Transcript Chapter 7-part1

Chapter 7
The Quantum-Mechanical Model
of the Atom
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
2
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
3
Electromagnetic Radiation
4
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
5
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
6
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  
-1
c

m
s
l m 
7
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
9
Electromagnetic Spectrum
Tro, Chemistry: A Molecular
Approach
10
Amplitude & Wavelength
11
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
12
Thermal Imaging using
Infrared Light
Using High Energy
Radiation
to Kill Cancer Cells
13
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
14
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
15
2-Slit Interference
16
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
17
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
analogy of the effect of throwing a
thousand ping-pong balls at a window
versus 1 baseball.
18
Particlelike Properties of
Electromagnetic Energy
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 
20
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?

What is the energy (in kJ/mol) of photons of radar waves with ν = 3.35 x
108 Hz?

What is the energy (in kJ/mol) of photons of an X-ray with λ = 3.44 x 10-9
m?
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
22
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
 n1 n 2 
1
23
7
-1
Examples of Spectra
Oxygen spectrum
Neon spectrum
24
Emission vs. Absorption Spectra
Spectra of Mercury
25
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
26
Bohr Model of H Atoms
27
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

What is the de Broglie wavelength (in meters) of a small car with a mass of
11500 kg traveling at a speed of 55.0 mi/h (24.6 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)?
examples

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)?

What is the velocity of an electron having a de Broglie wavelength that is
approximately the length of a chemical bond? Assume this length to be 1.2
x 10-10 m

Determine the wavelength of a neutron traveling at 1.00 x 102 m/s
(Massneutron = 1.675 x 10-24 g)
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
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
32