Transcript Atomic structure, spectroscopy, and quantum mechanics Chapter 5 1

Atomic structure, spectroscopy,
and quantum mechanics
Chapter 5
1
Key concepts
1.
2.
3.
4.
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6.
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13.
Know the general concepts behind the experiments leading to the discovery of the electron
and the proton.
Understand the general character of the atomic nucleus.
Know the relationship between wavelength and frequency of electromagnetic radiation (light):
=c
Understand the term quantum of energy, and the quantum nature of light: E=h
Describe the photoelectric effect.
Understand how the line spectra of atoms led to Bohr’s model of the atom. Also understand
the drawbacks of Bohr’s model.
Understand the wave nature of matter; use the DeBroglie formula for calculating the
wavelength of matter waves.
Explain the Heisenberg uncertainty principle, and know how it affects our understanding of the
atom.
Know that Schrodinger’s equation H=E leads to the atomic orbital. Know the four quantum
numbers used to describe an electron in any atomic orbital.
Be able to recognize the spatial representation of s, p, or d orbitals.
Understand how Pauli’s exclusion principle affects the population of electrons in any atomic
orbital.
Know how to write electronic configurations, and know what these represent.
Understand the reasoning behind the shape of the periodic table.
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God’s view of the world
vs. our view of the world
• Mos. 4:9. Believe in God; believe that he is, and that he created all things,
both in heaven and in earth; believe that he has all wisdom, and all power,
both in heaven and in earth; believe that man doth not comprehend all the
things which the Lord can comprehend.
• D & C 130:19. And if a person gains more knowledge and intelligence in
this life through his diligence and obedience than another, he will have so
much the advantage• in the world to come.
• While we may not “comprehend all the things which the Lord can
comprehend”, we are encouraged to obtain knowledge on all
subjects, including the workings of creation. This is where the
scientific method comes into play.
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Models and the scientific method
a)
b)
c)
d)
There is always a model that will explain any related set of bona fide
experiments.
Models should always start out simple and definite enough that
predictions can be made.
A model is of limited value except as it correlates a substantial body of
observable material.
Models that suggest important new experiments can be useful, even if
the theory must be modified.
Henry Eyring, Ann. Rev. Phys. Chem. 28, 1 (1977)
•
•
It is important to remember that we will be discussing a series of
experiments, data, and models. Models are meant to describe nature,
not the other way around. We change the model in order to better fit new
experimental evidence.
Models help us understand processes and mechanisms (how). Scientific
models rarely, if ever, help us understand the underlying purposes of
Nature (why). Increasing our understanding of our relationship to God
will help in that area…
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The electron (e-)
• Electric charge investigated from the
1800’s, but detailed characteristics first
outilined by J. J. Thomson
• Thomson used a cathode ray tube to
examine the electron’s properties
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Cathode ray tube
Cathode rays: radiation
produced in vacuum tubes
that travels from the
cathode ( - lead) to the
anode (+ lead)
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Thomson’s discoveries
1. Nature of the cathode ray is independent
of the cathode material.
2. A magnet can alter the path of the
cathode ray
3. Electron charge to mass ratio—
1.76  108 coulombs/gram
(Coulomb = unit of charge)
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• Thomson’s experiment is the forerunner of
the mass spectrometer (more on that in a
minute). Mass spectrometer measures
the mass-to-charge ratio of particles.
• With the mass/charge ratio known,
something needed to be learned about the
mass or charge of the particle in order to
determine the remaining property.
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Millikan oil-drop experiment
Produces
Small oil drops
Removes electrons
From atoms in air
Used to
Measure oil-drop
size
Attracts free electrons;
oil drop suspended when
Plate voltage is sufficient.
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Fig. 5-2, p.177
Millikan’s observations
• Charges on oil-drops are integral multiple of
some factor that is the fundamental charge of an
electron.
• What if you were working in Millikan’s lab? (#5)
13.458×10-19 C
17.308×10-19 C
15.373×10-19 C
28.844×10-19 C
17.303×10-19 C
11.545×10-19 C
15.378×10-19 C
19.214×10-19 C
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Electron mass
• Fundamental electron charge: 1.602  10-19 C
• With Millikan’s results, we can now find the mass
of an electron. How?
 me 
  ze  me
z
 e
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Canal rays: Protons
• A proton’s mass is 1836 times larger than an
electron. Thus, its charge-to-mass ratio is
__________ than the z/m for an electron.
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Fig. 5-3, p.178
Nature of the nucleus
• First model: “Plum
pudding” model (or
the gumdroppopcorn-ball model)
• Electrons are held
close to nucleus in a
“blob”.
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Rutherford gold foil experiment
• Utilized work of Madame Curie on radioactive
particles
–  -- high speed electrons
– -- gamma-rays (light), no charge
– --alpha-rays; +2 charge  charged nucleus of He
atom
• Rutherford used  rays in his experiment, firing
them at a piece of gold foil.
• Predict what will happen in the experiment…
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Fig. 5-4, p.179
At the molecular level…
• Most alpha particles
pass straight through
• Some are deflected at
very steep angles
• This can only occur if
the alpha particle is
repelled at close
range by a positively
charged particle.
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The nucleus
• Nucleus is very small, dense, highly
charged center of the atom. Electrons
spaced relatively widely about the nucleus.
Diameter of nucleus  10-14 m
Diameter of H atom  10-10 m = 1 Å
(Angström)
• If H nucleus was 1 m in diameter, electron
would be 10 km away (6.2 miles).
•
•
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Table 5-1, p.175
Mass spectrometer
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Fig. 5-8, p.184
Factors affecting ion deflection
1.
2.
3.
4.
Magnitude of accelerating voltage
Magnetic field strength
Particle mass
Particle charge
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Fig. 5-9, p.185
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Fig. 5-10a, p.185
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Fig. 5-10b, p.185
Electromagnetic
spectrum
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 = c
• as wavelength () increases, frequency ()
decreases. Product equal to speed of light
in vacuum (c).
• Some examples
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Planck’s constant
•
•
Blackbodies: emit energy at all frequencies
Behavior of blackbodies could not be explained by classical physics
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• Planck’s hypothesis: Energy is released
or absorbed from atoms in “chunks”, or
quanta.
• A quantum of energy E = h.
– h = 6.626  10-34 J-s  Planck’s constant
• Released or absorbed energy at frequency
 in whole multiples of h (h, 2h, 3h,
etc.)
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Photoelectric effect--Einstein
• To remove an electron from a metal
surface, a minimum energy (h) is
required.
• “Shining more light” does NOT increase
the energy, just the intensity of the light.
• Below minimum energy (frequency),
nothing happens.
•
http://wps.prenhall.com/wps/media/objects/166/170213/Media_Portfolio/PhotoelectricEffect/PhotoelectricEffect.MOV
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Einstein’s deduction
• light is made of photons (light particles,
quanta).
• Light has both wave properties and
particle properties
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Bohr model of the atom
• Line spectrum of atoms: discrete lines vs. “rainbow”.
• Rydberg series: empirically determined mathematical
series that describes hydrogen line spectrum.
• R = 1.097  107 m-1
1 1
 R 2  2 

 n1 n2 
1
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Bohr’s description of the atom
• 1. Electrons travel in orbits
around nucleus. Only certain
orbits, corresponding to certain
definite energies, are allowed.
• 2. An electron in a permitted
orbit has a specific energy in
an allowed state. An electron
in an allowed state will not
radiate energy.
• 3. Energy is only emitted or
absorbed when electrons
move from one orbit to another.
Energy is emitted or absorbed
as a photon, E=h
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• Advantages:
– Explains observed line spectrum of hydrogen.
– Explains quantized absorbtion and emission
of energy
• Disadvantage:
– Model works only for hydrogen or other 1electron atoms.
 Bohr’s model failed, but led to development
of the next step
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Dual nature of matter
• DeBroglie: Matter, like light, exhibits both wave
properties and particle properties.
• DeBroglie wavelength (matter waves)
• Example of matter waves: Scanning electron
microscope
h

mv
So….why do we not exhibit waves?
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• Examples:
– 0.25 kg ball moving at 90 mph. What is the
DeBroglie wavelength?
– What is the DeBroglie wavelength of a helium atom
(4.0 amu) moving 1000 m s-1?
• Matter waves are observable only with very
small, very fast particles. (atoms and electrons)
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Experimental evidence of
matter waves
Scanning electron microscope image of leafcutter ant head
http://www.mos.org/sln/SEM/gallery/guessit/7a.html
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Heisenberg uncertainty principle
• Because electrons are constantly moving very
fast, it is impossible to know precisely both the
position and momentum of an electron. (billiards
• The nature of an electron is probed by using
photons. But, the interaction of the photon with
the electron changes the nature of the electron.
• A well defined “orbit” of an electron around a
nucleus cannot be defined. The precise
behavior of an electron in an atom cannot be
directly determined.
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Schrodinger equation: H = E
•  = a wave function (from standing waves).
Wave functions define a region of space where it
is most likely to find the electron in an atom.
The square of the wavefunction, 2, represents
the “electron density” of that wavefunction.
• Orbitals: Wave functions giving solutions to the
Schrodinger equation. Orbitals are defined by
three quantum numbers. Electrons in an orbital
are defined using these numbers, plus one other.
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Four quantum numbers used to
define electrons in orbitals
Quantum number
name
symbol
values
Principal
n
1,2,3,…
Angular
momentum
l
0,…(n-1)
ml
- l,…+ l
ms
+1/2, -1/2
Magnetic
Spin
(we’ll talk more about spin later)
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Electron shells and subshells
• Electron shell: Orbitals that have the
same principal quantum number
– (same n).
• Subshell: Orbitals have the same principal
and orbital angular momentum quantum
numbers
– (same n and l)
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Representations of orbitals
• There are two components of an orbital, its
radial distribution and its angular
distribution.
• Angular distribution is commonly called the
orbital’s “shape”.
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s, p, and d orbital shapes
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http://www.shef.ac.uk/chemistry/orbitron/AOs/1s/index.html
• Radial distribution: An atom with n > 1 has at
least one node (an area where the electron
density is 0).
• As n increases, the number of nodes increases,
and the distance from the nucleus to the highest
electron density region also increases.
– Lower energy regions are forced closer to nucleus
• p. 208 & 209 in text give representations of s
and p orbitals. You should know these. You
should also be aware of the shapes of d orbitals
(p. 209). f orbitals are shown on p 210, but they
are rarely (never) encountered in this course.
http://wps.prenhall.com/wps/media/objects/166/170213/RadialElectronDistribution.html
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Electron-electron repulsion
• In the hydrogen atom, all orbitals with the
same n have the same energy. However,
in many-electron orbitals, repulsions
between the electrons cause differences in
energy between orbitals of the same n, but
different l.
http://wps.prenhall.com/wps/media/objects/166/170213/EnergyOrbitalsElectron.html
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Pauli exclusion principle
• no two electrons in an atom can have the
same four quantum numbers.
• The maximum number of electrons in
any orbital is two. The maximum
number of electrons in a shell (or
subshell) is 2x the number of orbitals in
the shell (or subshell).
• ms = +1/2 or –1/2 (up or down)
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Number of….
• Orbitals in a shell
• Electrons in a shell
• n2
• 2n2
• Orbitals in a subshell
• s=1; p=3; d=5
• - l to + l
• s?; p?; d?
• Electrons in a
subshell
MAXIMUM NUMBER OF ELECTRONS
IN ANY SINGLE ORBITAL IS ____!!!
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writing electronic configurations
• Electronic configurations: a method of
describing the orbital arrangement of
electrons in an atom.
• orbital notation: pictorially represents
electron positions in orbitals.
• Simplified notation: notes the number of
electrons in each subshell.
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Hund’s rule
•
What is degenerate?
For degenerate orbitals, lowest energy is
obtained when spin is maximized. this
means…
1. Electrons will fill the subshell orbitals, one at
a time, until each orbital has one electron.
2. All electrons will have the same spin (either
up or down, or either +1/2 or –1/2)
3. Only then will electrons be paired.
http://wps.prenhall.com/wps/media/objects/166/170213/ElectronConfigurations.html
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• Condensed electronic configurations
– A “shorthand” for writing complete electronic
configurations.
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Aufbau principle
• Describes the order in
which subshells are
filled. this order is
– 1s, 2s, 2p, 3s, 3p, 4s,
3d, 4p, 5s, 4d, 5p, 6s,
4f, 5d, 6p, 7s, 5f, 6d,
7p
• The ordering is due to
electron repulsions in
the higher orbitals
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The periodic table
• The shape of the table is a result of the order in
which the orbitals in the atoms are filled with
electrons
• Different areas of the table indicate which
subshell contains the valence (highest energy)
electrons.
• s-block
• p-block
• d-block
• using the periodic table is an excellent way to
remember the Aufbau principle.
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Fig. 5-31, p.219
Exceptions to the rule
in transition metals
•
•
p. 220, text.
These exceptions are due to the
closeness in energy of higher number
orbitals, and have to do with a balance
between electron promotion and electron
repulsion.
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Table 5-5, p.220