Transcript chapter 5

Chapter 5
Periodicity and Atomic Structure
Light and the Electromagnetic
Spectrum
Electromagnetic energy (“light”) is characterized by
wavelength, frequency, and amplitude.
Light and the Electromagnetic Spectrum
Light and the Electromagnetic Spectrum
n
l
Light and the Electromagnetic Spectrum
Wavelength x Frequency = Speed
l
m
x
n
= c
1
m
s
s
c is defined to be the rate of travel of all electromagnetic
energy in a vacuum and is a constant value—speed of light.
c = 3.00 x 108
m
s
Examples
◦ The light blue glow given off by mercury
streetlamps has a frequency of 6.88 x
1014 s-1 (or, Hz). What is the wavelength
in nanometers?
Electromagnetic Energy and Atomic
Line Spectra
Chapter 5/7
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Electromagnetic Energy and Atomic
Line Spectra
Line Spectrum: A series of discrete lines on an otherwise dark background as
a result of light emitted by an excited atom
Chapter 5/8
© 2012 Pearson Education, Inc.
Electromagnetic Radiation and Atomic
Spectra
Individual atoms give off
light when heated or
otherwise excited
energetically

◦
Provides clue to atomic
makeup
Consists of only few λ
Line spectrum – series of
discrete lines ( or
wavelengths) separated by
blank areas
◦
◦

E.g.
Lyman series
in the ultraviolet region
Electromagnetic Energy and Atomic
Line Spectra
Johann Balmer in 1885 discovered a mathematical relationship for the four
visible lines in the atomic line spectra for hydrogen.
1
=R
l
1
1
-
22
n2
Johannes Rydberg later modified the equation to fit every line in the entire
spectrum of hydrogen.
1
l
=R
1
m2
-
1
n2
R (Rydberg Constant) = 1.097 x 10-2 nm-1
Chapter 5/10
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The energy level of Hydrogen
Particlelike Properties of
Electromagnetic Energy

Photoelectric Effect:
Irradiation of clean metal
surface with light causes
electrons to be ejected from
the metal. Furthermore,
the frequency of the light
used for the irradiation
must be above some
threshold value, which is
different for every metal.
Examples
Solar energy, which is produced by photovoltaic cells.
These are made of semi-conducting material
which produce electricity when exposed to sunlight
it works on the basic principle of light striking the
cathode which causes the emmision of electrons,
which in turn produces a current.
Particlelike Properties of
Electromagnetic Energy
Particlelike Properties of
Electromagnetic Energy
Einstein explained the effect by assuming that a beam of light
behaves as if it were a stream of particles called photons.
Ephoton = hn
ν
E
Electromagnetic energy (light) is quantized.
h (Planck’s constant) = 6.626 x 10-34 J s
* 1mol of anything = 6.02 x 1023
Emission of Energy by Atom

How does atom emit light?
◦
◦
◦
◦
Atoms absorbs energy
Atoms become excited
Release energy
Higher-energy photon –>shorter
wavelength
◦ Lower-energy photon -> longer
wavelength
Examples
What
is the energy (in kJ/mol) of
photons of radar waves with ν = 3.35
x 108 Hz?
Calculate
the wavelength of light that
has energy 1.32 x 10-23 J/photon
Calculate
the energy per photon of
light with wavelength 650 nm
Particlelike Properties of
Electromagnetic Energy


Niels Bohr proposed in 1914 a model of the hydrogen
atom as a nucleus with an electron circling around it.
In this model, the energy levels of the orbits are
quantized so that only certain specific orbits
corresponding to certain specific energies for the
electron are available.
Niels Bohr Model
In each case the wavelength of the
emitted or absorbed light is exactly
such that the photon carries the
energy difference between the two orbits
Excitation by absorption of light and de-excitation by
emission of light
Wavelike Properties of Matter
Louis de Broglie in 1924 suggested that, if light can behave in some
respects like matter, then perhaps matter can behave in some respects like
light.
In other words, perhaps matter is wavelike as well as particlelike.
l= h
mv
The de Broglie equation allows the calculation of a “wavelength” of an
electron or of any particle or object of mass m and velocity v.
Examples

Calculate the de Broglie wavelength of the “particle” in
the following case
◦ A 25.0 bullet traveling at 612 m/s

What velocity would an electron (mass = 9.11 x 10-31kg)
need for its de Broglie wavelength to be that of red light
(750 nm)?
Quantum Mechanics and the Heisenberg
Uncertainty Principle
In 1926 Erwin Schrödinger proposed the quantum
mechanical model of the atom which focuses on the
wavelike properties of the electron.
In 1927 Werner Heisenberg stated that it is impossible to know
precisely where an electron is and what path it follows—a
statement called the Heisenberg uncertainty principle.
Quantum Mechanics and the Heisenberg
Uncertainty Principle

Heisenberg Uncertainty Principle – both the position
(Δx) and the momentum (Δmv) of an electron cannot be known
beyond a certain level of precision
1.
(Δx) (Δmv) > h
4π
2.
Cannot know both the position and the
momentum of an electron with a high degree of certainty
3.
If the momentum is known with a high degree of
certainty
i.
Δmv is small
ii.
Δ x (position of the electron) is large
4.
If the exact position of the electron is known
i.
Δmv is large
ii.
Δ x (position of the electron) is small
Wave Functions and Quantum Numbers
Wave
equation
solve
Wave function
or orbital (Y)
Probability of finding
electron in a region
of space (Y 2)
A wave function is characterized by three parameters called
quantum numbers, n, l, ml.
Wave Functions and Quantum
Numbers
Principal Quantum
Number (n)
• Describes the size and
energy level of the orbital
• Commonly called shell
• Positive integer (n = 1, 2,
3, 4, …)
• As the value of n
increases:
• The energy increases
• The average distance
of the e- from the
nucleus increases
Wave Functions and Quantum Numbers
Angular-Momentum Quantum Number (l)
• Defines the three-dimensional shape of the orbital
• Commonly called subshell
• There are n different shapes for orbitals
• If n = 1 then l = 0
• If n = 2 then l = 0 or 1
• If n = 3 then l = 0, 1, or 2
• etc.
• Commonly referred to by letter (subshell notation)
• l=0
s (sharp)
• l=1
p (principal)
• l=2
d (diffuse)
• l=3
f (fundamental)
• etc.
Wave Functions and Quantum Numbers
Magnetic Quantum Number (ml )
• Defines the spatial orientation of the orbital
• There are 2l + 1 values of ml and they can have any
integral value from -l to +l
• If l = 0 then ml = 0
• If l = 1 then ml = -1, 0, or 1
• If l = 2 then ml = -2, -1, 0, 1, or 2
• etc.
Wave Functions and Quantum Numbers
Wave Functions and Quantum
Numbers

Identify the possible values for each of the three
quantum numbers for a 4p orbital.

Give orbital notations for electrons in orbitals with the
following quantum numbers:
a) n = 2, l = 1, ml = 1
b) n = 4, l = 0, ml =0

Give the possible combinations of quantum numbers
for the following orbitals:
 A 3s orbital
b) A 4f orbital
The Shapes of Orbitals
Node: A surface of zero
probability for finding the
electron.
The Shapes of Orbitals
Electron Spin and the Pauli Exclusion
Principle
Electrons have spin which gives rise to a tiny magnetic field and to a spin
quantum number (ms).
Pauli Exclusion Principle: No two electrons in an atom can have the same four
quantum numbers.
Orbital Energy Levels in Multielectron
Atoms
Electron Configurations of Multielectron
Atoms
Effective Nuclear Charge (Zeff): The nuclear charge actually
felt by an electron.
Zeff = Zactual - Electron shielding
Electron Configurations of Multielectron
Atoms
Electron Configuration: A description of which orbitals are occupied by
electrons.
1s2 2s2 2p6 ….
Degenerate Orbitals: Orbitals that have the same energy level. For
example, the three p orbitals in a given subshell.
2px 2py 2pz
Ground-State Electron Configuration: The lowest-energy
configuration.
1s2 2s2 2p6 ….
Orbital Filling Diagram: using arrow(s) to represent occupied in an
orbital
Electron Configurations of Multielectron
Atoms
Aufbau Principle (“building up”): A guide for determining the filling
order of orbitals.
Rules of the aufbau principle:
1. Lower-energy orbitals fill before higher-energy orbitals.
2. An orbital can only hold two electrons, which must have opposite
spins (Pauli exclusion principle).
3. If two or more degenerate orbitals are available, follow Hund’s rule.
Hund’s Rule: If two or more orbitals with the same energy are available,
one electron goes into each until all are half-full. The electrons in the halffilled orbitals all have the same spin.
Electron Configurations of Multielectron
Atoms
Electron
Configuration
H:
1s1
He:
1 electron
s orbital (l = 0)
n=1
1s2
2 electrons
s orbital (l = 0)
n=1
Electron Configurations and the Periodic
Table
Valence Shell: Outermost shell or the highest energy .
Li: 2s1
Na: 3s1
Cl: 3s2 3p5
Br: 4s2 4p5
Electron Configurations and the
Periodic Table

Give expected ground-state electron configurations (or
the full electron configuration) for the following atoms,
draw – orbital filling diagrams and determine the
valence shell
◦ O (Z = 8)
◦ Ti (Z = 22)
◦ Sr (Z = 38)
◦ Sn (Z = 50)
Electron Configurations and Periodic
Properties: Atomic Radii
column
radius
row
radius
Electron Configurations and Periodic
Properties: Atomic Radii
Examples

Arrange the elements P, S and O
in order of increasing atomic
radius