Transcript PowerPoint 프레젠테이션

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
 CHARACTERISTICS OF ELECTROMAGNETIC WAVES
 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
For waves traveling at
the same velocity, the
longer the wavelength,
the smaller the
frequency
 Relationship between the wavelength and the frequency
c = 
6.1 THE WAVE NATURE OF LIGHT
 THE ELECTROMAGNETIC SPECTRUM
 Different properties of electromagnetic radiation comes
from their different wavelength
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 PHOTONS
 Although the wave model of light explains many aspects
of its behavior, this model cannot explain several
phenomena:
• Blackbody radiation
• Photoelectric effect
• Emission spectra
6.2 QUANTIZED ENERGY AND PHOTONS
 HOT OBJECTS AND THE QUANTIZATION OF ENERGY
 As a body is heated, it begins to emit radiation and
becomes first red, then orange, then yellow, then white as
its temperature increases
 The classical theory of radiation
predicts:
Intensity ∝ kT/4
 Max Planck explained it by
assuming that energy comes
in packets called quanta
E = h
h, Planck’s constant
6.626  10−34 J-s
6.2 QUANTIZED ENERGY AND PHOTONS
 THE PHOTOELECTRIC EFFECT AND PHOTONS
 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
photoelectric 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 PHOTONS
 THE PHOTOELECTRIC EFFECT AND PHOTONS
6.3 LINE SPECTRA AND THE BOHR MODEL
 LINE SPECTRA
 Radiation composed of a single wavelength is said to be
monochromatic
 Most common radiation sources
contain many different wavelength
6.3 LINE SPECTRA AND THE BOHR MODEL
 LINE SPECTRA
 For atoms and molecules one does not observe a
continuous spectrum, as one gets from a white light source.
 Only a line spectrum of discrete wavelengths is observed.
H2
Rydberg equation
RH, Rydberg constant
Ne
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
electron 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
allowed 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 MATTER
 Louis de Broglie suggested:
“If radiant energy could, under appropriate conditions
behave 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
applicable to all matters
6.4 THE WAVE BEHAVIOR OF MATTER
6.4 THE WAVE BEHAVIOR OF MATTER
 THE UNCERTAINTY PRINCIPLE

Heisenberg showed that the more precisely the
momentum 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
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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
particles, 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 ORBITALS
 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 higherenergy 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 ORBITALS
 These wave functions are
represented 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
location – probability density
 This is just a kind of statistical
knowledge – we cannot specify the
exact location of an electron
Figure 6.16
Electron-density distribution
6.5 QUANTUM MECHANICS AND ATOMIC ORBITALS
 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 ORBITALS
 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 ORBITALS
 MAGNETIC QUANTUM NUMBER
 The magnetic quantum number describes the threedimensional 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 ORBITALS
 ORBITALS AND QUANTUM NUMBERS
 Orbitals with the same value of n form a shell.
 Different orbital types within a shell are subshells.
6.5 QUANTUM MECHANICS AND ATOMIC ORBITALS
 ORBITALS AND QUANTUM NUMBERS

For a one-electron
hydrogen atom,
orbitals on the same
energy level have the
same energy.

That is, they are
degenerate.
Figure 6.17
6.5 QUANTUM MECHANICS AND ATOMIC ORBITALS
 ORBITALS AND QUANTUM NUMBERS
6.6 REPRESENTATIONS OF ORBITALS
 THE S ORBITALS
 Spherically symmetric
 There is only one s orbital for each value of n (l = 0, ml = 0)
 Radial probability function
 Nodes
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
resembles 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,
orbitals on the same energy
level are no longer
degenerate
 For a given value of n, the
energy of an orbital
increases 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 number,
ms
 The spin quantum number has
only 2 allowed values: +1/2 and
−1/2
6.7 MANY-ELECTRON ATOMS
 PAULI EXCLUSION PRINCIPLE
 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
6.8 ELECTRON CONFIGURATION
 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?
paired unpaired
6.8 ELECTRON CONFIGURATION
 HUND’S RULE
 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
(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
electron 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 PERIODIC TABLE
 The structure of the periodic
table reflects the orbital
structure
6.9 ELECTRON CONFIGURATIONS AND THE PERIODIC TABLE
 The periodic table is your best guide to the order in which
orbitals are filled
6.9 ELECTRON CONFIGURATIONS AND THE PERIODIC TABLE
6.9 ELECTRON CONFIGURATIONS AND THE PERIODIC TABLE
6.9 ELECTRON CONFIGURATIONS AND THE PERIODIC TABLE