Transcript Chapter 7 The Quantum-Mechanical Model of the Atom

Chemistry: A Molecular Approach, 1st Ed.
Nivaldo Tro
Roy Kennedy
Massachusetts Bay Community College
Wellesley Hills, MA
2007, Prentice Hall
The Behavior of the Very
Small
 electrons are incredibly small
 a single speck of dust has more electrons than the number of
people who have ever lived on earth
 electron behavior determines much of the behavior of
atoms
 directly observing electrons in the atom is impossible, the
electron is so small that observing it changes its behavior
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A Theory that Explains Electron Behavior
 the quantum-mechanical model explains the manner
electrons exist and behave in atoms
 helps us understand and predict the properties of atoms
that are directly related to the behavior of the electrons
 why some elements are metals while others are nonmetals
 why some elements gain 1 electron when forming an anion,
while others gain 2
 why some elements are very reactive while others are practically
inert
 and other Periodic patterns we see in the properties of the
elements
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The Nature of Light
its Wave Nature
 light is a form of electromagnetic radiation
 composed of perpendicular oscillating waves, one for the
electric field and one for the magnetic field


an electric field is a region where an electrically charged particle
experiences a force
a magnetic field is a region where an magnetized particle experiences a
force
 all electromagnetic waves move through space at the
same, constant speed
 3.00 x 108 m/s in a vacuum = the speed of light, c
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Electromagnetic Radiation
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Characterizing
Waves
 the amplitude is the height of the wave
 the distance from node to crest
 or node to trough
 the amplitude is a measure of how intense the light is – the
larger the amplitude, the brighter the light
 the wavelength, (l) is a measure of the distance covered by
the wave
 the distance from one crest to the next
 or the distance from one trough to the next, or the distance between
alternate nodes
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Wave Characteristics
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Characterizing Waves
 the frequency, (n) is the number of waves that pass a point
in a given period of time
 the number of waves = number of cycles
 units are hertz, (Hz) or cycles/s = s-1
 1 Hz = 1 s-1
 the total energy is proportional to the amplitude and
frequency of the waves
 the larger the wave amplitude, the more force it has
 the more frequently the waves strike, the more total force there
is
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The Relationship Between
Wavelength and Frequency
 for waves traveling at the same speed, the shorter the
wavelength, the more frequently they pass
 this means that the wavelength and frequency of
electromagnetic waves are inversely proportional
 since the speed of light is constant, if we know wavelength we
can find the frequency, and visa versa


n s  
l m 
-1
c
m
s
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Examples
 Calculate the wavelength of red light with a frequency
of 4.62 x 1014 s-1
 Calculate the wavelength of a radio signal with a
frequency of 100.7 MHz
Color
 the color of light is determined by its wavelength
 or frequency
 white light is a mixture of all the colors of visible light
 a spectrum
 RedOrangeYellowGreenBlueViolet
 when an object absorbs some of the wavelengths of
white light while reflecting others, it appears colored
 the observed color is predominantly the colors reflected
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Amplitude & Wavelength
12
Electromagnetic Spectrum
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The Electromagnetic Spectrum
 visible light comprises only a small fraction of all the
wavelengths of light – called the electromagnetic spectrum
 short wavelength (high frequency) light has high energy
 radiowave light has the lowest energy
 gamma ray light has the highest energy
 high energy electromagnetic radiation can potentially damage
biological molecules
 ionizing radiation
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Interference
 the interaction between waves is called interference
 when waves interact so that they add to make a larger wave it is
called constructive interference
 waves are in-phase
 when waves interact so they cancel each other it is called
destructive interference
 waves are out-of-phase
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Interference
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Diffraction
 when traveling waves encounter an obstacle or opening in
a barrier that is about the same size as the wavelength,
they bend around it – this is called diffraction
 traveling particles do not diffract
 the diffraction of light through two slits separated by a
distance comparable to the wavelength results in an
interference pattern of the diffracted waves
 an interference pattern is a characteristic of all light waves
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Diffraction
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2-Slit Interference
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The Photoelectric Effect
 it was observed that many metals emit electrons when a
light shines on their surface
 this is called the Photoelectric Effect
 classic wave theory attributed this effect to the light
energy being transferred to the electron
 according to this theory, if the wavelength of light is
made shorter, or the light waves intensity made brighter,
more electrons should be ejected
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The Photoelectric Effect
The Problem
 in experiments with the photoelectric effect, it was observed
that there was a maximum wavelength for electrons to be
emitted
 called the threshold frequency
 regardless of the intensity
 it was also observed that high frequency light with a dim
source caused electron emission without any lag time
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Einstein’s Explanation
 Einstein proposed that the light energy was delivered to the
atoms in packets, called quanta or photons
 the energy of a photon of light was directly proportional to
its frequency
 inversely proportional to it wavelength
 the proportionality constant is called Planck’s Constant, (h)
and has the value 6.626 x 10-34 J∙s
E  hn 
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hc
l
Examples
 Calculate the number of photons in a laser pulse with wavelength
337 nm and total energy 3.83 mJ
 What is the frequency of radiation required to supply 1.0 x 102 J
of energy from
8.5 x 1027 photons?
Ejected Electrons
 1 photon at the threshold frequency has just enough energy for
an electron to escape the atom
 binding energy, f
 for higher frequencies, the electron absorbs more energy than
is necessary to escape
 this excess energy becomes kinetic energy of the ejected
electron
Kinetic Energy = Ephoton – Ebinding
KE = hn - f
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Spectra
 when atoms or molecules absorb energy, that energy is
often released as light energy
 fireworks, neon lights, etc.
 when that light is passed through a prism, a pattern is
seen that is unique to that type of atom or molecule – the
pattern is called an emission spectrum
 non-continuous
 can be used to identify the material
 Rydberg analyzed the spectrum of hydrogen and found
that it could be described with an equation that involved
an inverse square of integers
 1
1 
 1.097 10 m
 2
2


l
n
n
2 
 1
1
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7
-1 
Identifying Elements with
Flame Tests
Na
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K
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Li
Ba
Emission vs. Absorption Spectra
Spectra of Mercury
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Bohr’s
Model
 Neils Bohr proposed that the electrons could only have
very specific amounts of energy
 fixed amounts = quantized
 the electrons traveled in orbits that were a fixed distance
from the nucleus
 stationary states
 therefore the energy of the electron was proportional the
distance the orbital was from the nucleus
 electrons emitted radiation when they “jumped” from an
orbit with higher energy down to an orbit with lower
energy
 the distance between the orbits determined the energy of the
photon of light produced
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Bohr Model of H Atoms
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Wave Behavior of Electrons
 de Broglie proposed that particles could have wave-like
character
 because it is so small, the wave character of electrons is
significant
 electron beams shot at slits show an interference pattern
 the electron interferes with its own wave
 de Broglie predicted that the wavelength of a particle was
inversely proportional to its momentum
l m 
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h
 
kg m 2
s2
mass (kg)  velocity (m  s -1 )
Electron Diffraction
however, electrons actually
present
an interference
if electrons
behave like pattern,
demonstrating
behave
particles, therethe
should
onlylike
waves
be two bright spots on the
target
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examples
 Calculate the wavelength of an electron traveling at 2.65 x 106
m/s
 Determine the wavelength of a neutron traveling at 1.00
x 102 m/s
(Massneutron = 1.675 x 10-24 g)
Uncertainty
Principle
h
Dx  Dv 
4
1
 
m
 Heisenberg stated that the product of the uncertainties in
both the position and speed of a particle was inversely
proportional to its mass
 x = position, Dx = uncertainty in position
 v = velocity, Dv = uncertainty in velocity
 m = mass
 the means that the more accurately you know the position
of a small particle, like an electron, the less you know
about its speed
 and visa-versa
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Uncertainty Principle
Demonstration
any experiment designed to
observe the electron results
in detection of a single
electron particle and no
interference pattern
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Determinacy vs.
Indeterminacy
 according to classical physics, particles move in a path
determined by the particle’s velocity, position, and forces
acting on it
 determinacy = definite, predictable future
 because we cannot know both the position and velocity
of an electron, we cannot predict the path it will follow
 indeterminacy = indefinite future, can only predict probability
 the best we can do is to describe the probability an
electron will be found in a particular region using
statistical functions
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