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2
Atoms
Conceptual Physics Fundamentals
2.1 The
Atomic Hypothesis
2.2 Characteristics
of Atoms
2.3 Atomic
Imagery
2.4 Atomic
Structure
2.5 The
Elements
2.6 Periodic
Table of the Elements
2.7 Relative
Sizes of Atoms
2.8 Isotopes
2.9 Molecules
2.10 Antimatter
2.11 Dark
Matter
The
goal of this chapter is to present atoms and their subatomic particles and thus
set the stage for subsequent chapters.
In the Practice Book:
•
Subatomic Particles
•
Melting Points of the Elements
•
Densities of the Elements
In
the Next-Time Questions book:
•
Germanium Capsules
•
Number of Carbon Atoms
•
Neon
•
Atomic Size
SUGGESTED PRESENTATION
Begin
by posing the situation of breaking a boulder into rocks, rocks into stones,
stones into pebbles, pebbles into gravel, gravel into sand, sand into powder,
and so forth until you get to the fundamental building block—the atom. Relate
how from the earliest days of science people wondered how far the idea of
breaking boulders into stones, pebbles, sand, powder, and so on, would go. Does
it ever end? Hundreds of years ago, people had no way of finding out, and they
instead carried on with philosophical speculation. Not until “modern” chemistry
in the late 1700s did people begin to get indirect evidence of some basic order
in the combinations of things. The first real “proof” that there were atoms was
given by Einstein in 1905, the same year he published his paper on relativity.
He calculated what kind of motion there ought to be in Brownian motion, based
on ideas we’ve considered already, like energy and momentum conservation, and
the idea of heat as atomic motion. Many of the “heavies” in physics at that
time didn’t believe in atoms until Einstein’s work.
Smallness of oms
Give
examples to convey the idea of the smallness of the atom—that is, an atom is as
many orders of magnitude smaller than a person as an average star is larger
than a person—so we stand between the atoms and the stars. The size of an atom
is to the size of an apple as the size of an apple is to the size of the Earth.
So if you want to imagine an apple full of atoms, think of the Earth,
solid-packed with apples.
CHECK
QUESTION: Ask what an atom would “look like” if viewed through a vertical bank
of about 40 high-powered optical microscopes stacked one atop the other. [It
turns out they wouldn’t have an appearance, at least not in the range of
frequencies we call light. The atom is smaller than the wavelength of light.]
Recycling of Atoms
State that if you put a drop of ink in a bathtub full of
water, that you (the students) know that in a short time you can sample any
part of the water and find ink in it. The atoms of ink spread out. We can get
an idea of how small atoms are from this fact: There are more atoms in a
thimbleful of ink than there are thimblefuls of water in the Atlantic
Ocean . That means if you throw a thimbleful of ink into the Atlantic Ocean and give it enough years to mix uniformly,
and then dip anywhere in the ocean with a thimble, you’ll have some atoms of
ink in your sample.
Atoms Are Mostly
Empty Space
Discuss
the Bohr model of the atom and the electrical role of the nucleus and
surrounding electrons. Stress the emptiness of the atom and lead into the idea
of solid matter being mostly empty space. State how our bodies are 99.999%
empty spaces, and how a particle, if tiny enough and not affected by electrical
forces, could be shot straight through us without even making a hole! Making a
direct hit with an atomic nucleus or an electron is as improbable as making a
direct hit with a planet or the Sun if you throw a gravity-free dart from outer
space at the solar system. Both the solar system and an atom are mostly empty
space. Walk through a beam of neutrons and very few if any will interact with
your body. Still smaller neutral particles called neutrinos, the most elusive
yet most numerous and fastest of all particles, pass through us every moment.
But they do so without consequence, for only very rarely, perhaps once or so
per year, do any make a bull’s-eye collision with any of our atomic nuclei.
They freely pass through the entire Earth with rare interactions.
LECTURE SKIT: Start with a sketch of an elementary model on
the chalkboard and indicate electrons as tiny fast-moving specks. State that
your drawing is all out of scale. That to be more accurate you need to draw the
nucleus much smaller. Erase the nucleus you first drew and replace it with a
speck tinier than the electrons. Note that the electrons are actually thousands
of times less massive than the atomic nucleus, so it would do far better to
just erase them. Erase everything except the tiny speck of a nucleus and,
perhaps, leaving the perimeter. “Thus, it is, we understand that atoms are made
mostly of empty space.” Finish up by noting that although the atom is mostly
empty space, the tiny, tiny subatomic particles it contains have these force
fields. It is the electric force of attraction between the electrons and the
protons that holds the electrons to the atomic nucleus. Likewise, it is the
electric force of repulsion between the electrons of one atom and the electrons
of another atom that causes the two atoms to repel. The exception, of course,
is when a chemical bond forms between those two atoms, which is a completely
different story.
Point
out that the atomic configurations you sketch on the board are simply models,
not to be taken as visually correct. For example, if the nuclei were drawn to
scale they would be scarcely visible specks. And the electrons don’t really
“orbit,” as your drawings suggest—such terms don’t seem to have much meaning at
the atomic level. It would be more precise to say they “swarm,” or are
“smeared,” around the central nuclei. Atomic models are discussed in Chapter
14, but it is good to set the stage at this point, especially if you plan on
skipping most or all of Chapter 14.
Electrical Forces
Discuss
the role of electrical forces in preventing us from oozing into our chairs and
so forth. Ask the class to imagine that the lecture table is a large magnet,
and that you wear magnetic shoes that are repelled by the table you “stand” on.
Ask them to imagine whether or not a sheet of paper could be passed between
your shoes and the table. For there is a space there. Then state that on the
submicroscopic scale that this is indeed what happens when you walk on any
solid surface. Only the repelling force isn’t magnetic, it’s electric! Discuss
the submicroscopic notion of things touching. Acknowledge that under very
special circumstances the nucleus of one atom can physically touch the nucleus
of another atom—that this is what happens in a thermonuclear reaction.
Mass Number and
Atomic Mass
Which
contributes most to an atom’s mass, protons or electrons? [Protons, by far.]
Which contributes to an atom’s size? [Electrons, by far.] Distinguish between
mass number and atomic mass. Help students write the chemical symbol for
specific elements with atomic numbers and atomic mass numbers.
The Elements
This section contains the first mention of the periodic
table. You might consider taking the opportunity to alleviate the fears some,
if not many, of your students will have about having to memorize this chart. Of
course, it is a good way to test memory skills, but memorizing the periodic
table has very little to do with learning physics. Instead, emphasize to
students that through this course they will instead learn how to “read” the
periodic table, which is a road map to the fundamental ingredients of all that
surrounds us.
This section
presents the modern definition of an element:
a substance that contains only one kind of atom. Note how it is that the terms
“element” and “atom” are sometimes used interchangeably. Generally, however,
“element” is used to indicate a macroscopic sample, while “atom” is used to
indicate the fundamental submicroscopic particle of the element.
The
Periodic Table
Elements are the
fundamental ingredients of all that surrounds us. Draw an analogy to how it is
that food ingredients, such as spices, properly organized in a kitchen allow a
cook to cook efficiently. Scientists have looked for a similar way to organize
the elements of nature. The end result is the periodic table.
Antimatter
Discuss
antimatter, and the speculations that other galaxies may be composed of
antimatter. There are even antiquarks. Our knowledge of quarks is relatively
new. Until recent times it was a fact that the fundamental building block of
matter was the protons, neutrons, and electrons discussed in this chapter. Now
it is a fact that the proton and neutron are not the fundamental particles, but
are composed of quarks. This change of view or advancement in our knowledge,
like others, is often cited as a weakness by people who do not understand what
science is about. Science is not a bag of answers to all the questions of the
world, but it is a process for finding answers to many questions about the
world. We continue to refine our models and add new layers to our
understanding—sometimes building onto layers and other times replacing layers.
It is unfortunate that some people see this as a weakness. This is remindful of
Bertrand Russell, who publicly changed his mind about certain ideas in the
course of his life—changes that were part of his growth, but were looked upon
by some as a sign of weakness. Likewise with physics. Our knowledge grows. And
that’s nice!
Dark Matter
Lest
anyone feel that physics is near its end insofar as what there is still to be
known, consider dark matter—today’s major science mystery. Whatever it is,
there is very little chance it will occupy any place on the periodic table of
the elements. How intriguing—most of the stuff of the universe isn’t on the
periodic table. And it is “out there.” Bear in mind, that we are “out there.”
Dark matter is likely infused in matter as we know it. Interesting point: There
is likely dark matter in the platinum-iridium cylinder that defines the
kilogram, locked in a glass case in France
Solutions to Chapter 2 Exercises
1. One.
2. In a water molecule, H2O, there
are three atoms, two hydrogens and one oxygen.
3. The average speed of molecules increases.
4. The speed at which the scent of a fragrance
travels is much less than the speed of the individual molecules that make it up
because of the many collisions among molecules. Although the molecular speed
between collisions is great, the rate of migration in a particular direction
through obstructing molecules is very much less.
5. The cat leaves a trail of molecules and atoms
on the grass. These in turn leave the grass and mix with the air, where they
enter the dog’s nose, activating its sense of smell.
6. A body would have no odor if all its
molecules remained within it. A body has odor only if some of its molecules
enter a nose.
7. The atoms that make up a newborn baby or
anything else in this world originated in the explosions of ancient stars. (See
Figure 2.8, my daughter Leslie.) The molecules
that make up the baby, however, were formed from atoms ingested by the mother
and transferred to her womb.
8. Water is not an element. It is a compound.
Its molecules are made of the atoms of elements hydrogen and oxygen.
9. Of the substances listed, H2, He,
Na, and U are pure elements. H2O and NaCl are compounds made of two
elements; three different elements contribute to H2SO4.
10. Agree
partially. It’s better to say an element is defined by the number of protons in
the nucleus. The number of protons and electrons are equal only when the
element is not ionized.
11. Brownian
motion is the result of more atoms or molecules bumping against one side of a
tiny particle than the other. This produces a net force on the particle, which
is set in motion. Such doesn’t occur for larger particles because the numbers
of bumps on opposite sides is more likely equal, producing no net force. The
number of bumps on a baseball is practically the same on all sides, with no net
force and no change in the baseball’s motion.
12. Individual
Ping-Pong balls are less massive than individual golf balls, so equal masses of
each means more Ping-Pong balls than golf balls.
13. Individual carbon atoms have less mass than
individual oxygen atoms, so equal masses of each means more carbons than
oxygens.
14. Since aluminum atoms are less massive than
lead atoms, more aluminum atoms than lead atoms compose a 1-kg sample.
15. Nine.
16. (a)
In both there are 27 protons (see periodic table). There are 32 neutrons in
Co-59 and 33
neutrons in Co-60.
(b)
The number of orbiting electrons matches the atomic number, 27.
17. The element is copper, atomic number 29. Any
atom having 29 protons is by definition copper.
18. Carbon. (See the periodic table.)
19. Lead.
20. Radon.
21. An atom gains an electron to become a
negative ion. Then it has more electrons than protons.
22. An atom loses an electron to become a
positive ion. Then it has more protons than electrons.
23. The capsule would be arsenic.
24. Neon, argon, krypton, xenon, and radon (the
noble gases).
25. Germanium has properties most like silicon,
as it is in the same column, Group XIV, as silicon in the periodic table.
26. The element below carbon in the periodic
table, silicon, has similar properties and could conceivably be the basis of
organic molecules elsewhere in the universe.
27. Protons contribute more to an atom’s mass,
and electrons more to an atom’s size.
28. The
hydrogen molecules, having less mass, move faster than the heavier oxygen
molecules.
29. Letting
the formula KE = 1⁄2 mv2 guide your thinking, for
the same speed the atom with greater mass has greater KE. Greater-mass carbon
therefore has greater KE than hydrogen for the same speed.
30. Electrical repulsion. Electrons speeding
around within an atom create an electrified cloud that repels the similar
clouds of other electrons, preventing the atoms from coalescing and keeping us
from falling through our chairs. (For the record, quantum effects play a large
role as well.)
31. You really are a part of every person around
you in the sense that you are composed of atoms not only from every person
around you, but from every person who ever lived on Earth! And the atoms that
now compose you will make up the atomic pool that others will draw upon.
32. With every breath of air you take, it is
highly likely that you inhale one of the atoms exhaled during your very first
breath. This is because the number of atoms of air in your lungs is about the
same as the number of breaths of air in the atmosphere of the world.
33. They
assumed hydrogen and oxygen were single-atom molecules with water’s formula
being H8O.
34. There would be a 100% conversion to radiant
energy.
35. Open-ended.
Solutions to Chapter 2 Problems
1. There are 16 grams of oxygen in 18 grams of
water. We can see from the formula for water, H2O, there are twice
as many hydrogen atoms (each of atomic mass 1) as oxygen atoms (each of atomic
mass 16). So the molecular mass of H2O is 18, with 16 parts oxygen
by mass.
2. A carbon atom is 12 times as massive as a
hydrogen atom, or 3 times as massive as four hydrogen atoms. A bit of reasoning
will show that for every 4 grams of hydrogen there will be 3 ´ 4 = 12 grams of carbon, which when totaled gives 16
grams. So there are 4 grams of hydrogen in 16 grams of methane.
3. The atomic mass of element A is 3⁄2 the
mass of element B. Why? Gas A has three times the mass of Gas B. If the equal
number of molecules in A and B had equal numbers of atoms, then the atoms in
Gas A would simply be three times as massive. But there are twice as many atoms
in A, so the mass of each atom must be half of three times as much—3⁄2.
4. The volume of the oil is like the volume of a
very large but very thin pancake, and equals its area multiplied by its
thickness. V = Ah, where V is the volume
(known) and A is the area (known from
measurement) and h is the thickness,
or diameter of the oil molecule. Solving for the thickness we get h = V/A, = (10-9 m3)/(1.0
m2) = 10-9 m (which is about ten atomic diameters). (This
makes a good lab exercise with diluted oleic acid.)
5. From the hint:
= 
= 
; x = 
= 1
6. There are 1022 breaths of air in
the world’s atmosphere, which is the same number of atoms in a single breath.
So for any one breath evenly mixed in the atmosphere, we sample one of Julius
Caesar’s atoms at any place or any time in the atmosphere.
7. The
total number of people who ever lived (6 ´ 109 ´ 20 = 120 ´ 109; roughly 1011
people altogether) is enormously smaller than 1022. How does 1022
compare to 1011? 1022 is (1011)2!
Multiply the number of people who ever lived by the same number, and you’ll get
1022, the number of air molecules in a breath of air. Suppose each
person on Earth journeyed to a different planet in the galaxy and every one of
those planets contained as many people as the Earth now contains. The total
number of people on all these planets would still be less than the number of
molecules in a breath of air. Atoms
are indeed small—and numerous!
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