Chapter 5 Models of the Atom

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Chapter 5Models of the Atom
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Atomic Models
Rutherford used existing ideas bout the atom and
proposed an atomic model in which the electrons
move around the nucleus. However, Rutherfords
atomic model could not explain the chemical
properties of element. Niels Bohr, a student of
Rutherfords, changed Rutherfords model to
include how the energy of an atom changes when it
absorbs or emits light. The Bohr Model he
proposed that an electron is found only in
specific circular paths, or orbits, around the
nucleus.
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The Bohr Model
Each possible electron orbit in Bohrs model has
a fixed energy. The fixed energies an electron
can have are called energy levels. The fixed
energy levels of electrons are somewhat like the
rungs of the ladder in which the lowest rung of
the ladder corresponds to the lowest energy
level. An electron can jump from one energy
level to another. Electrons in an atom cannot be
between energy levels.
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The Bohr Model
To move from one energy level to another, an
electron must gain or lose jus the right amount
of energy. In general, the higher an electron
is on the energy ladder, the farther it is from
the nucleus. A quantum of energy is the
amount of energy required to move and electron
from one energy level to another energy level.
The energy of an electron is said to be
quantized. The term quantum leap originates
from the ideas found in the Bohr model of the
atom.
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The Bohr Model
The amount of energy an electron gains or loses
in an atom is not always the same. The energy
levels in an atom are not equally spaced. The
higher energy levels are closer together. The
higher the energy level occupied by an electron,
the less energy it takes to move from that energy
level to the next energy level. The Bohr model
gave results in agreement with experiments for
the hydrogen atom (1e-), but failed to explain
the energies absorbed and emitted by atoms with
more than one electron.
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Refresher
Every atom, except hydrogen, consists of a small
dense nucleus composed of protons and neutron
that accounts for most of the mass of the
atom. Hydrogen is an exception because it has
only one proton in its nucleus. Negatively
charged electrons surround the nucleus and occupy
most of its volume. Electrons contribute little
to the mass of an atom.
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Energy Levels Example
When light shines on a fluorescent material, its
electrons absorb the energy and move to a higher
energy level. Almost immediately, the material
begins to emit light as the electrons drop back
down to their usual energy level.
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The Quantum Mechanical Model
The Rutherford planetary model and the Bohr model
of the atom are based on describing paths of
moving electrons as you would describe the path
of a large moving object. New theoretical
calculation and experimental results were
inconsistent with describing electron motion this
way. Austrian physicist Erwin Schrodinger used
these new results to devise and solve a
mathematical equation describing the behavior of
the electron in a hydrogen atom.
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The Quantum Mechanical Model
The Quantum Mechanical Model is the modern
description of the electrons in atoms comes from
the mathematical solution to the Schrodinger
equation. Like the Bohr model, the quantum
mechanical model restricts the energy of
electrons to certain values. Unlike the Bohr
model, the quantum mechanical model does not
involve an exact path the electron takes around
the nucleus. The quantum mechanical model
determines the allowed energies an electron can
have an how likely it is to find the electron in
various locations around the nucleus
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The Quantum Mechanical Model
How likely it is to find the electron in a
particular location is described by probability.
The quantum mechanical model describes of how
the electron moving around the nucleus is
similar to the motion of a rotating propeller
blade. The propeller blade has the same
probability of being anywhere in the blurry
regions it produces, but you cannot tells its
precise location at any instant.
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The Quantum Mechanical Model
The probability of finding an electron within a
certain volume of space surrounding the nucleus
can be represented as a fuzzy cloud. The cloud
is more dense where the probability of finding
the electron is high. The cloud is less dense
where the probability of finding the electron is
low. It is unclear where the cloud ends, there is
at least a slight chance of finding the electron
at a considerable distance form the nucleus.
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The Quantum Mechanical Model
Therefore, attempts to show probabilities as a
fuzzy cloud are usually limited to the volume in
which the electron is found 90 of the time. To
visualize an electron probability cloud, imagine
that you could mold a sack around the cloud so
that the electron was inside the sack 90 of the
time. The shape of the sack would then give you
a useful picture of the shape of the cloud.
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Atomic Orbitals
Atomic orbital is often thought of as a region of
space in which there is a high probability of
finding an electron. The energy levels of
electrons in the quantum mechanical model are
labeled by principal quantum numbers (n) n is
assigned the values of 1,2,3,4, For each
principal energy level, there may be several
orbitals with different shapes and at different
energy levels. These energy levels within a
principal energy level constitute energy
sublevels. Each energy sublevel corresponds to
an orbital of different shape describing where
the electron is likely to be found.
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Different atomic orbitals are denoted by letters.
s orbitals are spherical and p orbitals are
dumbbell-shaped. Because of the spherical
shape of an s orbital, the probability of finding
an electron at a given distance from the nucleus
in an s orbital does not depend on direction.
The three kinds of p orbitals have different
orientations in space.
P orbitals
s orbital
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There are five kinds of d orbitals.
d orbitals
4 of the five d orbitals have clover leaf shapes
but different orientations in space The shapes
of f orbitals are more complicated then for d
orbitals.
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Energy Level Energy Sublevel ( n) Number of Orbitals per Type Number of Orbitals per Level Number of e- per Sublevel Max e- in Sublevel Maximum e- in Energy Level (2n2)
n 1 1s 1 1 2e- 2e- 2 e-
n 2 2s 2p 1 3 4 2e- 2e- 2e- 6e- 8 e-
n 3 3s 3p 3d 1 3 5 9 2e- 2e- 2e- 2e- 6e- 10e- 18 e-
n 4 4s 4p 4d 4f 1 3 5 7 16 2e- 2e- 2e- 2e- 2e- 6e- 10e- 14e- 32 e-
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Questions
Why did Rutherfords atomic model need to be
replaced? It could not explain why metals or
compounds of metals give off characteristic color
when heated nor the chemical properties of the
elements. What was the basic new proposal in the
Bohr model of the atom. An electron is found only
in specific circular paths or orbits around the
nucleus.
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Questions
What does the quantum mechanical model determine
about electrons in atoms? It determines the
allowed energy levels an electron can have and
the likelihood of finding an electron in various
locations around the nucleus. How do two
sublevels of the same principal energy level
differ from each other? The sublevels have
different shapes. How can electrons in an atom
move from one energy level to another? By losing
or gaining just the right amount of energy a
quantum.
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Question
The energies of electrons are said to be
quantized. Explain what this means. In an atom,
the electrons can have certain fixed energy
levels. To move from one energy level to another
requires the emission or absorption of an exact
amount of energy, or quantum. Thus the energy of
the electron is said to be quantized.
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Question
How many orbitals are in the following
sublevels? 3p 3 2s 1 4p 3 3d 5 4f 7
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End of Section 5.1
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Electron Configuration

• In most natural phenomena, change proceeds toward
  the lowest possible energy.
• In the atom, electrons and the nucleus interact
  to make the most stable arrangement possible.
• The way in which electrons are arranged into
  various orbitals around the nuclei of atoms are
  called electron configuration.
• Three rules tell you how to find the electron
  configurations of atoms.
• The aufbau principle
• The Pauli exclusion principle
• Hunds rule

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Electron Configuration Rules

• aufbau Principle
• Electrons occupy the orbitals of lowest energy
  first.
• Pauli Exclusion Principle
• An orbital can hold a maximum of 2 electrons.
• 2 electrons in the same orbital must have
  opposite spins.
• An electron is "paired" if it is sharing an
  orbital with another electron with an opposite
  spin.
• An electron is "unpaired" if it is alone in
  an orbital
• Paired
  unpaired

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Electron Configuration Rules

• Hunds Rule
• Electrons occupy orbitals of the same energy in a
  way that makes the number of electrons with the
  same spin direction as large as possible.
• One electron enters each orbital until all the
  orbitals contain one electron with the same spin
  direction
• For example, three electron would occupy three
  orbitals of equal energy as follows
• Second electrons then occupy each orbital so that
  their spins are paired with the first electron in
  the orbital. Thus each orbital can eventually
  have two electrons with paired spins.

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Electron Configuration Practice
Write the electron configuration for each atom.
How many unpaired electrons does each atom
have? Carbon (atomic number 6 so 6 protons 6
electrons) 1s22s22p2 2 unpaired
electrons Argon 1s22s22p63s23p6 no unpaired
electrons Silicon 1s22s22p63s23p2 2 unpaired
electrons
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Exceptional Electron Configurations
Some actual electron configurations differ from
those assigned using the aufbau principle because
half-filled sublevels are not as stable as filled
sublevels. You can obtain correct electron
configurations for the elements up to vanadium
(atomic number 23) by following the aufbau
diagram for orbital filling. Cr
1s22s22p63s23p64s23d4 using aufbau Cr
1s22s22p63s23p64s13d5 correct
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Exceptional Electron Configurations
Transition elements are some exceptions to the
filling rules. These exceptions can be explained
by the atoms tendency to keep its energy as low
as possible. These exceptions help explain the
unexpected chemical behavior of transition
elements.
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Shorthand Electron Configurations
Electron configurations are often abbreviated by
naming the last element with a filled shell
(halogens) in brackets and listing only the
orbitals after the filled shell. Na
 1s22s22p63s1 shorthand    Na  Ne 3s1 Al
1s22s22p63s23p1 shorthand Al Ne 3s23p1
V 1s22s22p63s23p6 4s23d3 shorthand V
Ar 4s23d3
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End of Section 5.2
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Light
Neon signs are formed from glass tubes bent in
various shapes An electric current passing
through the gas in each glass tube makes the gas
glow with its own characteristic color. Each gas
glows with a specific color of light.
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Light
The quantum mechanical model grew out of the
study of light. Isaac Newton tried to explain
what was know about the behavior of light by
assuming that light consists of particles. By
1900, there was enough evidence to conclude that
light consisted of waves.
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Waves
Each complete wave cycle starts at zero,
increases to its highest value, passes through
zero to reach its lowest value, and returns to
zero again. Amplitude of a wave is the waves
height from zero to the crest. Wavelength (?) is
the distance between the crests.
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Waves
Frequency (?) is the number of wave cycles to
pass a given point per unit of time. The units
of frequency are usually cycles per second. The
SI unit of cycles per second is called a hertz
(Hz) A hertz can also be expressed as a
reciprocal seconds (s-1) Hz s-1
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Light
The product of frequency and wavelength always
equal a constant (c) the speed of light c
?? The wavelength and frequency of light are
inversely proportional to each other. As the
wavelength increases, the frequency
decreases. According to the wave model, light
consists of electromagnetic waves.
Electromagnetic radiation includes radio waves,
microwaves, infrared waves, visible light,
ultraviolet waves, X-rays, and gamma rays.
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Light
All electromagnetic waves travel in a vacuum at a
speed of 2.998 x 108 m/s c 2.998 x 108
m/s Sunlight consists of light with a continuous
range of wavelengths and frequencies. The color
of light depends on its frequency. When sunlight
passes through a prism, the different frequencies
separate into a spectrum of color. A rainbow is
an example of this phenomenon.
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Electromagnetic Spectrum
Each color of the spectrum blends into the next
in the order red, orange, yellow green, blue and
violet. In the visible spectrum, red light has
the longest wavelength and the lowest frequency.
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Sample Problems
What is the wavelength of radiation with a
frequency of 1.50 x 1013 Hz? Does this radiation
have a longer or shorter wavelength than red
light? c ?? or ? c / ? ? (2.998
x 108 m/s) / (1.50 x 1013 s-1) ? 2.00 x 10-5 m
(longer wavelength than red light) What frequency
is radiation with a wavelength of 5.00 x 10-8m?
In what regions of th e electromagnetic spectrum
is this radiation? c ?? or ? c /
? ? (2.998 x 108 m/s) / (5.00 x 10-8 m) ?
6.00 x 1015 s-1 (ultraviolet)
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Atomic Spectra
Passing an electric current through a gas in a
neon tube energizes the electrons of the atoms of
the gas, and causes them to emit light. When
atoms absorb energy, electrons move into higher
energy levels, and these electrons lose energy by
emitting light when they return to lower energy
levels. Ordinary light is made up of a mixture
of all the wavelengths of light. However, the
light emitted by atoms consists of a mixture of
only specific frequencies. Each specific
frequency of visible light emitted corresponds to
a particular color.
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When light passes through a prism, the
frequencies of light emitted by an element
separate into discrete lines to give the atomic
emission spectrum of the element.
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Atomic Spectra
Each discrete line in an emission spectrum
corresponds to one exact frequency of light
emitted by the atom. The emission spectrum for
each element is like a persons fingerprint. No
two elements have the same emission spectrum.
Atomic emission spectra are useful for
identifying elements.
Argons atomic emission spectra
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Explanation of Atomic Spectra
Atomic line spectra were known before Bohr
proposed his model of the H atom. However, Bohrs
model explained why the emission spectrum of H
consists of specific frequencies of light. In
the Bohr model, the lone electron in the H atom
can have only certain specific energies. The
lowest possible energy of the electron is its
ground state. In the ground state, the
electrons principal quantum number is 1
(n1) Excitation of the electron by absorbing
energy raises it from the ground state to an
excited state with n 2,3,4,5
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Explanation of Atomic Spectra
A quantum of energy in the form of light is
emitted when the electron drops back to a lower
energy level. The emission occurs in a single
abrupt step, called an electronic transition.
Bohr knew from earlier work that the quantum of
energy (E) is related to the frequency (?) of the
emitted light by the equation E h x ? h is
the fundamental constant of nature, the Planck
constant and is equal to 6.626 x 10-34 Js
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Explanation of Atomic Spectra

• The light emitted by an electron moving from a
  higher to a lower energy level has a frequency
  directly proportional to the energy change of the
  electrons.
• Each transition produces a line of a specific
  frequency in the spectrum.
• Three groups of lines in the hydrogen spectrum
  correspond to the transition of electrons from
  higher energy levels to lower energy levels
• Lyman series corresponds to the transition to the
  n1 energy level
• Balmer series corresponds to the transition to
  the n2 energy level (smaller change in e- energy
  than transitions to n1)
• Paschen series corresponds to the transition to
  the n3 energy level. (smaller change in e-
  energy than transitions to n1 and n2)

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Explanation of Atomic Spectra
(Transition to n 3 energy level, infrared range
of spectra)
(Transition to n 2 energy level Visible end of
the spectra)
(Transition to the n 1 energy level Ultraviolet
part of the spectra)
The light emitted by an electron moving from a
higher to a lower energy level has a frequency
directly proportional to the energy change of the
electrons. Each transition produces a line of a
specific frequency in the spectrum.
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Explanation of Atomic Spectra
Spectral lines for the transactions from higher
energy levels to n4 and n5 also exist. The
spectral lines in each group become more closely
spaced at increases values of n because the
energy levels become closer together There is an
upper limit to the frequency of emitted light for
each set of lines. The upper limit exists because
an electron with enough energy completely escapes
the atom.
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Explanation of Atomic Spectra
Bohrs of the atom was only partially
satisfactory. It explained the emission spectrum
of hydrogen, but not the emission spectra of
atoms with more than one electron. The quantum
mechanical model displaced the Bohr model of the
atom. The quantum mechanical model is based on
the description of the motion of material objects
as waves.
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Questions
Suppose an electron in its ground state at energy
level one absorbs enough energy to jump to level
two. What type of radiation will it emit when it
returns to the ground state? Ultraviolet
radiation If you observed a hydrogen gas
discharge tube through a diffraction grating
could you see the line corresponding to this
emission? No, the human eye cannot detect
radiation in the UV range. Which series of lines
could you detect? The Balmer series, which has
frequencies in the visible region of the spectrum.
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Questions
Compare the energy of the Paschen and Balmer
series. The Paschen series has lower energy.
What do you notice about the spacing of the
enrgy levels from n 1 to n 7? The levels are
not evenly spaced. The lines get closer as the
distance from the nucleus increases.
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Quantum Mechanics
Albert Einstein successfully explained
experimental data by proposing that light could
be described as quanta of energy. The quanta
behave as if they were particles. Light
quanta are called photons. Although the wave
nature of light was well known, the dual
wave-particle behavior of light was difficult for
scientists to accept. Louis de Broglie a French
graduate student, asked an important question
Given that light behaves as waves and particles,
can particles of matter behave as waves? The
proposal that matter moves in a wavelike way
would not be accepted unless experiments
confirmed its validity.
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Quantum Mechanics
Two scientists, Clinton Davisson and Lester
Germer at Bell Labs, had been studying the
bombardment of metals with beams of electrons.
They noticed that the electrons reflected from
the metal surface produced curious patterns. The
patterns were like those obtained when X-rays
(which are electromagnetic waves) reflect from
metal surfaces. The electrons, believed to be
particles, were reflected as if they were waves.
. Louis de Broglie was awarded the Nobel Prize
for his work on the wave nature of matter.
Davisson also received the Nobel Prize for his
experiments demonstrating the wave nature of
electrons.
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Quantum Mechanics
Today, the wavelike properties of beams of
electrons are useful in magnifying objects. The
electrons in an electron microscope have much
smaller wavelengths than visible light. This
allows a much clearer enlarged image of a very
small object than is possible with an ordinary
microscope.
Dust mite. Yuck!
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Quantum Mechanics
De Broglies equation predicts that all moving
objects have wavelike behavior. Why cant we
observe the wavelike motion for ordinary objects
like baseballs? The mass of the object must be
very small in order for its wavelength to be
large enough to observe. The older theory is
called classical mechanics and it adequately
describes the motions of bodies much larger than
atoms. The newer theory, quantum mechanics,
describes the motion of subatomic particles and
atoms as waves.
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Quantum Mechanics
German physicist Werner Heisenberg examined
another feature of quantum mechanics that is
absent is classical mechanics. The Heisenberg
uncertainly principle states that it is
impossible to know exactly both the velocity and
the position of a particle at the same time.
This limitation is critical in dealing with
small particles such as electrons. The
Heisenberg uncertainty principle does not matter,
however, for ordinary-sized objects such as cars
or airplanes.
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Quantum Mechanics
To understand the Heisenberg uncertainty
principle, consider how you determine the
location of an object. . To locate a set of
keys in a dark room, you can use a flashlight.
You see the keys when the light bounces off them
and strikes your eyes. To locate an electron,
you might strike it with a photon of light. The
electron has such a small mass that striking it
with a photon affects its motion in a way that
cannot be predicted precisely.
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Recap
The frequency and wavelength of light waves are
inversely related. As the wavelength increases,
the frequency decreases. (c ??) The
electromagnetic spectrum consists of radiation
over a broad band of wavelengths. The visible
light portion is very small. It is in the 10-7 m
wavelength rand 1015 Hz (s-1) frequency range.
When atoms absorb energy, electrons move into
higher energy levels, and these electrons lose
energy by emitting light when they return to
lower energy levels.
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Recap
A prism separates light into the colors it
contains. For white light this produces a rainbow
of colors. Light from a helium lamp produces
discrete lines. An electron microscope can
produce sharp images of a very small object,
because of the small wavelength of a moving
electron compared with that of light. The
Heisenberg uncertainty principle states that it
is impossible to know exactly both the velocity
and the position of a particle at the same time.

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Questions
How are wavelength and frequency of light
related? They are inversely proportional to each
other. c ?? Describe the cause of atomic
emission spectrum of an element. Electrons in
atoms absorb energy as they move to higher energy
levels, then lose the energy by emitting it as
light as they drop back. How is the change in
electron energy related to the frequency of light
emitted in atomic transitions? The light emitted
in an electronic transition from a higher to a
lower energy level has a frequency that is
directly proportional to the energy change of the
electron. E h?
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Questions
How does quantum mechanics differ from classical
mechanics? Quantum mechanics describes the
motions of atoms and subatomic particles
classical mechanics describes the motions of
larger bodies. Which electron transitions with
an atom are responsible for the Lyman
series? Electron transitions from higher levels
to n 1 Arrange the following in order of
decreasing wavelength infrared radiation from a
heat lamp, dental X-rays, signal from a shortwave
radio station. Signal from a shortwave radio
station, infrared radiation, dental X-rays
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End of Chapter 5