Hewitt - Conceptual Physics 10e - #TitanPride...The solid floor you have fallen into is, except for...

Extraordinary twentieth-century physicist RichardFeynman contributedenormously to our under-standing of atoms andphysics in general.

Imaginethat you inhabit the world of Alice in Wonderland when she shrank in size.Pretend that you're standing on a chair and then you step off it and fall in slow

motion to the floor-and, as you fall, you continually shrink. As you fall toward thewooden floor, you brace yourself for impact; and, as you get nearer and nearer, becom-ing smaller and smaller, you notice that the surface of the floor is not as smooth as itfirst looked. Great crevices appear that are the microscopic irregularities that are foundin all wood. In falling into one of these canyon-sized crevices, you again brace yourselffor impact, only to find that the bottom of the canyon consists of many other crevices.Falling farther while growing even smaller, you notice the solid walls throb and pucker.The throbbing surfaces consist of hazy blobs, mostly spherical, some egg-shaped, somelarger than others, and all oozing into each other, making up long chains of compli-cated structures. Falling still farther, you brace for impact as you approach one of thesecloudy spheres closer and closer, smaller and smaller, and-Wowl You have entered anew universe. You fall into a sea of emptiness, occupied by occasional specks whirlingpast at unbelievably high speeds. You are in an atom, as empty of matter as the solarsystem. The solid floor you have fallen into is, except for specks of matter here andthere, mostly empty space. If you continue falling, you might fall many meters through"solid" matter before making a direct hit with a subatomic speck.

All matter, however solid it appears, is made up of tiny building blocks, which them-selves are mostly empty space. These are atoms-which can combine to form mole-cules, which, in turn flock together to form the matter that we see around us.

The Atomic Hypothesis

210

The idea that matter is composed of atoms goes back to the Greeks in the fifthcentury BC. Investigators of nature back then wondered whether matter wascontinuous or not. We can break a rock into pebbles, and the pebbles into finegravel. The gravel can be broken into fine sand, which then can be pulverizedinto powder. Perhaps it seemed to the fifth-century Greeks that there was asmallest bit of rock, an "atom," that could not be divided any further.

Aristotle, the most famous of the early Greek philosophers, didn't agreewith the idea of atoms. In the fourth century BC, he taught that all matter is

FIGURE 11.1An early model ofthe atom,with a central nucleus andorbiting electrons, much likea solar system with orbitingplanets.

~ ICS

Evidence for Atoms

We can't "see" atomsbecause they're toosmall. We can't seethe farthest star either.There's much that wecan't see. But thatdoesn't prevent inves-tigation of such thingsor even collectingindirect evidence.

Chapter 11 The Atomic Nature of Matter 211

composed of various combinations of four elements-earth, air, fire, and water.This view seemed reasonable because, in the world around us, matter is seenin only four forms; solids (earth), gases (air), liquids (water), and the state offlames (fire). The Greeks viewed fire as the element of change, since fire wasobserved to produce changes on substances that burned. Aristotle's ideas aboutthe nature of matter lasted for more than 2000 years.

The atomic idea was revived in the early 1800s by an English meteorolo-gist and school teacher, John Dalton. He successfully explained the nature ofchemical reactions by proposing that all matter is made of atoms. He and oth-ers of the time, however, had no direct evidence for their existence. Then, in1827, a Scottish botanist named Robert Brown noticed something very unusualin his microscope. He was studying grains of pollen suspended in water, andhe saw that the grains were continually moving and jumping about. At first hethought the grains were some kind of moving life forms, but later he found thatdust particles and grains of soot suspended in water moved in the same way.This perpetual jiggling of particles-now called Brownian motion-results fromcollisions between visible particles and invisible atoms. The atoms are invisiblebecause they're so small. Although he couldn't see the atoms, Brown could seethe effect they had on particles he could see. It's like a super-giant beach ballbeing bounced around by a crowd of people at a football game. From a high-flying airplane, you wouldn't see the people because they are small relative tothe enormous ball, which you would be able to see. The pollen grains thatBrown observed moved because they were constantly being jostled by the atoms(actually, by the atomic combinations referred to as molecules) that made upthe water surrounding them.

All this was explained in 1905 by Albert Einstein, the same year thathe announced the theory of special relativity. Until Einstein's explanation-which made it possible to find the masses of atoms-many prominentphysicists remained skeptical about the existence of atoms. So we see thatthe reality of the atom was not firmly established until the early twentiethcentury.

In 1963, the importance of atoms was emphasized by the American physi-cist Richard Feynman, who stated that, if some cataclysm were to destroy allscientific knowledge and only one sentence could be passed on to the next gen-eration of creatures, the statement with the most information in the least wordswould be: "All things are made of atoms-little particles that move around inperpetual motion, attracting each other when they are a little distance apart,but repelling upon being squeezed into one another." All matter-shoes, ships,sealing wax, cabbages, and kings-any material we can think of-is made ofatoms. This is the atomic hypothesis, which now serves as a central foundationof all of science.

Characteristics of AtomsAtoms, the building blocks of matter, are incredibly tiny. An atom is as manytimes smaller than you as an average star is larger than you. A nice way tosay this is that we stand between the atoms and the stars. Or another way of

21 2 Part Two Properties of Matter

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How long would ittake you to count toone million? If eachcount takes onesecond, countingnonstop to a millionwould take 11.6 days.To count to a billion(109

) would take31.7 years. To countto a trillion (1012

)

would take 31,700years. Counting to1022 would take aboutten thousand times theage of the universe!

Smell discriminationfor salmon has beenmeasured in parts pertrillion-quite incredi-ble. Pacific salmonuse other navigationdevices in the openocean, including sen-sitivity to polarizedlight, ocean currents,magnetic fields, andtemperature andsalinity gradients.

Atoms Are Recyclable

stating the smallness of atoms is that the diameter of an atom is to the diam-eter of an apple as the diameter of an apple is to the diameter of the Earth. So,to imagine an apple full of atoms, think of the Earth solid-packed with apples.Both have about the same number.

Atoms are numerous. There are about 100,000,000,000,000,000,000,000atoms in a gram of water (a thimbleful). In scientific notation, that's 1023 atoms.The number 1023 is an enormous number, more than the number of drops ofwater in all the lakes and rivers of the world. So there are more atoms in athimbleful of water than there are drops of water in the world's lakes and rivers.In the atmosphere, there are about 1022 atoms in a liter of air. Interestingly, thevolume of the atmosphere contains about 1022 liters of air. That's an incredi-bly large number of atoms, and the same incredibly large number of liters ofatmosphere. Atoms are so small and so numerous that there are about as manyatoms in the air in your lungs at any moment as there are breathfuls of air inthe Earth's atmosphere.

Atoms get around. Atoms are perpetually moving. They migrate fromone location to another. In solids, the rate of migration is low; in liquids,it is greater; and in gases, migration is greatest. Drops of food coloring ina glass of water, for example, soon spread to color the entire glass of water.The same would be true of a cupful of food coloring thrown into an ocean:It would spread around and later be found in every part of the world'soceans.

Water dilution is a main reason for salmon being able to return to theirbirthplaces. Atoms and molecules from soil and vegetation in a lake or astream make that water unique. Likewise with salmon spawning habitats.Once hatched, young salmon remain in local streams for two years beforebeginning their voyage to the ocean, where they remain for an average offour years. What also goes into the ocean, of course, is water from the regionin which they grew up. The original water composition is diluted as it trav-els to the ocean. In the ocean, it is further diluted-but never to zero. Whenthe time comes to return to their original habitat, salmon follow their noses.They swim in a direction where concentrations of familiar water becomegreater. In time, they'll encounter the source of that water. Humans can dis-cern different bottled waters, and salmon have enormously more ability tosense the difference in waters, as bloodhounds have a similar sensitivity toair composition.

Atoms and molecules in the atmosphere spread around much more thanthey do in the ocean. Atoms and molecules in air zip around at speeds up toten times the speed of sound. They spread rapidly, so oxygen that surroundsyou today may have been halfway across the country a few days ago. TakingFigure 11.2 further, your exhaled breaths of air quite soon mix with otheratoms in the atmosphere. After the few years it takes for your breath to mixuniformly in the atmosphere, anyone, anywhere on Earth, who inhales abreath of air will take in, on the average, one of the atoms in that exhaledbreath of yours. But you exhale many, many breaths, so other people breathein many, many atoms that were once in your lungs-that were once a partof you; and, of course, vice versa. Believe it or not, with each breath you takein, you breathe atoms that were once a part of everyone who ever lived! Con-sidering that the atoms we exhale were part of our bodies (the nose of a dog

r~~~Ii&0,]FIGURE 11.2There are as many atoms ina normal breath of air asthere are breathfuls of air inthe atmosphere of the Earth.

Life is not measuredby the number ofbreaths we take, butby the moments thattake our breathaway. -George Car/in


has no trouble discerning this), it can be truly said that we are literally breath-ing one another.

Atoms are ageless. Many atoms in your body are nearly as old as the uni-verse itself. When you breathe, for example, only some of the atoms that youinhale are exhaled in your next breath. The remaining atoms are taken intoyour body to become part of you, and they later leave your body by variousmeans. You don't "own" the atoms that make up your body; you borrow them.We all share from the same atom pool, as atoms forever migrate around, within,and among us. So some of the atoms in the nose you scratch today could havebeen part of your neighbor's ear yesterday!

Most people know that we are all made of the same kinds of atoms. Butwhat most people don't know is that we are made of the same atoms-atomsthat cycle from person to person as we breathe and as our perspiration is vapor-ized. We recycle atoms on a grand scale.

So the origin of the lightest atoms goes back to the origin of the universe,and most heavier atoms are older than the Sun and the Earth. There are atomsin your body that have existed since the first moments of time, recyclingthroughout the universe among innumerable forms, both nonliving and living.You're the present caretaker of the atoms in your body. There will be manywho will follow you.

CHECK YOURSELF

1. Which are older, the atoms in the body of an elderly person or those in the bodyof a baby?

2. World population grows each year. Does this mean that the mass of the Earthincreases each year?

3. Are there really atoms that were once a part of Albert Einstein incorporated inthe brains of all the members of your family?

CHECI( YOUR ANSWERS

1. The age of the atoms in both is the same. Most of the atoms were manufac-tured in stars that exploded before the solar system came into existence.

2. The greater number of people increases the mass of the Earth by zero. The atomsthat make up our bodies are the same atoms that were here before we wereborn-we are but dust, and unto dust we shall return. Human cells are merelyrearrangements of material already present. The atoms that make up a baby form-ing in its mother's womb must be supplied by the food the mother eats. And thoseatoms originated in stars-some of them in far-away galaxies. (Interestingly, themass of the Earth does increase by the incide~ce of roughly 40,000 tons of inter-planetary dust each year, but not by the birth and survival of more people.)

3. Quite so, and of Oprah Winfrey too. However, these atoms are combined differ-ently than they were previously. If you experience one of those days when youfeel like you'll never amount to anything, take comfort in the thought that manyof the atoms that now constitute your body will live forever in the bodies of allthe people on Earth who are yet to be.

214 Part Two Properties of Matter

Atomic Imagery

FIGURE 11.3Information about the shipis revealed by passing wavesbecause the distance be-tween wave crests is smallcompared with the size ofthe ship. The passing wavesreveal nothing about thechain.

FIGURE 11.4The strings of dots are chainsof thorium atoms imagedwith a scanning electronmicroscope. This historicphotograph of individualatoms was taken in 1970by researchers at the Universityof Chicago's Enrico FermiInstitute.

Atoms are too small to be seen with visible light. You could connect an arrayof optical microscopes atop one another and never "see" an atom because lightis made up of waves, and atoms are smaller than the wavelengths of visiblelight. The size of a particle visible under the highest magnification must be largerthan the wavelengths of visible light. This is better understood by an analogywith water waves. A ship is much larger than the water waves that roll on byit. As Figure 11.3 shows, water waves can reveal features of the ship. The wavesdiffract as they pass the ship. But diffraction is nil for waves that pass by theanchor chain, revealing little or nothing about it. Similarly, waves of visible lightare too coarse compared with the size of an atom to show details of the sizeand shape of atoms. Atoms are incredibly small.

Yet here in Figure 11.4 we see a picture of atoms-the historic 1970 imageof chains of individual thorium atoms. The picture is not a photograph but anelectron micrograph-it was not made with light but with a thin electron beamin a scanning electron microscope (SEM) developed by Albert Crewe at theUniversity of Chicago's Enrico Fermi Institute. An electron beam, such as theone that sprays a picture on an early television screen, is a stream of particlesthat have wave properties. The wavelength of an electron beam is smaller thanthe wavelengths of visible light, and atoms are larger than the tiny wavelengthsof an electron beam. Crewe's electron micrograph is the first high-resolutionimage of individual atoms.

In the mid-1980s, researchers developed a new kind of microscope-thescanning tunneling microscope (STM). It employs a sharp tip that is scannedover a surface at a distance of a few atomic diameters in a point-by-point andline-by-line fashion. At each point, a tiny electric current, called a tunneling cur-rent, is measured between the tip and the surface. Variations in the currentreveal the surface topology. The image of Figure 11.5 beautifully shows theposition of a ring of atoms. The ripples shown in the ring of atoms reveal thewave nature of matter. This image, among many others, underscores the delight-ful interplay of art and science.

Because we can't see inside an atom, we construct models. A model isan abstraction that helps us to visualize what we can't see, and, importantly,it enables us to make predictions about unseen portions of the natural world.

FIGURE 11.5An image of 48 iron atomspositioned into a circularring that "corrals" electronson a copper crystal surface;taken with a scanningtunneling microscope at theIBM Almaden Laboratory inSan Jose, California.

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Sometimes a model isuseful even when it'sincorrect. Scotsman

.James Watt con-structed a workablesteam engine in theeighteenth centurybased on a model ofheat that turned outto be quite incorrect.


H'Idrogen-1 electron

in 1 shell Aluminum -13 electronsin 3 shells

Lithium -3 electrons in 2 shells

Helium-2 electrons

in 1 shell

FIGURE 11.6The classical model ofthe atom consists of a tiny nucleus surrounded by electrons that orbitwithin spherical shells. As the charges of nuclei increase, electrons are pulled closer, and theshells become smaller.

The model of the atom most familiar to the general public is akin to thatof the solar system. As with the solar system, most of an atom's volume isempty space. At the center is a tiny and very dense nucleus in which mostof the mass is concentrated. Surrounding the nucleus are "shells" of orbit-ing electrons. These are the same electrically charged electrons that consti-tute the electric current in your calculator. Although electrons electricallyrepel other electrons, they are electrically attracted to the nucleus, which hasa net positive charge. As the size and charge of the nuclei increase, electronsare pulled closer, and the shells become smaller. Interestingly, the uraniumatom, with its 92 electrons, is not appreciably larger in diameter than thelightest atom, hydrogen. This model was first proposed in the early twentiethcentury, and it reflects a rather simplified understanding of the atom. It wassoon discovered, for example, that electrons don't orbit the atom's centerlike planets orbit the Sun. Like most early models, however, the planetaryatomic model served as a useful stepping stone to further understanding andmore accurate models. Any atomic model, no matter how refined, is nothingmore than a symbolic representation of the atom and not a physical pictureof the actual atom.

Atomic StructureNearly all the mass of an atom is concentrated in the atomic nucleus, whichoccupies only a few quadrillionths of its volume. The nucleus, therefore, isextremely dense. If bare atomic nuclei could be packed against each other intoa lump 1 centimeter in diameter (about the size of a large pea), the lump wouldweigh 133,000,000 tons! Huge electrical forces of repulsion prevent such closepacking of atomic nuclei because each nucleus is electrically charged and repelsall other nuclei. Only under special circumstances are the nuclei of two or moreatoms squashed into contact. When this happens, a violent kind of nuclear reac-tion may occur. Such a reaction, a thermonuclear fusion reaction, occurs in the


centers of stars and ultimately makes them shine. (We'll discuss these nuclearreactions in Chapter 34.)

The principal building block of the nucleus is the nucleon, which is in turncomposed of fundamental particles called quarks (Chapter 32). When a nucleonis in an electrically neutral state, it is a neutron; when it is in an electricallycharged state, it is a proton. All protons are identical; they are copies of oneanother. Likewise with neutrons: Each neutron is like every other neutron. Thelighter nuclei have roughly equal numbers of protons and neutrons; more mas-sive nuclei have more neutrons than protons. Protons have a positive electriccharge that repels other positive charges but attracts negative charges. So likekinds of electrical charges repel one another, and unlike charges attract oneanother. It is the positive protons in the nucleus that attract a surrounding cloudof negatively charged electrons to constitute an atom. (We'll return to nucleonsin Chapter 33 and to electric charge in Chapter 22.)

As we'll explore in Chapter 22, electrons make up the flow of electricityin electrical circuits. They are exceedingly light, almost 2000 times lighter thannucleons, and thus they contribute very little mass to the atom. An electron inone atom is identical to any electron in or out of any other atom. Electronsrepel other electrons, but a multitude of electrons can be held together withinan atom because of their attraction to the positively charged nucleus.

The number of protons in the nucleus is electrically balanced by an equalnumber of electrons whirling about the nucleus. The atom itself is electricallyneutral, so it normally doesn't attract or repel other atoms. But when atomsare close together, the negative electrons on one atom may at times be closerto the positive nucleus of another atom, which results in a net attractionbetween the atoms. That is why some atoms combine to form molecules.

The fact that electrons repel other electrons has interesting consequences.When the atoms of your hand push against the atoms of a wall, for example,electrical repulsions prevent your hand from passing through the wall. Thesesame electrical repulsions prevent us from falling through the solid floor. Theyalso allow us the sense of touch. Interestingly, when you touch someone, youratoms don't meet the atoms of the one you touch. Instead, the atoms get closeenough so that you sense electrical repulsion forces. There is still a tiny, thoughimperceptible, gap of space between you and the person you are touching.

CHECK YOURSELF

Why do electrically neutral atoms repel one another when they are close?

CHECK YOUR ANSWER

In an electrically neutral atom, the number of positive protons is balanced bythe same number of negative electrons. Electrons, however, reside on the outersurface of the atom, meaning that the atomic surface is negatively charged.Two or more atoms, therefore, can't get together without an electrical repulsionbetween their outer surfaces. Hence, we can't walk through walls. Sometimes,however, electrons are able to jump from one atom to the next. This occursduring a chemical reaction, in which atoms are able to link together to formlarger structures, such as molecules.


The Elements

FIGURE 11.7Any element consists onlyof one kind of atom. Goldconsists only of gold atoms,a flask of gaseous nitrogenconsists on Iyof nitrogenatoms, and the carbon of agraphite pencil is composedonly of carbon atoms.

When a substance is composed of atoms of the same kind, we call that sub-stance an element. A pure 24-carat gold ring, for example, is composed onlyof gold atoms. A gold ring with a lower carat value is composed of gold andother elements, such as nickel. The silvery liquid in a barometer or thermome-ter is the element mercury. The entire liquid consists of only mercury atoms.Of course if a substance contains only a single kind of atom, it can correctlybe called an element. An atom of a particular element is the smallest sample ofthat element. Although atom and element are often used interchangeably,element is preferred when referring to macroscopic quantities. For example, wespeak of isolating a mercury atom from a flask of the element mercury.

The lightest element of all is hydrogen. In the universe at large, it is the mostabundant element-more than 90% of the atoms in the known universe arehydrogen atoms. Helium, the second-lightest element, provides most of theremaining atoms in the universe. Heavier atoms in our surroundings were man-ufactured by the fusion of light elements in the hot, high-pressure cauldrons deepwithin the interiors of stars. The heaviest elements form when huge stars implodeand then explode-supernovas. Nearly all the elements on Earth are remnantsof stars that exploded long before the solar system came into existence.

Just as dots of only three colors of light combine to form almost every per-ceivable color on a television screen, only about 100 distinct elements form all thematerials we know about. To date, more than 112 elements are known. Of these,about 90 occur in nature. The others are produced in the laboratory with high-energy atomic accelerators and nuclear reactors. These laboratory-produced ele-ments are too unstable (radioactive) to occur naturally in appreciable quantities.

From a pantry containing less than 100 elements, we have the atoms thatconstitute almost every simple, complex, living, or nonliving substance in theknown universe. More than 99% of the material on Earth is formed from onlyabout a dozen of the elements. The other elements are relatively rare. Livingthings are composed primarily of five elements: oxygen (0), carbon (C), hydro-gen (H), nitrogen (N), and calcium (Ca). The letters in parentheses representthe chemical symbols for these elements.

FIGURE 11.8Both you and Leslie aremade of stardust-in thesense that the carbon,oxygen, nitrogen, and otheratoms that make up yourbody originated in the deepinteriors of ancient stars thathave long since exploded.


The Periodic Table of the Elements

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Interestingly, of every200 atoms in our bod-ies, 126 are hydrogen,51 are oxygen, andjust 19 are carbon.

Elements are classified by the number of protons their atoms contain, which istheir atomic number. Hydrogen, containing one proton per atom, has atomicnumber 1; helium, containing two protons per atom, has atomic number 2; andso on in sequence to the heaviest naturally occurring element, uranium, withatomic number 92. The numbers continue beyond atomic number 92 throughthe artificially produced transuranic (beyond uranium) elements. The arrange-ment of elements by their atomic numbers makes up the periodic table of theelements (Figure 11.9).

The periodic table is a chart that lists atoms by their atomic number andalso by their electrical arrangements. Like the rows of a calendar that list thedays of the week, each element, from left to right, has one more proton andelectron than the preceding element. Reading down the table, each element hasone more shell than the one above. The inner shells are filled to their capaci-ties, and the outer shell mayor may not be, depending on the element. Onlythe elements at the far right of the table, like the column of Saturdays on a cal-endar, have their outer shells filled to capacity. These are the noble gases-helium, neon, argon, krypton, xenon, and radon. The periodic table is thechemist's road map-and much more. Most scientists consider the periodictable to be the most elegant organizational chart ever devised. The enormoushuman effort and ingenuity that went into finding its regularities makes a fas-cinating atomic detective story. 1

Elements may have up to seven shells, and each shell has its own capacityfor electrons. The first and innermost shell has a capacity for two electrons whilethe second shell has a capacity for eight electrons. The arrangement of electronsin the shells dictates such properties as melting and freezing temperatures, elec-trical conductivity, and the taste, texture, appearance, and color of substances.The arrangements of electrons quite literally give life and color to the world.

Models of the atom evolve with new findings. The classical model of theatom has given way to a model that views the electron as a standing wave-altogether different from the idea of an orbiting particle. This is the quantummechanical model, introduced in the 1920s. Quantum mechanics is the theoryof the small-scale world that includes predicted wave properties of matter. Itdeals with "lumps" occurring at the subatomic level-lumps of matter or lumpsof such things as energy and angular momentum. (More about the quantum inChapters 31 and 32).

IsotopesWhereas the number of protons in a nucleus exactly matches the number ofelectrons around the nucleus in a neutral atom, the number of protons in thenucleus need not match the number of neutrons there. For example, all hydrogen

1A clearly written discussion of the periodic table by my nephew, John Suchocki, is in Chapter 5 of hisConceptual Chemistry, 2nd ed. (Benjamin Cumrnings, 2004). Also see Chapter 14 of Conceptual PhysicalScience, 3rd ed., by Hewitt, Suchocki, and Hewitt (Addison-Wesley, 2004). Interesting material!

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Don't confuse anisotope with an ion,which is an atom thatis electrically chargedowing to an excess ora deficiency ofelectrons.

In order for two chem-icals to bond, theymust first collide inthe proper orientation.Second, they musthave sufficient kineticenergies to initiate thebreaking of chemicalbonds so that newones can form.

nuclei have a single proton but most have no neutrons. A small percentage con-tain one neutron and an even smaller percentage contain two neutrons. Simi-larly, most iron nuclei with 26 protons contain 30 neutrons, while a small per-centage contain 29 neutrons. Atoms of the same element that contain differentnumbers of neutrons are isotopes of the element. The various isotopes of anelement all have the same number of electrons, and so, for the most part, theybehave identically. The hydrogen atoms in H20, for example, mayor may notcontain a neutron. The oxygen doesn't "know the difference." But if significantamounts of the hydrogen atoms have neutrons, then the H20 is slightly heav-ier, and it's appropriately called "heavy water."

We identify isotopes by their mass number, which is the total number of pro-tons and neutrons (in other words, the number of nucleons) in the nucleus. Ahydrogen isotope with one proton and no neutrons, for example, has a mass num-ber of 1, and is referred to as hydrogen-L Likewise, an iron atom with 26 protonsand 30 neutrons has a mass number of 56 and is referred to as iron-56. An ironatom with 26 protons and only 29 neutrons would be called iron-55.

The total mass of an atom is called its atomic mass. This is the sum of themasses of all the atom's components (electrons, protons, and neutrons). Becauseelectrons are so much less massive than protons and neutrons, their contribu-tion to atomic mass is negligible. Atoms are so small that expressing theirmasses in units of grams or kilograms is not practical. Instead, scientists use aspecially defined unit of mass known as the atomic mass unit or amu. A nucleonhas a mass of about 1 amu. An atom with 12 nucleons, such as carbon-12,therefore, has a mass of about 12 amu. The periodic table lists atomic massesin units of amu.

Most elements have a variety of isotopes. The atomic mass for each elementlisted in the periodic table is the weighted average of the masses of these isotopesbased on the occurrence of each isotope on Earth. For example, carbon with sixprotons and six neutrons has an atomic mass of 12.000 amu. About one percentof all carbon atoms, however, contain seven neutrons. The heavier isotope raisesthe average atomic mass of carbon from 12.000 amu to 12.011 amu.

CHECK YOURSELF

1. Which contributes more to an atom's mass, electrons or protons? Which con-tributes more to an atom's volume (its size)?

2. Which is represented by a whole number-the mass number or the atomic mass?3. Do two isotopes of iron have the same atomic number? The same atomic mass number?

CHECK YOUR ANSWERS

1. Protons contribute more to an atom's mass; electrons contribute more to its size.

2. The mass number is always given as a whole number, such as hydrogen-1 orcarbon-12. Atomic mass, by contrast, is the average mass of the various isotopesof an element and is thus represented by a fractional number.

3. The two isotopes of iron have the same atomic number 26, because they eachhave 26 protons in the nucleus. They have different atomic mass numbers if theyhave different numbers of neutrons in the nucleus.


Compounds and Mixtures

FIGURE 11.10Table salt (NaCI) is a crys-talline compound that is notmade of molecules. Thesodium and chlorine atomsare arranged in a repeatingpattern in which each atomis surrounded by six atomsof the other kind.

A pure chemical material that consists of more than one kind of atom is calleda compound. Examples of simple compounds include water, ammonia, andmethane. A compound is uniquely different from the elements from which itis made, and it can only be separated into its constituent elements by chemicalmeans. Sodium, for example, is a metal that reacts violently with water. Chlorineis a poisonous yellow-green gas. Yet the compound of these two elements is theharmless white crystal (NaCI) that you sprinkle on your potatoes. Consider alsothat, at ordinary temperatures, the elements hydrogen and oxygen are bothgases. When combined, they form the compound water (H20), a liquid-quitedifferent.

Not all substances react with one another chemically when they are broughtclose together. A substance that is mixed together without chemically bondingis called a mixture. Sand combined with salt is a mixture. Hydrogen and oxy-gen gas form a mixture until ignited, whereupon they form the compound water.A common mixture that we all depend on is nitrogen and oxygen together witha little argon and small amounts of carbon dioxide and other gases. It is theair that we breathe.

CHECK YOURSELF

Is common table salt an element, a compound, or a mixture?

MoleculesA molecule consists of two or more atoms held together by the sharing of elec-trons. (We say such atoms are covalently bonded.) A molecule may be as sim-ple as the two-atom combination of oxygen (02) or the two-atom combinationof nitrogen (N2), which are the elements that constitute most of the air we

CHECI< YOUR ANSWER

Salt is not an element. If it were, you'd see it listed in the periodic table. Pure tablesalt is a compound of the elements sodium and chlorine, represented in Figure 11.10.Notice that the sodium atoms (green) and the chlorine atoms (yellow) are arranged ina three-dimensional repeating pattern-a crystal. Each sodium atom is surroundedby six chlorine atoms, and each chlorine atom is surrounded by six sodiums. Interest-ingly, there are no separate sodium-chlorine groups that can be labeled rnolecules.f

21n a strict sense, common table salt is a mixture-often with small amounts of potassium iodide and sugar.The iodine in the potassium iodide has virtually wiped out a common affliction of earlier times, a swelling ofthe thyroid gland known as endemic gaiter. Tiny amounts of sugar prevent oxidation of the salt, whichotherwise would turn yellow.


People have always sought healers for help with physicalpain and fear. As treatment, traditional healers oftenadminister herbs, or chant, or wave their hands over apatient's body. And improvement, more often than not,actually occurs! This is the placebo effect. A placebo maybe a healing practice or a substance (pill) containingelements or molecules that have no medical value. But,remarkably, the placebo effect does have a biologicalbasis. It so happens that, when you are fearful or in pain,your brain response is not to mobilize your body's healingmechanism-it instead prepares your body for some ex-ternal threat. It's an evolutionary adaptation that assignshighest priority to preventing additional injury. Stress hor-mones released into the bloodstream increase respiration,blood pressure, and heart rate-changes that usuallyimpede recovery. The brain prepares your body for action;recovery can wait.

That's why the first objective of a good healer orphysician is to relieve stress. Most of us begin feelingbetter even before leaving the healer's (or doctor's) office.Prior to 1940, most medicine was based on the placeboeffect, when about the only medicines doctors had intheir bags were laxatives, aspirin, and sugar pills. In abouthalf the cases, a sugar pill is as effective in stopping painas an aspirin. Here's why: Pain is a signal to the brainthat something is wrong and needs attention. The signalis induced at the site of inflammation by prostaglandinsreleased by white blood cells. Aspirin blocks the productionof prostaglandins and therefore relieves the pain. The

mechanism for pain reliefby a placebo is altogetherdifferent. The placebo fools the brain into thinking thatwhatever is wrong is being cared for. Then the pain signalis lowered by the release of endorphins, opiate-likeproteins found naturally in the brain. So, instead ofblocking the production of prostaglandins, the endorphinsblock their effect. With pain alleviated, the body can focuson healing.

The placebo effect has always been employed (andstill is!) by healers and others who claim to have wondrouscures that lie outside modern medicine. These healers ben-efit from the public's tendency to believe that, if 8 followsA, then 8 is caused by A. The cure could be due to thehealer, but it could also merely be the body repairing itself.Although the placebo effect can certainly influence theperception of pain, it has not been shown to influence thebody's abilityto fight infection or repair injury.

Is the placebo effect at work for those who believethat better health is bequeathed to those who wearcrystals, magnets, or certain metal bracelets? If so, isthere any harm in thinking so-even if there is no scien-tific evidence for it? Harboring positive beliefs is usuallyquite harmless-but not always. For serious problemsrequiring modern medical treatment, reliance on theseaids can be disastrous ifused to the exclusion of modernmedical treatment. The placebo effect has rea/limitations.

*Adapted from Voodoo Science: The Road from Foolishness to Fraud,by Robert L. Park, Oxford UniversityPress, NewYork,2000.

breathe. Two atoms of hydrogen combine with a single atom of oxygen to forma water molecule (H20). Changing a molecule by one atom can make a big dif-ference. In chlorophyll, for example, there is a ring of hydrogen, carbon, andoxygen atoms that surrounds a single magnesium atom. Substitute an iron atomfor the magnesium atom and it becomes a ring most similar to that found inhemoglobin (an oxygen-carrying protein in our blood). So one atom can makethe difference between a molecule that a plant can use and one that a personcan use.

FIGURE 11.11Models ofsimple molecules.The atoms in a moleculeare not Just mixed togetherbut are joi ned in a well-defined way.


CHECK YOURSELF

How many atomic nuclei are in a single oxygen atom? In a single oxygen molecule?

Energy is required to pull molecules apart. We can understand this by con-sidering a pair of magnets stuck together. Just as some "muscle energy" isrequired to pull the magnets apart, the breaking apart of molecules requiresenergy. During photosynthesis, plants use the energy of sunlight to break apartthe bonds within atmospheric carbon dioxide and water. The major product ofphotosynthesis is carbohydrate molecules, which retain this solar energy untilthe plant is oxidized, either slowly by rotting or quickly by burning. Then theenergy that came from the sunlight is released back into the environment. Sothe slow warmth of decaying compost or the quick warmth of a campfire isreally the warmth of stored sunlight!

More things can burn besides those that contain carbon and hydrogen. Iron"burns" (oxidizes) too. That's what rusting is-the slow combination of oxygenatoms with iron atoms, releasing energy. When the rusting of iron is speeded up,it makes nice hand-warmer packs for skiers and winter hikers. Any process inwhich atoms rearrange to form different molecules is called a chemical reaction.

Our sense of smell is sensitive to exceedingly small quantities of molecules.Our olfactory organs easily detect small concentrations of such noxious gasesas hydrogen sulfide (the stuff that smells like rotten eggs), ammonia, and ether.The smell of perfume is the result of molecules that rapidly evaporate and dif-fuse haphazardly in the air until some of them get close enough to your noseto be inhaled. They are just a few of the billions of jostling molecules that, intheir aimless wanderings, happen to wind up in the nose. You can get an ideaof the speed of molecular diffusion in the air when you are in your bedroomand smell food very soon after the oven door has been opened in the kitchen.

Antimatter

FIGURE 11.12An atom of anti matter has anegatively charged nucleussurrounded by positrons.

Whereas matter is composed of atoms with positively charged nuclei and neg-atively charged electrons, antimatter is composed of atoms with negative nucleiand positive electrons, or positrons.

Positrons were first discovered in 1932, in cosmic rays bombarding theEarth's atmosphere. Today, antiparticles of all types are regularly produced inlaboratories using large nuclear accelerators. A positron has the same mass as anelectron and the same magnitude of charge but the opposite sign. Antiprotonshave the same mass as protons but are negatively charged. The first completeartificial anti-atom, a positron orbiting an antiproton, was constructed in 1995.Every charged particle has an antiparticle of the same mass and opposite charge.

CHECK YOUR ANSWER

There is one nucleus in an oxygen atom (0), and two in the combination of twooxygen atoms-an oxygen molecule (02),


Neutral particles (such as the neutron) also have antiparticles, which are alikein mass and in some other properties but opposite in certain other properties.For every particle there is an antiparticle. There are even antiquarks.

Gravitational force does not distinguish between matter and antimatter-eachattracts the other. Also, there is no way to indicate whether something is madeof matter or antimatter by the light it emits. Only through much subtler, hard-to-measure nuclear effects could we determine whether a distant galaxy is madeof matter or antimatter. But, if an antistar were to meet a star, it would be adifferent story. They would mutually annihilate each other, with most of thematter converting to radiant energy (this is what happened to the anti-atomcreated in 1995, which rapidly annihilated in a puff of energy). This process,more so than any other known, results in the maximum energy output per gramof substance-E = mc'', with a 100% mass conversion.3 (Nuclear fission andfusion, by contrast, convert less than 1% of the matter involved.)

There cannot be both matter and antimatter in our immediate environment,at least not in appreciable amounts or for appreciable times. That's because some-thing made of antimatter would be completely transformed to radiant energy assoon as it touched matter, consuming an equal amount of normal matter in theprocess. If the Moon were made of antimatter, for example, a flash of energeticradiation would result as soon as one of our spaceships touched it. Both thespaceship and an equal amount of the antimatter Moon would disappear in aburst of radiant energy. We know the Moon is not antimatter because this didn'thappen during the Moon missions. (Actually, astronauts weren't in this kind ofdanger, for previous evidence showed that the Moon is made of ordinary matter.)But what about other galaxies? There is strong reason to believe that in the partof the universe we know (the "observable universe"), galaxies are made only ofnormal matter-apart from the occasional transitory antiparticle. But what of theuniverse beyond? Or other universes? We don't know.

CHECK YOURSELF

If a one-gram body of antimatter meets a ten-gram body of matter, what mass survives?

Dark MatterWe know that the elements in the periodic table are not confined to our planet.From studies of radiation coming from other parts of the universe, we find thatstars and other objects "out there" are composed of the same particles we have

CHECK YOUR ANSWER

Nine grams of matter survive(the other two grams are transformed into radiant energy).

3Somc physicists speculate that, right after the Big Bang, the early universe hod hillions of times more particlesthan it has now, and that a near total extinction of matter and antimatter caused by their mutual anihilarionleft only the relatively small amount of matter now present in the universe.

Finding the nature ofthe dark matter andthe nature of thevacuum energy arehigh-priority quests inthese times. What wewill have learned bymidcentury will likelydwarf all that we haveever known.


on Earth. Stars emit light that produces the same "atomic spectra" (Chapter 30)as the elements in the periodic table. How wonderful to find that the laws thatgovern matter on Earth extend throughout the observable universe. Yet thereremains one troubling detail. In the closing years of the twentieth century, astro-physicists found there is a lot more mass out there than we can directly see.

Astrophysicists talk of the dark matter-matter we can't see that tugs on starsand galaxies that we can see. Gravitational forces within galaxies are measuredto be far greater than visible matter can account for. Only in this twenty-first cen-tury has it been confirmed that some 23 % of matter in the universe is composedof the unseen dark matter. Whatever dark matter is, most or all of it is likely tobe "exotic" matter-very different from the elements that make up the periodictable, and different from any extension of the present list of elements. Much ofthe rest of the universe is dark energy (briefly mentioned in Chapter 7), whichpushes outward on the expanding universe. Both dark matter and dark energymake up some 90% of the universe. Dark matter and dark energy seem to bedifferent stuff. At this writing, neither has been identified. Speculations aboundabout dark matter and dark energy, but we don't know what they are.

Richard Feynman often used to shake his head and say he didn't know any-thing. When he and other top physicists say they don't know anything, theymean that what they do know is closer to nothing than to what they can know.Scientists know enough to realize that they have a relatively small handle onan enormous universe still full of mysteries. From a looking-backward point ofview, today's scientists know enormously more than their forebears a centuryago, and scientists then knew much more than their forebears. But, from ourpresent vantage point, looking forward, there is so much yet to be learned.Physicist John A. Wheeler, Feynman's graduate-school advisor, sees the nextlevel of physics going beyond how to why-to meaning. We have scarcelyscratched the surface.

Summary of TermsAtom The smallest particle of an element that has all of

the element's chemical properties.Brownian motion The haphazard movement of tiny parti-

cles suspended in a gas or liquid resulting from theirbombardment by the fast-moving atoms or moleculesofthe gas or liquid.

Atomic nucleus The core of an atom, consisting oftwobasic subatomic particles-protons and neutrons.

Element A pure substance consisting of only one kind ofatom.

Atomic number The number that designates the identityof an element, which is the number of protons in thenucleus of an atom; in a neutral atom, the atomicnumber is also the number of electrons in the atom.

The periodic table of the elements A chart that lists theelements in horizontal rows by their atomic numberand in vertical columns by their similar electron arrange-ments and chemical properties. (See Figure 11.9.)

Quantum mechanics The theory of the small-scaleworld that includes predicated wave propertiesof matter.

Isotopes Different forms of an atom that contains thesame number of protons but different numbers ofneutrons.

Atomic mass unit (amu) The standard unit of atomicmass, which is equal to one-twelfth the mass of thecommon atom of carbon, arbitrarily given the value ofexactly 12. One amu has a mass of 1.661 X 10-24

grams.Compound A material in which atoms of different

elements are chemically bonded to one another.Mixture A substance whose components are mixed

together without combining chemically.Molecule A group of atoms held together by a sharing of

electrons. Atoms combine to form molecules.Antimatter A "complementary" form of matter composed

of antiparticles having the same mass as particles ofordinary matter but being opposite in charge.


Dark matter Unseen and unidentified matter that is evidentby its gravitational pull on stars in the galaxies. Alongwith dark enerl)', dark matter constitutes perhaps 90%of the stuff ofthe universe.

Suggested ReadingFeynman, R. P., R. B. Leighton, and M. Sands. The Feynman

Lectures on Physics, vol. I, chap. 1. Reading, Mass.:Addison-Wesley, 1963.

Rigden, John S. Hydrogen: The Essential Element. Cambridge,Mass.: Harvard University Press, 2002.

Suchocki, J. Conceptual Chemistry, 2nd ed., chap. 5.San Francisco: Benjamin Cummings, 2004. Containsan excellent treatment of the periodic table.

Review QuestionsThe Atomic Hypothesis

1. What causes dust particles and tiny grains of soot tomove with Brownian motion?

2. Who first explained Brownian motion and made aconvincing case for the existence of atoms?

3. According to Richard Feynman, when do atomsattract each other, and when do they repel?

Atom Characteristics4. How does the approximate number of atoms in the

air in your lungs compare with the number of breathsof air in the atmosphere of the Earth?

5. Are most of the atoms around us younger or olderthan the Sun?

Atomic Imagery6. Why can atoms not be seen with a powerful optical

microscope?

7. Why can atoms be seen with an electron beam?

8. What is the purpose of a model in science?

Atomic Structure9. How does the mass of an atomic nucleus compare

with the mass of an atom as a whole?

10. What is a nucleon?

11. How does the mass and electric charge of a protoncompare with the mass and charge of an electron?

12. Since atoms are mostly empty space, why don't wefall through a floor we stand on?

The Elements13. What is the lightest of the elements?

14. What is the most abundant element in the knownuniverse?

15. How were elements heavier than hydrogen formed?

16. Where did the heaviest elements originate?

17. What are the five most common elements in livingthings?

Periodic Table of the Elements18. What does the atomic number of an element tell you

about the element?

19. What is characteristic of the columns in the periodictable?

Isotopes20. What are isotopes?

21. Distinguish between mass number and atomic mass.

Compounds and Mixtures22. What is a compound? Give three examples.

23. What is a mixture? Give three examples.

Molecules24. How does a molecule differ from an atom?

25. Compared with the energy it takes to separate oxygenand hydrogen from water, how much energy is givenoff when they recombine? (What general physicsprinciple is illustrated here?)

Antimatter26. How do matter and antimatter differ?

27. What occurs when a particle of matter and a particleof antimatter meet?

Dark Matter28. What is the evidence that dark matter exists?

ProjectA candle will burn only if oxygen is present. Will a candleburn twice as long in an inverted liter jar as it will in aninverted half-liter jar? Try it and see.

Exercises1. How many types of atoms can you expect to find in a

pure sample of any element?

2. How many individual atoms are in a water molecule?

3. When a container of gas is heated, what happens tothe average speed of its molecules?

4. The average speed of a perfurne-vapor molecule atroom temperature may be about 300 rn/s, but you'llfind the speed at which the scent travels across theroom is much less. Why?

5. A cat strolls across your backyard. An hour later, adog with his nose to the ground follows the trail ofthe cat. Explain this occurrence from a molecularpoint of view.

6. Ifno molecules in a body could escape, would thebody have any od or?

7. Where were the atoms that make up a newborninfant "manufactured"?

8. Which of the following is not an element: hydrogen,carbon, oxygen, water?

9. Your friend says that what makes one element dis-tinct from another is the number of electrons aboutthe atomic nucleus. Do you agree wholeheartedly,partially, or not at all? Explain.

10. Can two different elements contain the same totalnumber of protons? If so, give an example.

11. What is the cause of the Brownian motion of dustparticles? Why aren't larger objects, such as base-balls, similarly affected?

12. Why is Brownian motion apparent only for micro-scopic particles?

13. Why don't equal masses of golf balls and Ping-Pongballs contain the same number of balls?

14. Why don't equal masses of carbon atoms and oxygenatoms contain the same number of particles?

15. Which contains more atoms: 1 kg of lead or 1 kg ofaluminum?

16. Which of the following are pure elements: H2, H20,He, Na, NaCl, H2S04, U?

17. How many atoms are in a molecule of ethanol,C2H60?

18. The atomic masses of two isotopes of cobalt are 59and 60. (a) What is the number of protons and neu-trons in each? (b) What is the number of orbiting elec-trons in each when the isotopes are electrically neutral?

19. A particular atom contains 29 electrons, 34 neutrons,and 29 protons. What is the atomic number ofthiselement, and what is its name?

20. Gasoline contains only hydrogen and carbon atoms,yet nitrogen oxide and nitrogen dioxide are producedwhen gasoline burns. What is the source of the nitro-gen and oxygen atoms?

21. A tree is composed mainly of carbon. Where doesthis carbon come from?

22. How do the number of protons in an atomic nucleusdictate the chemical properties of the element?

23. Which would be the more valued result: taking oneproton from each nucleus in a sample of gold oradding one proton to each gold nucleus? Explain.

24. If two protons and two neutrons are removed fromthe nucleus of an oxygen atom, what nucleus remains?


25. What element results if you add a pair of protons tothe nucleus of mercury? (See the periodic table.)

26. What element results if two protons and two neu-trons are ejected from a radium nucleus?

27. How does an ion differ from an atom?

28. To become a negative ion, does an atom lose or gainan electron?

29. To become a positive ion, does an atom lose or gainan electron?

30. Fish don't live very long in water that has been boiledand brought back to room temperature. Provide anexplanation for this fact.

31. You could swallow a capsule of germanium withoutill effects. But, if a proton were added to each ofthegermanium nuclei, you would not want to swallowthe capsule. Why? (Consult the periodic table.)

32. An ozone molecule and an oxygen molecule are bothpure oxygen. How are they different?

33. If you eat metallic sodium or inhale chlorine gas, youstand a strong chance of dying. When these two ele-ments combine, however, you can safely sprinkle theresulting compound on your popcorn for bettertaste. What is going on?

34. What results when water is chemically decomposed?

35. Helium is an inert gas, meaning that it doesn't read-ily combine with other elements. What five otherelements would you also expect to be inert gases?(See the periodic table.)

36. What element results if one of the neutrons in anitrogen nucleus is converted by radioactive decayinto a proton?

37. Which ofthe following elements would you predictto have properties most like those of silicon (Si): alu-minum (AI), phosphorus (P), or germanium (Ge)?(Consult the periodic table.)

38. Carbon, with a half-full outer shell of electrons-fourin a shell that can hold eight-readily shares itselectrons with other atoms and forms a vast numberof molecules, many of which are the organic mole-cules that form the bulk of living matter. Looking atthe periodic table, what other element do you thinkmight play a role like carbon in life forms on someother planet?

39. Which contributes more to an atom's mass-electrons or protons? Which contributes more toan atom's size?

40. A hydrogen atom and a carbon atom move at thesame speed. Which has the greater kinetic energy?

41. In a gaseous mixture of hydrogen and oxygen gas,both with the same average kinetic energy, whichmolecules move faster on average?


42. The atoms that constitute your body are mostlyempty space, and structures such as the chair you'resitting on are composed of atoms that are alsomostly empty space. So why don't you fall throughthe chair?

43. When 50 cubic centimeters (crn ") of alcohol aremixed with SO ern:' of water, the volume ofthe mix-ture is only 98 ern". Can you offer an explanation forthis?

44. (a) From an atomic point of view, why must you heata solid to melt it? (b) If you have a solid and a liquidat room temperature, what conclusion can you drawabout the relative strengths of their interatomicforces?

45. In what sense can you truthfully say that you are apart of every person in history? In what sense can yousay that you will tangibly contribute to every personon Earth who will follow?

46. What are the chances that at least one of the atomsexhaled by your very first breath will be in your nextbreath?

47. Hydrogen and oxygen always react in a 1:8 ratio bymass to form water. Early investigators thought thismeant that oxygen was eight times more massivethan hydrogen. What chemical formula did these in-vestigators assume for water?

48. When antimatter meets matter, what is produced,and how much percentage wise?

49. Somebody told your friend that, if an antimatteralien ever set foot upon the Earth, the whole worldwould explode into pure radiant energy. Your friendlooks to you for verification or refutation of thisclaim. What do you say?

SO. Make up a multiple-choice question that will testyour classmates on the distinction between any twoterms in the Summary of Terms list.

Problems1. How many grams of oxygen are there in 18 g of

water?

2. How many grams of hydrogen are there in 16 g ofmethane gas? (The chemical formula for methaneis CH4.)

3. Gas A is composed of diatomic molecules (twoatoms to a molecule) of a pure element. Gas B iscomposed of monatomic molecules (one atom to a"molecule") of another pure element. Gas A has

three times the mass of an equal volume of gas B atthe same temperature and pressure. How do theatomic masses of elements A and B compare?

4. A teaspoon of an organic oil dropped on the surfaceofa quiet pond spreads out to cover almost an acre.The oil film has a thickness equal to the size of a mol-ecule. In the lab, when you drop 0.001 milliliter(10-9 m3

) ofthe organic oil on the still surface ofwater, you find that it spreads to cover an area of1.0 m2

. If the layer is one molecule thick, what is thesize ofa single molecule?

The problems that follow require some knowledge of exponents.

5. The diameter of an atom is about 10-10 m. (a) Howmany atoms make a line a millionth of a meter(10-6 m) long? (b) How many atoms cover a squarea millionth ofa meter on a side? (c) How manyatoms fill a cube a millionth of a meter on a side?(d) If a dollar were attached to each atom, whatcould you buy with your line of atoms? With yoursquare of atoms? With your cube of atoms?

6. There are approximately 1023 H20 molecules in athimbleful of water and 1046 H20 molecules in theEarth's oceans. Suppose that Columbus threw a thim-bleful of water into the ocean and that those watermolecules have by now mixed uniformly with all thewater molecules in the oceans. Can you show that, ifyou dip a sample thimbleful of water from anywherein the ocean, you'll probably scoop up at least oneof the molecules that was in Columbus's thimble?(Hint: The ratio ofthe number of molecules in athimble to the number of molecules in the ocean willequal the ratio of the number of molecules in questionto the number ofmolecules the thimble can hold.)

7. There are approximately 1022 molecules in a singlemedium-sized breath of air and approximately 1044

molecules in the atmosphere ofthe whole world.The number 1022 squared is equal to 1044 So howmany breaths of air are there in the world's atmo-sphere? How does this number compare with thenumber of molecules in a single breath? !fall themolecules from Julius Caesar's last dying breath arenow thoroughly mixed in the atmosphere, how manyof these, on the average, do we inhale with eachsingle breath?

8. Assume that the present world population of about6 X 109 people is about 1/20 the number of peoplewho ever lived on Earth. How does the number ofpeople who ever lived compare to the number of airmolecules in a single breath?

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