Chapter 5 - Valencia College

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Transcript Chapter 5 - Valencia College

Chapter 5
Models of
the Atom
Vanessa N. Prasad-Permaul
Valencia College
CHM1025
© 2011 Pearson Education, Inc.
Chapter 5
1
Dalton Model of the Atom
 John Dalton proposed that all matter is made
up of tiny particles.
 These particles are molecules or atoms.
 Molecules can be broken down into atoms by
chemical processes.
 Atoms cannot be broken down by chemical or
physical processes.
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Dalton Model
 According to the law of definite composition,
the mass ratio of carbon to oxygen in carbon
dioxide is always the same. Carbon dioxide is
composed of one carbon atom and two oxygen
atoms.
 Similarly, two atoms of hydrogen and one atom
of oxygen combine to give water.
 Dalton proposed that two hydrogen atoms could
substitute for each oxygen atom in carbon
dioxide to make methane with one carbon atom
and four hydrogen atoms. Indeed, methane is
CH4!
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Dalton Atomic Theory
A Summary of Dalton Atomic Theory:
An element is composed of tiny, indivisible,
indestructible particles called atoms.
1. All atoms of an element are identical and have
the same properties.
2. Atoms of different elements combine to form
compounds.
3. Compounds contain atoms in small whole
number ratios.
4. Atoms can combine in more than one ratio to
form different compounds.
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Dalton Atomic Theory,
Continued
 The first two parts of atomic theory were
later proven incorrect. We will see this later.
 Proposals 3, 4, and 5 are still accepted today.
 The Dalton theory was an important step in
the further development of atomic theory.
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Subatomic Particles

About 50 years after Dalton’s proposal,
evidence was seen that atoms were
divisible.

Two subatomic particles were discovered.
1. Negatively charged electrons, e–.
2. Positively charged protons, p+.

An electron has a relative charge of -1, and a
proton has a relative charge of +1.
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Thomson Model of the Atom
 J. J. Thomson proposed a subatomic model
of the atom in 1903.
 Thomson proposed that
the electrons were
distributed evenly
throughout a homogeneous
sphere of positive charge.
 This was called the
plum pudding model
of the atom.
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Mass of Subatomic Particles
 Originally, Thomson could only calculate the
mass-to-charge ratio of a proton and an
electron.
 Robert Millikan determined the charge of an
electron in 1911.
 Thomson calculated the masses of a proton
and electron:
 An electron has a mass of 9.11 × 10-28 g.
 A proton has a mass of 1.67 × 10-24 g.
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Types of Radiation

There are three types of radiation:
1. Alpha (a)
2. Beta (b)
3. Gamma (g)

Alpha rays are composed of helium atoms
stripped of their electrons (helium nuclei).

Beta rays are composed of electrons.

Gamma rays are high-energy
electromagnetic radiation.
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Rutherford Gold Foil
Experiment
 Rutherford’s student
fired alpha particles at
thin gold foils. If the
plum pudding model of
the atom was correct, α
particles should pass
through undeflected.
 However, some of the
alpha particles were
deflected backward.
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Explanation of Scattering
 Most of the alpha particles passed through the
foil because an atom is largely empty space.
 At the center of an atom is the atomic nucleus,
which contains the atom’s protons.
 The alpha particles that
bounced backward
did so after striking
the dense nucleus.
did
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Rutherford Model of the Atom
 Rutherford proposed a new model of the atom:
The negatively charged electrons are distributed
around a positively charged nucleus.
 An atom has a diameter
of about 1 × 10-8 cm and
the nucleus has a diameter
of about 1 × 10-13 cm.
 If an atom were the size
of the Astrodome, the
nucleus would be the size
of a marble.
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Subatomic Particles Revisited
 Based on the heaviness of the nucleus,
Rutherford predicted that it must contain
neutral particles in addition to protons.
 Neutrons, n0, were discovered about 30 years
later. A neutron is about the size of a proton
without any charge.
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Atomic Notation
 Each element has a characteristic number of
protons in the nucleus. This is the atomic
number, Z.
 The total number of protons and neutrons in the
nucleus of an atom is the mass number, A.
 We use atomic notation to display the number
of protons and neutrons in the nucleus of an
atom:
mass number (p+ and n0)
atomic number (p+)
A
Z
Sy
symbol of the element
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Using Atomic Notation
 An example:
29
Si
14
 The element is silicon (symbol Si).
 The atomic number is 14; silicon has 14 protons.
 The mass number is 29; the atom of silicon has 29
protons + neutrons.
 The number of neutrons is A – Z = 29 – 14 = 15
neutrons.
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Example 5.1 Atomic Notation
Given the atomic notation for the following atoms, draw a diagram showing the
arrangement of protons, neutrons, and electrons.
(a)
(b)
Solution
We can draw a diagram of an atom by showing protons and neutrons in the nucleus
surrounded by electrons.
(a) Since the atomic number is 9 and the mass number is 19, the number of
neutrons is 10 (19 – 9). If there are 9 protons, there must be 9 electrons.
(b) Since the atomic number is 47 and the mass number is 109, the number of
neutrons is 62 (109 – 47). If there are 47 protons, there must be 47 electrons.
Exercise 5.1 Atomic Notation
Practice Exercise
Given the following diagram, indicate the nucleus using atomic notation.
Concept Exercise
Can atoms of different elements have the same atomic number?
Isotopes
 All atoms of the same element have the same
number of protons.
 Most elements occur naturally with varying
numbers of neutrons.
 Atoms of the same element that have a
different number of neutrons in the nucleus
are called isotopes.
 Isotopes have the same atomic number, but
different mass numbers.
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Isotopes, Continued
 We often refer to an isotope by stating the
name of the element followed by the mass
number.
60
 Cobalt-60 is
 Carbon-14 is
37
Co
14
6
C
 How many protons and neutrons does an
atom of lead-206 have?
 The atomic number of Pb is 82, so it has 82
protons.
 Pb-206 has 206 – 82 = 124 neutrons.
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Example 5.2 Nuclear Composition of Isotopes
State the number of protons and the number of neutrons in an atom of each of the
following isotopes.
(a)
(b) mercury-202
Solution
The subscript value refers to the atomic number (p+), and the superscript value refers to the
mass number (p+ and n0).
(a) Thus,
has 17 p+ and 20 n0 (37 – 17 = 20).
(b) In the periodic table, we find that the atomic number of mercury is 80. Thus, the
atomic notation,
, indicates 80 p+ and 122 n0 (202 – 80 = 122).
Exercise 5.2 Nuclear Composition of Isotopes
Practice Exercise
State the number of protons and the number of neutrons in an atom of each of the
following isotopes.
(a)
(b) uranium-238
Concept Exercise
Can atoms of different elements have the same mass number?
Simple and Weighted Averages
 A simple average assumes the same number
of each object.
 A weighted average takes into account the
fact that we do not have equal numbers of all
the objects.
 A weighted average is calculated by
multiplying the percentage of the object (as a
decimal number) by its mass for each object
and adding the numbers together.
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Average Atomic Mass


Since not all isotopes of an atom are present
in equal proportions, we must use the
weighted average.
Copper has two isotopes:
1.
63Cu, with
a mass of 62.930 amu and 69.09%
abundance.
2. 65Cu, with a mass of 64.928 amu and 30.91%
abundance.

The average atomic mass of copper is:
(62.930 amu)(0.6909) + (64.928amu)(0.3091)
= 63.55 amu
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Example 5.3 Calculation of Atomic Mass
Silicon is the second most abundant element in Earth’s crust. Calculate the atomic mass of
silicon given the following data for its three natural isotopes:
Solution
We can find the atomic mass of silicon as follows:
28Si: 27.977 amu  0.9221 = 25.80 amu
29Si: 28.976 amu  0.0470 = 1.36 amu
30Si: 29.974 amu  0.0309 = 0.926 amu
28.09 amu
Exercise 5.3 Calculation of Atomic Mass
Practice Exercise
Calculate the atomic mass of copper given the following data:
Concept Exercise
A bag of marbles has 75 large marbles with a mass of 2.00 g each, and 25 small
marbles with a mass of 1.00 g each.
Calculate (a) the simple average mass, and (b) the weighted average mass of the
marble collection.
Periodic Table
 We can use the periodic table to obtain the atomic
number and atomic mass of an element.
 The periodic table shows the atomic number,
symbol, and atomic mass for each element.
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Example 5.4 Nuclear Composition from the
Periodic Table
Refer to the periodic table on the inside cover of this textbook and determine the atomic
number and atomic mass for iron.
Solution
In the periodic table we observe
The atomic number of iron is 26, and the atomic mass is 55.85 amu. From the
periodic table information, we should note that it is not possible to determine the
number of isotopes for iron or their mass numbers.
Exercise 5.4 Nuclear Composition from the
Periodic Table
Practice Exercise
Refer to the periodic table on the inside cover of this text and determine the atomic
number and mass number for the given radioactive isotope of radon gas.
Concept Exercise
Which of the following is never a whole number value: atomic number, atomic
mass, or mass number?
Wave Nature of Light
 Light travels through space as a wave, similar
to an ocean wave.
 Wavelength is the distance light travels in one
cycle.
 Frequency is the number of wave cycles
completed each second.
 Light travels at a constant speed: 3.00 × 108
m/s (given the symbol c).
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Wavelength Versus Frequency
 The longer the wavelength of light, the lower the
frequency.
 The shorter the wavelength of light, the higher the
frequency.
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Radiant Energy Spectrum
 The complete radiant energy spectrum is an
uninterrupted band, or continuous spectrum.
 The radiant energy spectrum includes many
types of radiation, most of which are invisible
to the human eye.
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Visible Spectrum
 Light usually refers to radiant energy that is
visible to the human eye.
 The visible spectrum is the range of
wavelengths between 400 and 700 nm.
 Radiant energy that has a wavelength lower
than 400 nm and greater than 700 nm cannot
be seen by the human eye.
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Example 5.5 Properties of Light
Considering blue light and yellow light, which has the
(a) longer wavelength?
(b) higher frequency?
(c) higher energy?
Solution
Referring to Figure 5.9, we notice that the wavelength of yellow light is about 600
nm and that of blue light is about 500 nm. Thus,
(a) yellow light has a longer wavelength than blue light.
(b) blue light has a higher frequency because it has a shorter wavelength.
(c) blue light has a higher energy because it has a higher frequency.
Exercise 5.5 Properties of Light
Practice Exercise
Considering infrared light and ultraviolet light, which has the
(a) longer wavelength?
(b) higher frequency?
(c) higher energy?
Concept Exercise
The energy of light (increases/decreases) as the wavelength increases. The energy of
light (increases/decreases) as the frequency increases.
The Quantum Concept
 The quantum concept states that energy is
present in small, discrete bundles.
 For example:
 A tennis ball that rolls down a ramp loses potential
energy continuously.
 A tennis ball that rolls down a staircase loses potential
energy in small bundles. The loss is quantized.
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Bohr Model of the Atom
 Niels Bohr speculated that electrons orbit
about the nucleus in fixed energy levels.
 Electrons are found only in specific energy
levels, and nowhere else.
 The electron energy
levels are quantized.
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Example 5.6 Quantum Concept
State whether each of the following scientific instruments gives a continuous or a
quantized measurement of mass:
(a) triple-beam balance
(b) digital electronic balance
Solution
Refer to Figure 2.3 if you have not used these balances
in the laboratory.
(a) On a triple-beam balance a small metal rider is
moved along a beam. Since the metal rider can be
moved to any position on the beam, a triple-beam
balance gives a continuous mass measurement.
(b) On a digital electronic balance the display
indicates the mass of an object to a particular decimal
place, for example, 5.015 g. Since the last digit in the
display must be a whole number, a digital balance gives
a quantized mass measurement.
Figure 2.3 Balances for Measuring
Mass (a) A platform balance having an
uncertainty of ±0.1 g. (b) A beam balance
having an uncertainty of ±0.01 g. (c) A
digital electronic balance having an
uncertainty of ±0.001 g.
Exercise 5.6 Quantum Concept
Practice Exercise
State whether each of the following musical instruments
produces continuous or quantized musical notes:
(a) acoustic guitar
(b) electronic keyboard
Concept Exercise
Complete the following quantum analogy: a water wave
is to a drop of water, as a light wave is to a _______.
Figure 2.3 Balances for Measuring
Mass (a) A platform balance having an
uncertainty of ±0.1 g. (b) A beam balance
having an uncertainty of ±0.01 g. (c) A
digital electronic balance having an
uncertainty of ±0.001 g.
Emission Line Spectra
 When an electrical voltage is passed across a gas
in a sealed tube, a series of narrow lines is seen.
 These lines are the emission line spectrum. The
emission line spectrum for hydrogen gas shows
three lines: 434 nm, 486 nm, and 656 nm.
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Evidence for Energy Levels
 Bohr realized that this was the evidence he
needed to prove his theory.
 The electric charge temporarily excites an
electron to a higher orbit. When the electron
drops back down, a photon is given off.
 The red line is the
least energetic and
corresponds to an
electron dropping
from energy level 3
to energy level 2.
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“Atomic Fingerprints”
 The emission line spectrum of each element is
unique.
 We can use the line spectrum to identify elements
using their “atomic fingerprint.”
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Example 5.7 Emission Spectra and Energy
Levels
Explain the relationship between an observed emission line in a spectrum and electron
energy levels.
Solution
When an electron drops from a higher to a lower energy level, light is emitted. For
each electron that drops, a single photon of light energy is emitted. The energy lost
by the electron that drops equals the energy of the photon that is emitted. Several
photons of light having the same energy are observed as a spectral line.
Exercise 5.7 Emission Spectra and Energy
Levels
Practice Exercise
Indicate the number and color of the photons emitted for each of the following
electron transitions in hydrogen atoms:
(a) 1 e– dropping from energy level 3 to 2
(b) 10 e– dropping from energy level 3 to 2
(c) 100 e– dropping from energy level 4 to 2
(d) 500 e– dropping from energy level 5 to 2
Concept Exercise
Which of the following statements are true according to the Bohr model of the
atom?
(a) Electrons are attracted to the atomic nucleus.
(b) Electrons have fixed energy as they circle the nucleus.
(c) Electrons lose energy as they drop to an orbit closer to the nucleus.
Critical Thinking:“Neon Lights”
 Most “neon” signs don’t actually contain neon gas.
 True neon signs are red in color.
 Each noble gas has its own emission spectrum, and
signs made with each have a different color.
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Energy Levels and Sublevels
 It was later shown that electrons occupy
energy sublevels within each level.
 These sublevels are given the designations s,
p, d, and f.
 These designations are in reference to the sharp,
principal, diffuse, and fine lines in emission spectra.
 The number of sublevels in each level is the
same as the number of the main level.
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Energy Levels and Sublevels,
Continued
 The first energy level has one sublevel designated
1s.
 The second energy level has two sublevels
designated 2s and 2p.
 The third energy level has three sublevels
designated 3s, 3p, and 3d.
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Electron Occupancy in
Sublevels
 The maximum number of electrons in each of
the energy sublevels depends on the sublevel:
 The s sublevel holds a maximum of 2 electrons.
 The p sublevel holds a maximum of 6 electrons.
 The d sublevel holds a maximum of 10 electrons.
 The f sublevel holds a maximum of 14 electrons.
 The maximum electrons per level is obtained
by adding the maximum number of electrons
in each sublevel.
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Electrons per Energy Level
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Example 5.8 Energy Levels, Sublevels, & Electrons
What is the maximum number of electrons that can occupy the third energy level?
Solution
The third energy level is split into three sublevels: 3s, 3p, and 3d. The maximum
number of electrons that can occupy each sublevel is as follows:
s sublevel = 2 e–
p sublevel = 6 e–
d sublevel = 10 e–
The maximum number of electrons in the third energy level is found by adding the
three sublevels together:
3s + 3p + 3d = total electrons
2 e– + 6 e– + 10 e– = 18 e–
The third energy level can hold a maximum of 18 electrons. Of course, in elements
where the third energy level of an atom is not filled, there are fewer than 18
electrons.
Exercise 5.8 Energy Levels, Sublevels, and
Electrons
Practice Exercise
What is the maximum number of electrons that can occupy the fourth energy level?
Answers: 4s, 4p, 4d, 4f; 32 e– (2 e– + 6 e– + 10 e– + 14 e–)
Concept Exercise
What is the theoretical number of sublevels in the tenth energy level?
Electron Configurations
 Electrons are arranged about the nucleus in a
regular manner. The first electrons fill the
energy sublevel closest to the nucleus.
 Electrons continue filling each sublevel until it
is full, and then start filling the next closest
sublevel.
 A partial list of sublevels in order of increasing
energy is as follows:
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d …
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Filling Diagram for Energy Sublevels
 The order
 For now, use
Figure 5.16 to
predict the
order of
sublevel
filling.
Increasing Energy
does not
strictly follow
1, 2, 3, etc.
Core
[He]
[Ne]
[Ar]
[Kr]
[Xe]
[Rn]
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
7p
Chapter 5
3d
4d 4f
5d 5f
6d
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Example 5.9 Order of Sublevels
Solution
If you do not know the order of sublevels, refer to the
filling diagram in Figure 5.16.
(a) Although the third energy level has 3s 3p, and 3d
sublevels, the 3d sublevel does not immediately follow the
3p. Instead, the 4s sublevel follows the 3p and precedes the
3d. Thus,
3s, 3p, 4s
(b) Although the fourth energy level has 4s, 4p, 4d, and 4f
sublevels, the 4f sublevel does not immediately follow the
4d. Instead, the 5p sublevel begins accepting electrons after
the 4d is filled. Thus,
4p, 5s, 4d, 5p
Increasing Energy
According to increasing energy, what is the next energy sublevel after each of the
following sublevels?
(a) 3p
(b) 4d
Core
[He]
[Ne]
[Ar]
[Kr]
[Xe]
[Rn]
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
7p
3d
4d 4f
5d 5f
6d
Figure 5.16 Filling Diagram for
Energy Sublevels The order of
sublevel filling is arranged
according to increasing energy.
Electrons first fill the 1s sublevel
followed by the 2s, 2p, 3s, 3p, 4s,
3d, 4p, 5s, 4d, 5p, and 6s
sublevels.
Exercise 5.9 Order of Sublevels
Which sublevel gains electrons after each of the following
sublevels is filled?
(a) 2s
(b) 5p
Concept Exercise
The energy difference between sublevels
(increases/decreases) moving away from the nucleus.
Increasing Energy
Practice Exercise
Core
[He]
[Ne]
[Ar]
[Kr]
[Xe]
[Rn]
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
7p
3d
4d 4f
5d 5f
6d
Figure 5.16 Filling Diagram for
Energy Sublevels The order of
sublevel filling is arranged
according to increasing energy.
Electrons first fill the 1s sublevel
followed by the 2s, 2p, 3s, 3p, 4s,
3d, 4p, 5s, 4d, 5p, and 6s
sublevels.
Electron Configurations
 The electron configuration of an atom is a
shorthand method of writing the location of
electrons by sublevel.
 The sublevel is written followed by a
superscript with the number of electrons in
the sublevel. For example, if the 2p sublevel
contains two electrons, it is written 2p2.
 The electron sublevels are arranged
according to increasing energy.
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Writing Electron Configurations
 First, determine how many electrons are in the
atom. Bromine has 35 electrons.
 Arrange the energy sublevels according to
increasing energy:
 1s 2s 2p 3s 3p 4s 3d …
 Fill each sublevel with electrons until you have
used all the electrons in the atom:
 Fe: 1s2 2s2 2p6 3s2 3p6 4s2 3d 10 4p5
 The sum of the superscripts equals the atomic
number of bromine (35).
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Example 5.10 Electron Configuration
Write the predicted electron configuration for each of the following elements:
(a) F
(b) Sr
Solution
Refer to the periodic table to find the atomic number of an element.
(a) The atomic number of fluorine is 9; therefore, the number of electrons is 9. We
can fill sublevels with 9 electrons as follows :
F: 1s2 2s2 2p5
(b) The atomic number of strontium is 38; therefore, the number of electrons is 38.
We can fill sublevels with 38 electrons as follows:
Sr:
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2
To check your answer, find the total number of electrons by adding up the
superscripts. The total is 38 e–; this agrees with the atomic number for Sr.
Exercise 5.10 Electron Configuration
Practice Exercise
Write the predicted electron configuration for each of the following elements:
(a) argon
(b) cadmium
Concept Exercise
Refer to the periodic table and state whether Cr or Mn has more electrons in the
outermost d sublevel.
.
Quantum Mechanical Model
 An orbital is the region of space where there is a
high probability of finding an atom.
 In the quantum mechanical atom, orbitals are
arranged according to their size and shape.
 The higher the energy of an orbital, the larger its
size.
• All s orbitals
have spherical
shapes.
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Shapes of p Orbitals
 Recall that there are three different p sublevels.
 All p orbitals have dumbbell shapes.
 Each of the p orbitals has the same shape, but each
is oriented along a different axis in space.
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Shapes of d Orbitals
 Recall that there are five different d sublevels.
 Four of the d orbitals have a clover-leaf shape and
one has a dumbbell and doughnut shape.
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Location of Electrons in an
Orbital
 The orbitals are the region of space in which the
electrons are most likely to be found.
 An analogy for an electron in a p orbital is a fly
trapped in two bottles held end to end.
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Example 5.11 Atomic Orbitals
Describe the relative size, energy, and shape for each of the following orbitals:
(a) 4s versus 3s and 5s
(b) 4p versus 3p and 5p
Solution
The size and energy of an orbital is indicated by the number; the shape of the orbital
is designated by the letter.
(a) Size and energy are greater for a 4s orbital than for a 3s orbital, but less than for
a 5s orbital. The shape of a 4s orbital—and all s orbitals—is similar to the shape
of a sphere.
(b) Size and energy are greater for a 4p orbital than for a 3p orbital, but less than
for a 5p orbital. The shape of a 4p orbital—and all p orbitals—is similar to the
shape of a dumbbell.
Exercise 5.11 Atomic Orbitals
Practice Exercise
Select the orbital in each of the following pairs that fits the description:
(a) the higher energy orbital: 3p or 4p
(b) (b)the larger size orbital: 4d or 5d
Concept Exercise
Which of the following statements are true according to the quantum mechanical
model of the atom?
(a) Orbitals represent quantum energy levels for electrons.
(b) Orbitals represent probability boundaries for electrons.
(c) Orbitals can have different shapes.
Chapter Summary
 Atoms are composed of protons, neutrons,
and electrons.
 The protons and neutrons are located in the
nucleus, and the electrons are outside the
nucleus.
 Atoms are mostly empty space.
 The number of protons is referred to as the
atomic number for the atom.
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Chapter Summary, Continued
 All atoms of the same element have the same
number of protons.
 Isotopes are atoms with the same number of
protons, but differing numbers of neutrons.
 The mass number for an isotope is the total
number of protons plus neutrons.
 The atomic mass of an element is the
weighted average of the masses of all the
naturally occurring isotopes.
Chapter 5
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66
Chapter Summary, Continued
 Light has properties of both waves and particles.
 The particles of light are referred to as photons.
 The energy of photons is quantized.
 Electrons exist around the nucleus of atoms in
discrete, quantized energy levels.
 Electrons fill energy sublevels, starting with the
lowest energy sublevel and filling each
successive level of higher energy.
Chapter 5
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67
Which postulate of Dalton’s atomic
theory has been shown to be
incorrect?
All atoms of an element are identical and
have the same properties.
b. Atoms of different elements combine to form
compounds.
c. Compounds contain atoms in small whole
number ratios.
d. Atoms can combine in more than one ratio to
form different compounds.
a.
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How many protons, neutrons, and
electrons are in uranium-235?
92 protons, 92 neutrons, 143 electrons
b. 92 protons, 92 neutrons, 235 electrons
c. 92 protons, 143 neutrons, 92 electrons
d. 92 protons, 235 neutrons, 92 electrons
a.
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The average atomic mass of silicon is
28.09 amu. The masses of 28Si, 29Si,
and 30Si are 27.977 amu, 28.976 amu,
and 29.974 amu, respectively. Which is
the most abundant isotope?
a. 28Si
b. 29Si
c. 30Si
d. The isotopes are equally
abundant.
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What is the maximum number of
electrons that can occupy a 3d
sublevel?
a.
b.
c.
d.
2
6
10
14
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What element has the electron
configuration
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d2 ?
a.
b.
c.
d.
Ca
Ge
Pr
Zr
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