertainty principle
  • quantum numbers
  • orbitals

46
Chemistry-140 Lecture 19
  • The Wave Equation Orbitals
  • Solutions to the wave equation are called
    orbitals and
  • each has a characteristic energy.
  • An orbital is a region for which there is a high
    probability of finding the electron it is not a
    path or trajectory.

47
Chemistry-140 Lecture 19
  • The Wave Equation Quantum Numbers
  • Variables in the wave equation are called quantum
    numbers. The Bohr model used only one variable
    or quantum number, n. The quantum mechanical
    model uses three quantum numbers, n, l ml to
    describe each orbital

y n, l, m (r, q, f) Rnl(r)Clm(q, f)
48
Chemistry-140 Lecture 19
  • Quantum Numbers
  • The principal quantum number (n) has possible
    values of
  • It describes the relative size of the orbital

n 1, 2, 3,...
49
Chemistry-140 Lecture 19
  • Quantum Numbers
  • The angular momentum quantum number (l)
  • has possible values of
  • It describes the shape of the orbital.
  • The value of l is often referred to by a letter
    equivalent
  • 0 s, 1 p, 2 d, 3 f, .... (the rest are
    alphabetical)

l 0, 1, 2, ...n-1
50
Chemistry-140 Lecture 19
  • Quantum Numbers
  • The magnetic quantum number ( ml ) has values
  • It describes the orientation of the orbital in
    space.

ml -l,... -1, 0, 1, ...l
51
Chemistry-140 Lecture 19
  • Electronic Shells Sub-shells
  • A collection of orbitals with the same value of n
  • is called an electron shell
  • A collection of orbitals with the same values of
    n and l is called an electronic subshell. A
    subshell can be referred to using n and the
    letter equivalent of l,

1s, 2s, 2p, 3s, 3p 3d, 3f etc
52
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53
Chemistry-140 Lecture 19
  • s Orbitals
  • The s orbitals are those for which l 0. All s
    orbitals are spherical. There is one s orbital
    in each s subshell.

54
Chemistry-140 Lecture 19
  • Probability Density in Orbitals

55
Chemistry-140 Lecture 19
  • Radial Distribution in Orbitals

56
Chemistry-140 Lecture 19
  • p Orbitals
  • The p orbitals are those for which l 1. All p
    orbitals are "dumbbell" or "figure-eight" shaped.
    There are
  • three p orbitals in each p subshell..

57
Chemistry-140 Lecture 19
  • d Orbitals
  • The d orbitals are those for which l 2.
  • There are five d orbitals in each d subshell.
  • Four are "four-leaf clovers" the fifth looks
    like a p orbital with the addition of a ring
    around the centre

58
Chemistry-140 Lecture 19
  • d Orbitals
  • The d orbitals are those for which l 2.
  • There are five d orbitals in each d subshell.
  • Four are "four-leaf clovers" the fifth looks
    like a p orbital with the addition of a ring
    around the centre

59
Chemistry-140 Lecture 19
Nodal Planes in Orbitals
60
Chemistry-140 Lecture 19
  • f Orbitals
  • The f orbitals are those for which l 3.
  • There are seven f orbitals in each f subshell.
  • Each has 8 lobes

61
Chemistry-140 Lecture 19
  • Textbook Questions From Chapter 7
  • EM Radiation 22, 28, 30
  • Photoelectric Effect 32
  • Bohr Atom 35, 38, 40
  • Matter Waves 42
  • Quantum Mechanics 46, 48, 50, 57, 58, 60
  • General Conceptual 68, 72, 77, 79, 91
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