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6.1 The Wave Nature of Light. To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation Electromagnetic radiation A form of energy exhibiting wave-like behavior as it travels through space - PowerPoint PPT Presentation
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6.1 THE WAVE NATURE OF
LIGHT
To understand the electronic structure of atoms, one must
understand the nature of electromagnetic radiation
Electromagnetic radiation
•A form of energy exhibiting wave-like behavior as it
travels through space
•Visible light, IR, and X-rays share certain fundamental
characteristics
•All types of electromagnetic radiation move through a
vacuum at a speed of 3.00 × 108 m/s, the speed of light
6.1 THE WAVE NATURE OF LIGHT
Wavelength (), amplitude, and frequency ()•The distance between corresponding points on adjacent waves is
the wavelength
•The number of waves passing a given point per unit of time is the
frequency
Relationship between the wavelength and the frequency
c =
CHARACTERISTICS OF ELECTROMAG-
NETIC WAVES
For waves traveling at the same velocity, the longer the wavelength, the smaller the fre-quency
6.1 THE WAVE NATURE OF LIGHT
Different properties of electromagnetic radiation comes
from their different wavelength
THE ELECTROMAGNETIC SPECTRUM
6.1 THE WAVE NATURE OF LIGHT
COMMON WAVELENGTH UNITS
6.1 THE WAVE NATURE OF LIGHT
SAMPLE EXERCISE 6.1
1. Which wave has the higher frequency?
2. Visible light and IR
3. Blue light and red light
6.1 THE WAVE NATURE OF LIGHT
6.2 QUANTIZED ENERGY AND PHO-
TONS
Although the wave model of light explains many aspects
of its behavior, this model cannot explain several phe-
nomena:
•Blackbody radiation
•Photoelectric effect
•Emission spectra
6.2 QUANTIZED ENERGY AND PHO-TONS
As a body is heated, it begins to emit radiation and be-
comes first red, then orange, then yellow, then white as its
temperature increases
HOT OBJECTS AND THE QUANTIZATION OF
ENERGY
The classical theory of radiation
predicts:
Intensity kT/4 Max Planck explained it by as-
suming that energy comes in
packets called quanta E = h
h, Planck’s constant 6.626 10−34 J-s
6.2 QUANTIZED ENERGY AND PHO-TONS THE PHOTOELECTRIC EFFECT AND PHO-
TONS Light with a specific frequency or greater causes a metal to emit electrons, but light of lower frequency has no effect
Einstein used Planck’s assumption to explain the photoelec-tric effect.
He concluded that energy is proportional to frequency:
E = h h, Planck’s constant
6.626 10−34 J-s.
6.2 QUANTIZED ENERGY AND PHO-TONS THE PHOTOELECTRIC EFFECT AND PHO-
TONS
6.3 LINE SPECTRA AND THE BOHR MODEL
Radiation composed of a single wavelength is said to be
monochromatic
Most common radiation sources contain
many different wavelength
LINE SPECTRA
6.3 LINE SPECTRA AND THE BOHR MODEL
LINE SPECTRA
H2 Ne
For atoms and molecules one does not observe a continu-ous spectrum, as one gets from a white light source.
Only a line spectrum of discrete wavelengths is observed.
Rydberg equationRH, Rydberg constant
High voltage under reduced pressure of different gases produces different colors of light
6.3 LINE SPECTRA AND THE BOHR MODEL
BOHR’S MODEL
The classical “microscopic solar system” model of the atom
cannot explain the line spectrum
Bohr’s postulates
• Electrons in an atom can only occupy certain orbits
(corresponding to certain energies).
• An electrons in a permitted orbit have a specific energy and is in
an “allowed” state. An electron in an allowed energy state will
not radiate energy and therefore will not spiral into the nucleus
• Energy is emitted or absorbed by the electron only as the elec-
tron changes from one allowed energy state to another. This
energy is emitted or absorbed as a photon, E = h
6.3 LINE SPECTRA AND THE BOHR MODEL THE ENERGY STATES OF THE HYDROGEN
ATOM Bohr calculated the energies
corresponding to each al-
lowed orbit for the electron in
the hydrogen atom
RH is the Rydberg constant
n is the principal quantum
number
Ground state & excited state
6.3 LINE SPECTRA AND THE BOHR MODEL THE ENERGY STATES OF THE HYDROGEN
ATOM
The equation is corresponding to the experimental equation
6.3 LINE SPECTRA AND THE BOHR MODEL THE ENERGY STATES OF THE HYDROGEN
ATOM
6.3 LINE SPECTRA AND THE BOHR MODEL
LIMITATIONS OF THE BOHR MODEL
Significance of the Bohr model
•Electrons exist only in certain discrete energy levels, which
are described by quantum numbers
•Energy is involved in moving an electron from one level to
another
The model cannot explain the spectra of other atoms and
why electrons do not fall into the positively charged nucleus
6.4 THE WAVE BEHAVIOR OF MAT-
TER Louis de Broglie suggested:
“If radiant energy could, under appropriate conditions be-
have as though it were a stream of particles, could matter,
under appropriate conditions, possibly show the properties
of a wave?”
An electron moving about the
nucleus of an atom behaves like
a wave and therefore has a
wavelength
de Broglie’s hypothesis is appli-
cable to all matters
6.4 THE WAVE BEHAVIOR OF MAT-
TER
6.4 THE WAVE BEHAVIOR OF MATTER
THE UNCERTAINTY PRINCIPLE Heisenberg showed that the more precisely the mo-
mentum of a particle is known, the less precisely is its position known:
In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!
If we have 1% of uncertainty in the speed of electron in hydrogen atom (diameter, 1 × 10-10 m)
6.4 THE WAVE BEHAVIOR OF MATTER
Whenever any measurement is made, some uncertainty exists
This limit is not a restriction on how well instruments can be made; rather, it is inherent in nature
No practical consequences on ordinary-sized objects Enormous implications when dealing with subatomic parti-
cles, such as electrons Short wavelength of light for accuracy in position High energy light will change the electron’s motion There is an uncertainty in simultaneously knowing either
the position or the momentum of the electron that cannot be reduced beyond a certain minimum level
6.5 QUANTUM MECHANICS AND ATOMIC OR-
BITALS Erwin Schrödinger developed a mathematical treatment into which
both the wave and particle nature of matter could be incorporated.
He treated the electron in
a hydrogen atom like the
wave on a guitar string
Overtones vs higher- en-
ergy standing waves
Nodes vs zero amplitude
Solving Schrödinger’s
equation for the hydrogen
atom leads to a series of
mathematical functions –
wave functions
6.5 QUANTUM MECHANICS AND ATOMIC OR-
BITALS These wave functions are repre-
sented by the symbol (psi)
The wave function has no direct
physical meaning
The square of the wave equation,
2, represents the probability that
the electron will be found at that lo-
cation – probability density
This is just a kind of statistical
knowledge – we cannot specify the
exact location of an electron
Figure 6.16 Electron-density distribu-tion
6.5 QUANTUM MECHANICS AND ATOMIC OR-BITALS
ORBITALS AND QUANTUM NUMBERS Solving the wave equation gives a set of wave functions,
or orbitals, and their corresponding energies. Each orbital describes a spatial distribution of electron
density. An orbital is described by a set of three quantum numbers.
PRINCIPAL QUANTUM NUMBER The principal quantum number, n, describes the energy
level on which the orbital resides. The values of n are integers ≥ 1.
6.5 QUANTUM MECHANICS AND ATOMIC OR-BITALS
ANGULAR MOMENTUM QUANTUM NUMBER
This quantum number defines the shape of the orbital.
Allowed values of l are integers ranging from 0 to n − 1.
We use letter designations to communicate the different
values of l and, therefore, the shapes and types of orbitals.
6.5 QUANTUM MECHANICS AND ATOMIC OR-BITALS
MAGNETIC QUANTUM NUMBER
The magnetic quantum number describes the three-di-
mensional orientation of the orbital.
Allowed values of ml are integers ranging from −l to l :
−l ≤ ml ≤ l
Therefore, on any given energy level, there can be up to 1
s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.
6.5 QUANTUM MECHANICS AND ATOMIC OR-BITALS
Orbitals with the same value of n form a shell.
Different orbital types within a shell are subshells.
ORBITALS AND QUANTUM NUMBERS
6.5 QUANTUM MECHANICS AND ATOMIC OR-BITALS
ORBITALS AND QUANTUM NUMBERS
For a one-electron hy-
drogen atom, orbitals
on the same energy
level have the same
energy.
That is, they are de-
generate.
Figure 6.17
6.5 QUANTUM MECHANICS AND ATOMIC OR-BITALS
ORBITALS AND QUANTUM NUMBERS
6.6 REPRESENTATIONS OF ORBITALS
Spherically symmetric
There is only one s orbital for each value of n (l = 0, ml = 0)
Radial probability function
Nodes
THE S ORBITALS
6.6 REPRESENTATIONS OF ORBITALS
THE S ORBITALS
Figure 6.21 probability density in the s orbitals of hydrogen.
6.6 REPRESENTATIONS OF ORBITALS
THE P ORBITALS
The value of l for p orbitals is 1 and the orbital has
three magnetic quantum number ml.
They have two lobes with a node between them.
6.6 REPRESENTATIONS OF ORBITALS
THE d AND f ORBITALS The value of l for a d orbital is 2 and the orbital has five
magnetic quantum number ml.
Four of the five d orbitals have 4 lobes; the other resem-bles a p orbital with a doughnut around the center.
6.7 MANY-ELECTRON ATOMS
ORBITALS AND THEIR ENERGIES
As the number of electrons
increases, though, so does
the repulsion between them.
In many-electron atoms, or-
bitals on the same energy
level are no longer degener-
ate
For a given value of n, the
energy of an orbital in-
creases with increasing
value of l.
In the 1920s, it was discovered that a beam of neutral
atoms is separated into two groups when passing them
through a nonhomogeneous magnetic field
Electron has two equivalent magnetic field
6.7 MANY-ELECTRON ATOMS
ELECTRON SPIN
Observation of closely spaced
double lines in spectrum of
many-electron atoms
Electrons have spin.
Spin magnetic quantum num-
ber, ms
The spin quantum number has
only 2 allowed values: +1/2 and
−1/2
No two electrons in the same atom can have identical sets of quantum numbers.
An orbital can hold a maximum of two electrons and they must have opposite spins
6.7 MANY-ELECTRON ATOMS
PAULI EXCLUSION PRINCIPLE
Electron distribution in orbitals of an atom. The ground state: the most stable electron configuration of
an atom The orbitals are filled in order of increasing energy with no
more than two electrons per orbital Consider the lithium atom
•How many electrons?•Electron configuration?
6.8 ELECTRON CONFIGURATION
paired unpaired
For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized
- Hund’s rule
6.8 ELECTRON CONFIGURATION
HUND’S RULE
6.8 ELECTRON CONFIGURATION
HUND’S RULE
6.8 ELECTRON CONFIGURATION
(b) How many unpaired electrons exist?
6.8 ELECTRON CONFIGURATION
Drawbacks to using x-rays for medical imaging MRI overcomes the drawbacks
6.8 ELECTRON CONFIGURATION
TRANSITION METALS The condensed electron configuration includes the elec-
tron configuration of the nearest noble-gas element of lower atomic number
Note that the 19th electron of potassium is occupied in 4s (not 3d)
Transition metals: elements in the d-block of the periodic table
Lanthanides and actinides
6.9 ELECTRON CONFIGURATIONS AND THE PERI-ODIC TABLE
The structure of the periodic table reflects the orbital struc-ture
6.9 ELECTRON CONFIGURATIONS AND THE PERI-ODIC TABLE
The periodic table is your best guide to the order in which orbitals are filled
6.9 ELECTRON CONFIGURATIONS AND THE PERI-ODIC TABLE
6.9 ELECTRON CONFIGURATIONS AND THE PERI-ODIC TABLE
6.9 ELECTRON CONFIGURATIONS AND THE PERI-ODIC TABLE