Chapter 7: ELECTRONS IN ATOMS AND PERIODIC PROPERTIES - PowerPoint PPT Presentation

1 / 53
About This Presentation
Title:

Chapter 7: ELECTRONS IN ATOMS AND PERIODIC PROPERTIES

Description:

Chapter 7: ELECTRONS IN ATOMS AND PERIODIC PROPERTIES. Problems: 7.1-7.16, 7.18-7.27, 7.31-7.56, 7.61-7.107, 7.109-7.119, 7.124-7.125, 7.128-7.134 – PowerPoint PPT presentation

Number of Views:91
Avg rating:3.0/5.0
Slides: 54
Provided by: seatt84
Category:

less

Transcript and Presenter's Notes

Title: Chapter 7: ELECTRONS IN ATOMS AND PERIODIC PROPERTIES


1
Chapter 7 ELECTRONS IN ATOMS AND PERIODIC
PROPERTIES
  • Problems 7.1-7.16, 7.18-7.27, 7.31-7.56,
    7.61-7.107, 7.109-7.119, 7.124-7.125, 7.128-7.134

2
Electromagnetic Radiation
  • Electromagnetic (EM) Spectrum a continuum of the
    different forms of electromagnetic radiation or
    radiant energy

3
Radar Radio Waves
Weather systems
A galaxy imaged in the visible spectrum.
Radio telescopes. This is the Very Large Array
(VLA) in NM.
The same galaxy imaged in the radio spectrum at
the VLA.
4
Thermal Imaging Detecting IR radiation
Much of a persons energy is radiated away from
the body in the form of infrared (IR) energy. You
can produce more IR energy to warm yourself by
moving aroundthis is why you shiver when you go
outside in the cold with no coat on. This process
is called thermogenesis.
Why does your mother insist you wear a hat in the
winter?
5
IR Photography
Image obtained with IR film, which is really
film that is activated by light at 700-900 nm.
6
Electromagnetic Radiation
  • Electromagnetic radiation or light is a form of
    energy.
  • Has both electric (E) and magnetic (H) components.
  • Characterized by
  • Wavelength (?)
  • Amplitude (A)

7
Electromagnetic Radiation (cont.)
  • Wavelength (l) The distance between two
    consecutive peaks in the wave.

Increasing Wavelength
l1 gt l2 gt l3
Unit length (m)
8
Electromagnetic Radiation (cont.)
  • Frequency (n) The number of waves (or cycles)
    that pass a given point in space per second.

Decreasing Frequency
n1 lt n2 lt n3
Units 1/time (1/sec) or, Hertz (Hz)
9
Electromagnetic Radiation (cont.)
  • The product of wavelength (l) and frequency (n)
    is a constant.

(?)(?) c
Speed of light
c 3 x 108 m/s
c is a constant, independent of ?
10
Properties of Waves
  • Wavelength (?) is the distance from peak-to-peak
    in a wave.
  • Frequency (?) is the number of waves in a
    specific time frame (usually per second Hz)
  • As wavelength goes up, frequency goes down (and
    vice versa)
  • Electromagnetic waves travel at the speed of
    light
  • ? ? c
  • c speed of light 3 x 108 m/s

11
What statement is true when comparing red light
to blue light?
A. Red light travels at a greater speed than
blue light.
B. Blue light travels at greater speed than red
light.
C. The wavelength of blue light is longer.
D. The wavelength of red light is longer.
12
Behavior of Waves
  • Waves refract, diffract and interact
  • Refraction The bending of light as it passes
    from one medium to another of different density

Light is also bent by liquids, causing the straw
to appear disconnected.
Refraction throught a prism separates white light
into its separate components (light of different
wavelengths) without changing the light itself.
13
Behavior of Waves
  • Diffraction The bending of electromagnetic
    radiation as it passes around an edge of an
    object or through a narrow opening.

What causes the bright and dark spots?
14
Behavior of Waves
  • Waves interact by adding together or cancelling
    each other out

15
Light is a Wave, Right?
  • Back in the old days
  • It was generally agreed that matter and light
    were distinct.
  • Matter was particulate in nature, light could be
    described using waves.
  • Physicists circa 1900 had it all figured out
  • One famous physicist asserted that within ten
    years or so all the major problems in physics
    would be solved.
  • The only thing left, really, was this niggling
    little problem with black-body radiation

16
The State of Physics Before 1900
  • Newton discovered light could be separated by a
    prism in 170
  • Heat, electricity and phlogiston were weightless,
    imponderable fluids responsible for most
    observed processes
  • It wasnt until the early 1800s that the
    following, revolutionary ideas were put forth
    light was a wave, atoms existed, and air could
    trap heat (the greenhouse effect).

17
Physics in the early 1900s
  • The end of the 1800s saw an explosion of real
    scientific progress.
  • Thermodynamics, electromagnetism and the kinetic
    molecular theory were well-developed.
  • There were still some problems, though, that
    needed explaining
  • Blackbody radiation, new particle discoveries,
    what was the ether?, radioactivity, the
    instability of the atom, the photoelectric
    effect.
  • There had to be one theory to explain them all

18
The big problem
  • Black body radiation When a metal object is
    heated, it begins to glow. If it is heated hot
    enough, it glows white hot, emitting all the
    wavelengths of visible light but little to none
    in the UV range or higher.
  • Current (at the time) theories by Maxwell could
    not explain this common phenomenon.
  • Max Planck proposed a new theory of light that
    it behaved as a wave, but with particle-like
    properties.
  • Light traveled in particle-like packets he called
    quanta (a single one is called a quantum).
  • Each quantum was the smallest amount of energy
    found in nature.

19
Light as Energy
  • Planck found that in order to model this
    behavior, one has to envision that energy (in the
    form of light) is lost in integer values
    according to

DE nhn
frequency
Energy Change
n 1, 2, 3 (integers)
h Plancks constant 6.626 x 10-34 Js
20
Light as Energy (cont.)
  • In general the relationship between frequency and
    photon energy is

h 6.636 x 10-34 Js c 2.9979 x 108 m/s 1 Hz
1 s-1
Ephoton h?
Example What is the energy of a 500 nm
photon?
? c/? (3x108 m/s)/(5.0 x 10-7 m)
? 6 x 1014 1/s
E h? (6.626 x 10-34 Js)(6 x 1014 1/s) 4 x
10-19 J
21
Energy Quantization
The student can stop only at certain points on a
flight of stairs. Her distance from the ground is
quantized.
The student can stop at any point on the ramp.
Her distance from the ground changes continuously.
Similarly, atomic energy levels are like
stepsthe energies available to an atom do not
form a continuum, they are quantized.
22
Evidence of Quantization
  • Black-body Radiation (Planck)
  • A system can transfer energy in packets of size
    hn.
  • These packets are called quanta
  • Prior to this discovery it was thought that
    systems could absorb or emit any amount of
    energy.
  • Other observations supported this quantum view
  • Atomic Emission spectra (Balmer, Rydberg, Bohr)
  • Light emitted from excited atoms occurs in
    discrete lines rather than a continuum.
  • Photoelectric Effect (Einstein)
  • Energy itself is actually quantized into packets
    called photons.
  • This means energy has a particle-like nature as
    well as a wave-like nature.
  • Electron Diffraction Patterns (Davisson Germer)
  • Matter also has a wave-like nature!!

23
Atomic Emission
  • When we heat a sample of an element, the atoms
    become excited. When the atom relaxes it emits
    visible light. The color of the light depends on
    the element.

When the light emitted from excited atoms is
passed through a prism, we see discrete bands of
color at specific wavelengths.
24
Photon Emission
An excited atom relaxes from high E to low E by
emitting a photon. We can determine the energy
difference (?E) between levels by measuring the
wavelength of the emitted photon.
Emission of photon
?E hc/? ? ? hc/?E If ? 410 nm, ?E
4.52 x 10-19 J
25
The Photoelectric Effect
  • Observed by Albert Einstein in 1905 Light
    shining on a clean metal surface causes the
    emission of electrons but only when the light has
    a minimum threshold frequency (?0)
  • When ?lt?0 ? no electrons are emitted
  • When ?gt?0 ? electrons are emitted, more e
    emitted with greater intensity of light

? lt ?0
? gt ?0
Einstein applied Planck's quantum theory to
light light exists as a stream of "particles"
called photons.
26
The Photoelectric Effect (cont)
Frequency determines whether e- are ejected, and
their KE (velocity).
Intensity determines the number of e- that are
ejectedbut they will all have the same velocity!!
27
The Photoelectric Effect (cont.)
As frequency of incident light is increased,
kinetic energy of emitted e- increases linearly.
  • hn0
  • Workfunction energy needed to release e-

Light apparently behaves as a particle.
28
The Photoelectric Effect (cont.)
For Na with F 4.4 x 10-19 J, what wavelength
corresponds to ?o?
0
h? F 4.4 x 10-19 J
hc/? 4.4 x 10-19 J
? 4.52 x 10-7 m 452 nm
29
Electron Diffraction Patterns
  • Light is shined through a crystal, and its
    waveforms are scattered. When they come out the
    other side, they create interference patterns on
    a detector plate.

Diffraction can only be explained by treating
light as a wave instead of a particle.
30
Diffraction of Particles?
  • Turns out we can get similar interference
    patterns by bombarding crystals with beams of
    high energy electrons also
  • This can only be explained by treating matter as
    a wave.

31
de Broglie Wavelength
  • If matter exhibits wave-like properties, we
    should be able to determine the wavelength of a
    particle.
  • Recall the energy of a photon, and the definition
    of the speed of light
  • Substituting, E hc/?
  • Using Einsteins relationship, E mc2,

Ephoton h? c ?? ? ? c/?
 
 
32
de Broglie Wavelength
  • We can generalize this relationship to any
    velocity (v)
  • What is the de Broglie wavelength of an electron
    traveling at the speed of light? (melectron
    9.31 x 10-31 kg)
  • What is the de Broglie wavelength of a 80 kg
    student walking across campus at 3 m/s?

 
 
? (6.626 x 10-34 Js)/(9.31x10-31 kg)(3x108
m/s) 2.37 x 10-12 m
? (6.626 x 10-34 Js)/(80 kg)(3 m/s) 2.76 x
10-36 m
You are a wave, too, but you have a VERY small
wavelength!!
33
What does all this mean for matter?
  • Scientists needed to find a way to explain how
    light, usually thought of as a wave, could behave
    like a particle AND how matter, which was usually
    thought of as a particle, could behave as a wave.
  • They started with the hydrogen emission spectrum
  • Balmer and Rydberg developed equations that
    predicted where these lines should appear (even
    before anyone had observed them).

34
The Bohr Model
  • Balmer and Rydberg didnt know why their
    equations worked.
  • Niels Bohr used their equations and observations
    to develop a quantum model for H.
  • Central idea electron circles the nucleus in
    only certain allowed circular orbitals.
  • Bohr postulated that there is Coulombic
    attraction between e- and nucleus. However,
    classical physics is unable to explain why an H
    atom doesnt simply collapse. Why doesnt the
    electron just spiral into the nucleus?

35
The Bohr Model of the atom
Principle Quantum number n An index of the
energy levels available to the electron.
656
486
434
410
36
The Bohr Model (cont.)
  • Bohr model for the H atom is capable of
    reproducing the energy levels given by the
    empirical formulas of Balmer and Rydberg.

Z atomic number (1 for H)
n integer (1, 2, .)
Ry x h -2.178 x 10-18 J
37
The Bohr Model (cont.)
Energy levels get closer together as n
increases At n infinity, E 0 ? the electron
is free (not a part of the atom)
38
The Bohr Model (cont.)
We can use the Bohr model to predict what DE is
for any two energy levels
39
The Bohr Model (cont.)
Example At what wavelength will emission from n
4 to n 1 for the H atom be observed?
1
4
40
The Bohr Model (cont.)
Example What is the longest wavelength of light
that will result in removal of the e- from H?
?
1
41
Extension to Higher Z
The Bohr model can be extended to any single
electron system.must keep track of Z (atomic
number).
Z atomic number
n integer (1, 2, .)
Examples He (Z 2), Li2 (Z 3), etc.
42
Extension to Higher Z (cont.)
Example At what wavelength will emission from n
4 to n 1 for the He atom be observed?
2
1
4
43
So what happened to the Bohr Model?
  • Although it successfully described the line
    spectrum of hydrogen and other one-electron
    systems, it failed to accurately describe the
    spectra of multi-electron atoms.
  • The Bohr model was soon scrapped in favor of the
    Quantum Mechanical model, although the vocabulary
    of the Bohr model persists.
  • However, Bohr pioneered the idea of quantized
    electronic energy levels in atoms, so we owe him
    big.

Thanks Niels Bohr!
44
Quantum Concepts
  • The Bohr model was capable of describing the
    discrete or quantized emission spectrum of H.
  • But the failure of the model for multielectron
    systems combined with other issues (the
    ultraviolet catastrophe, workfunctions of metals,
    etc.) suggested that a new description of atomic
    matter was needed.

45
Quantum Concepts (cont.)
  • This new description was known as wave mechanics
    or quantum mechanics.
  • Recall, photons and electrons readily demonstrate
    wave-particle duality.
  • The idea behind wave mechanics was that the
    existence of the electron in fixed energy levels
    could be though of as a standing wave.

46
Quantum Concepts (cont.)
  • What is a standing wave?

A standing wave is a motion in which
translation of the wave does not occur.
In the guitar string analogy
(illustrated), note that standing waves
involve nodes in which no motion of the
string occurs.
Note also that integer and half- integer
values of the wavelength correspond to
standing waves.
47
Quantum Concepts (cont.)
  • Louis de Broglie suggested that for the e- orbits
    envisioned by Bohr, only certain orbits are
    allowed since they satisfy the standing wave
    condition.

not allowed
48
Quantum Concepts (cont.)
  • Erwin Schrodinger developed a mathematical
    formalism that incorporates the wave nature of
    matter
  • H, the Hamiltonian, is a special kind of
    function that gives the energy of a quantum
    state, which is described by the wavefunction, Y.

49
Quantum Concepts (cont.)
  • What is a wavefunction?

a probability amplitude
  • Probability of finding a particle in space

The probability distribution for the hydrogen 1s
orbital in three-dimensional space
Probability
With the wavefunction, we can describe spatial
distributions.
The probability of finding the electron at points
along a line drawn from the nucleus outward in
any direction for the hydrogen 1s orbital.
50
Hydrogens Electron
Cross section of the hydrogen 1s orbital
probability distribution divided into successive
thin spherical shells (b) The radial probability
distribution
The surface contains 90 of the total electron
probability (the size of the orbital, by
definition)
51
Quantum Concepts (cont.)
  • Another limitation of the Bohr model was that it
    assumed we could know both the position and
    momentum of an electron exactly.
  • Werner Heisenberg observed that there is a
    fundamental limit to how well one can know both
    the position and momentum of a particle.

where
Uncertainty in position
Uncertainty in momentum
52
Quantum Concepts (cont.)
  • Example
  • What is the uncertainty in velocity for an
    electron in a 1 Å radius orbital in which the
    positional uncertainty is 1 of the radius. (1 Å
    10-10 m)

?x (1 Å)(0.01) 1 x 10-12 m
HUGE!
53
Quantum Concepts (cont.)
  • Example (youre quantum as well)
  • What is the uncertainty in position for a 80
    kg student walking across campus at 1.3 m/s with
    an uncertainty in velocity of 1.

?p m?v (80kg)(0.013 m/s) 1.04 kg.m/s
Very smallwe know where you are.
Write a Comment
User Comments (0)
About PowerShow.com