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Chapter 2

CHEM 130 Chapter Notes - Chapter 2: Louis De Broglie, Electronic Correlation, Photon

Department
Chemistry
Course Code
CHEM 130
Professor
Carol Ann Castaneda
Chapter
2

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o One of the ways that energy travels through space is by electromagnetic radiation
o Waves have three primary characteristics:
Wavelength
Frequency
Speed
o Wavelength: the distance between two consecutive peaks or troughs in a wave
o Frequency: the number of waves per second that pass a given point in space
o Since all types of electromagnetic radiation travel at the speed of light, short-wavelength
radiation must have a high frequency
o The wave with the shortest wavelength has the highest frequency
o The wave with the longest wavelength has the lowest frequency
o This implies an inverse relationship between wavelength and frequency
(wavelength in meters)(frequency in cycles per second) = speed of light
Speed of light = 3.00 x 108 m/s
o Radiation provides an important means of energy transfer
2.2: The Nature of Matter
o 19th century:
Matter and energy were distinct
Matter was thought to consist of particles, whereas energy in the form of light was
described as a wave
Particles were things that has mass and whose position in space could be specified
Waves were described as massless and delocalized, their position in space could not be
specified
o 20th century:
Experimental results suggested that this picture was incorrect
Max Planck, while studying the radiation profiles emitted by solid bodies heated to
incandescence, Planck found that the results could not be explained in terms of the
physics of his day
Matter could absorb or emit quantity of energy
Planck could account for these observation only by postulating that energy can be
gained or lost only in whole-number multiples of the quantity hv, where h is a constant
called Planck's constant, determined by experiment to have a value of 6.626 x 10-34 J x s
The change in energy for a system can be represented by:
(Delta)E = nhv
N is an integer
H is Planck's constant
V is the frequency of the electromagnetic radiation absorbed or emitted
It had always be assumed that the energy of matter was continuous, which meant that
the transfer of any quantity of energy was possible
Now it seemed clear that energy is in fact quantized and can occur only in discrete
units of size hv
Each of these small "packets" of energy is called a quantum
A system can transfer energy only in whole quanta
o Albert Einstein proposed that electromagnetic radiation is itself quantized

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Einstein suggested that electromagnetic radiation can be viewed as a stream of
"particles" called photons
The energy of each photon is given by the expression:
E(photon) = hv = hc/wavelength
H = Planck's constant
o The photoelectric effect refers to the phenomenon in which electrons are emitted from the
surface of a metal when light strikes it
Studies in which the frequency of the light is varied show that no electrons are emitted
by a given metal below a specific threshold frequency
For light with frequency lower than threshold frequency no electrons are emitted,
regardless of the intensity of light
For light with frequency greater than the threshold frequency, the number of electrons
emitted increases with the intensity of the light
For light with frequency greater than the threshold frequency, the kinetic energy of the
emitted electrons increases linearly with the frequency of the light
o These observations can be explained by assuming that electromagnetic radiation is quantized
and that the threshold frequency represents the minimum energy required to remove the
electron from the metal's surface
o Because a photon with energy less than E0 cannot remove an electron, light with a frequency
less than the threshold frequency produces no electrons
o On the other hand, for light with energy greater than E0, the energy in excess of that required
to remove the electron is given to the electron as kinetic energy (KE)
Keelectron = 1/2mv2 = hv - hv0
o A greater intensity means that more photons are available to release electrons
o Arthur Compton performed experiments involving collisions of X rays and the electrons that
showed that photos do exhibit the apparent mass calculated from the preceding equation
o Conclusions from the work of Planck and Einstein:
Energy is quantized. It can occur only in discrete units called quanta.
Electromagnetic radiation, which was previously though to exhibit only wave properties,
seems to show certain characteristics of particulate matter as well
Dual nature of light
o Diffraction results when light is scattered from a regular array of points or lines
o A diffraction pattern can be explained only in terms of waves
o All matter exhibits both particulate and wave properties
2.3: The Atmospheric Spectrum of Hydrogen
o Another important study was the study of the emission of light by excited hydrogen atoms
o When a sample of hydrogen gas receive a high-energy spark, the H2 molecules absorb energy,
and some of the H -- H bonds are broken
o The resulting hydrogen atoms are excited, they contain excess energy, which they release by
emitting light of various wavelengths to produce what is called the emission spectrum of the
hydrogen atom
o Continuous spectrum: contains all the wavelengths of visible light
o Line spectrum: Few lines, each of which corresponds to a discrete wavelength
o The hydrogen emission spectrum is called a line spectrum
o What is the significance of the line spectrum of hydrogen?
It indicates that only certain energies are allowed for the electron in the hydrogen atom
The energy of the electron in the hydrogen atom is quantized

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o A given change in energy from a high to a lower level would give a wavelength of light that can
be calculated from Planck's equation
o The discrete line spectrum of hydrogen shows that only certain energies are possible; the
electron energy levels are quantized
o In contrast, if any energy level were allowed the emission spectrum would be continuous
2.4: The Bohr Model
o Niels Bohr developed a quantum model for the hydrogen atom
o Bohr proposed that the electron in a hydrogen atom moves around the nucleus only in certain
allowed circular orbits
o Bohr reasoned that the tendency of the revolting electron to fly off the atom must be just
balanced by its attraction for the positively charged nucleus
o The electron should emit light and lose energy - and thus be drawn into the nucleus
o Ground state: lowest possible energy state
o The fact that the atom loses energy when the electron changes from a higher energy level to a
lower one makes sense, because the electron moves closer to the nucleus
o As opposite charges move closer together, the potential energy decreases
o The energy lost is carried away from the atom by the production of a photon
o At this time we must emphasize two important points about the Bohr model:
The model correctly fits the quantized energy levels of the hydrogen atom and
postulates only certain allowed orbits for the electron
As the electron becomes more tightly bound, its energy becomes more negative relative
to the zero-energy reference state. As the electron is brought closer to the nucleus,
energy is released from the system.
o At first Bohr's model appeared to be very promising
o The energy levels calculated by Bohr closely agreed with the values obtained from hydrogen
emission spectrum
o However, when Bohr's model was applied to atoms other than hydrogen, it did not work at all
2.5: The quantum mechanical model of the atom
o Werner Heisenberg, Louis de Broglie and Erwin Schrodinger developed what became known
as wave mechanics, or quantum mechanics
o Broglie originated the idea that the electron, previously considered to be a particles, also
shows wave properties
o To Schrödinger and de Broglie, the electron bound to the nucleus seemed similar to a standing
wave, and they began research on a wave mechanical description of the atom
o Wave function: A function of the coordinates of the electron's position in three-dimensional
space and H (with a roof) represents a set of mathematical instructions called an operator
The operator contains mathematical terms that produce the total energy of the atom
when they are applied to the wave function
E expressed the total energy of the atom
o A specific wave function is called an orbital
o The wave function is called the 1s orbital
o Heisenberg uncertainty principle: There is a fundamental limitation to just how precisely we
can know both the position and momentum of a particle at a given time
o Probability distribution: The square of the function indicates the probability of finding an
electron near a particular point in space
o The darkness of a point indicates the probability of finding an electron at that position
o The probability of finding the electron at a particular position is greatest close to the nucleus
and drops off rapidly as the distance from the nucleus increases