31Section2.1AtomicTheoryReviewElectron(negative charge)C+Proton (positivecharge)Neutron (uncharged)FIGURE 2-2Bohr model of the atom. Electrons travel around the nucleus at incrediblespeeds, making billions of trips in a fraction of a second. The force of attraction betweenthe electrons and the protons in the nucleus keeps them in orbit.The basic structure of Figure 2-2applies to all elements,but each ele-ment has its own unique combination of electrons,protons,and neutrons.Forexample,thehydrogen atom,the simplestof all atoms,hasoneprotonand one electron, while the copper atom has 29 electrons,29protons,and 35neutrons.Silicon, which is importantbecause of its use intransistors andotherelectronicdevices,has14electrons,14protons,and14neutrons.Electrons orbit thenucleus in spherical orbits called shells,designatedbylettersK,L, M,N,and so on (Figure2-3).Only certain numbersof elec-Nucleustronscan existwithinanygivenshell.Forexample,therecanbeupto2electrons in theK shell,up to8 in theLshell,up to18 in theM shell,and upto 32 in the N shell.The number in any shell depends on the element.Forinstance, the copper atom, which has 29 electrons, has all three of its innershells completely filled but its outer shell (shell M) has only 1 electron, Fig-ure 2-4.This outermost shell is called its valence shell, and the electron in itis called its valence electron.No element can have more than eight valence electrons; when a valenceFIGURE2-3Simplified representa-shell has eight electrons, it is filled. As we shall see,the number of valencetionoftheatom.Electronstravel inspherical orbits called “shells."electrons that an element has directlyaffects its electrical properties
Section 2.1 ■ Atomic Theory Review 31 Electron (negative charge) Proton (positive charge) Neutron (uncharged) FIGURE 2–2 Bohr model of the atom. Electrons travel around the nucleus at incredible speeds, making billions of trips in a fraction of a second. The force of attraction between the electrons and the protons in the nucleus keeps them in orbit. The basic structure of Figure 2–2 applies to all elements, but each element has its own unique combination of electrons, protons, and neutrons. For example, the hydrogen atom, the simplest of all atoms, has one proton and one electron, while the copper atom has 29 electrons, 29 protons, and 35 neutrons. Silicon, which is important because of its use in transistors and other electronic devices, has 14 electrons, 14 protons, and 14 neutrons. Electrons orbit the nucleus in spherical orbits called shells, designated by letters K, L, M, N, and so on (Figure 2–3). Only certain numbers of electrons can exist within any given shell. For example, there can be up to 2 electrons in the K shell, up to 8 in the L shell, up to 18 in the M shell, and up to 32 in the N shell. The number in any shell depends on the element. For instance, the copper atom, which has 29 electrons, has all three of its inner shells completely filled but its outer shell (shell N) has only 1 electron, Figure 2–4. This outermost shell is called its valence shell, and the electron in it is called its valence electron. No element can have more than eight valence electrons; when a valence shell has eight electrons, it is filled. As we shall see, the number of valence electrons that an element has directly affects its electrical properties. Nucleus L K N M FIGURE 2–3 Simplified representation of the atom. Electrons travel in spherical orbits called “shells.”
32Chapter2VoltageandCurrentShell K (2 electrons)ValenceValence shell-electron(1 electron),OONucleus29OC.LShell L (8 electrons)L Shell M (18 electrons)FIGURE2-4Copper atom.The valence electron is loosely bound.Electrical ChargeIn the previous paragraphs, we mentioned the word“charge".However,weNWneed to look at its meaning in more detail. First, we should note that electri-cal charge is an intrinsic property of matter that manifests itself in the formofforces-electrons repel otherelectronsbutattractprotons,whileprotonsrepel each other but attract electrons. It was through studying these forcesthat scientists determined that the charge on the electron is negative whilethatontheproton ispositive.However, the way in which we use the termcharge"extends beyondthis. To illustrate, consider again the basic atom of Figure 2-2. It has equalnumbers of electrons and protons, and since their charges are equal andopposite, they cancel, leaving the atom as a whole uncharged.However, ifthe atom acquires additional electrons(leaving it withmore electrons thanprotons),we saythat it (the atom)is negatively charged; conversely,if itloses electrons and is left with fewer electrons than protons,we say that it ispositively charged. The term“charge"in this sense denotes an imbalancebetweenthenumberofelectronsandprotons present intheatom.Now move up to the macroscopic level.Here, substances in their normalstate are also generally uncharged; that is,theyhave equal numbers of elec-trons and protons.However,thisbalanceis easilydisturbed-electrons canbe stripped from their parent atoms by simple actions such as walking acrossa carpet, sliding off a chair, or spinning clothes in a dryer. (Recall "staticcling")Consider two additional examples from physics. Suppose you rub anebonite (hard rubber) rod with fur. This action causes a transfer of electronsfrom thefur to the rod.The rod therefore acquires an excess of electronsandis thus negatively charged.Similarly,when a glass rod is rubbed with silk,electrons aretransferredfrom theglass rodtothesilk,leavingtherod withadeficiency and, consequently, a positive charge. Here again, charge refers toanimbalanceofelectronsandprotons.As the above examples illustrate,"charge" can refer to the charge on anindividual electron or to the charge associated with a whole group of elec-trons. In either case, this charge is denoted by the letter Q, and its unit of mea-surement in the SI system is the coulomb.(The definition of the coulomb isconsidered shortly.)Ingeneral,the chargeQassociated with agroup ofelec-trons is equal to the product of the number of electrons times the charge oneach individual electron.Since charge manifests itself in the form offorces,charge is defined in terms of these forces. This is discussed next
Electrical Charge In the previous paragraphs, we mentioned the word “charge”. However, we need to look at its meaning in more detail. First, we should note that electrical charge is an intrinsic property of matter that manifests itself in the form of forces—electrons repel other electrons but attract protons, while protons repel each other but attract electrons. It was through studying these forces that scientists determined that the charge on the electron is negative while that on the proton is positive. However, the way in which we use the term “charge” extends beyond this. To illustrate, consider again the basic atom of Figure 2–2. It has equal numbers of electrons and protons, and since their charges are equal and opposite, they cancel, leaving the atom as a whole uncharged. However, if the atom acquires additional electrons (leaving it with more electrons than protons), we say that it (the atom) is negatively charged; conversely, if it loses electrons and is left with fewer electrons than protons, we say that it is positively charged. The term “charge” in this sense denotes an imbalance between the number of electrons and protons present in the atom. Now move up to the macroscopic level. Here, substances in their normal state are also generally uncharged; that is, they have equal numbers of electrons and protons. However, this balance is easily disturbed—electrons can be stripped from their parent atoms by simple actions such as walking across a carpet, sliding off a chair, or spinning clothes in a dryer. (Recall “static cling”.) Consider two additional examples from physics. Suppose you rub an ebonite (hard rubber) rod with fur. This action causes a transfer of electrons from the fur to the rod. The rod therefore acquires an excess of electrons and is thus negatively charged. Similarly, when a glass rod is rubbed with silk, electrons are transferred from the glass rod to the silk, leaving the rod with a deficiency and, consequently, a positive charge. Here again, charge refers to an imbalance of electrons and protons. As the above examples illustrate, “charge” can refer to the charge on an individual electron or to the charge associated with a whole group of electrons. In either case, this charge is denoted by the letter Q, and its unit of measurement in the SI system is the coulomb. (The definition of the coulomb is considered shortly.) In general, the charge Q associated with a group of electrons is equal to the product of the number of electrons times the charge on each individual electron. Since charge manifests itself in the form of forces, charge is defined in terms of these forces. This is discussed next. 32 Chapter 2 ■ Voltage and Current Valence shell (1 electron) Shell K (2 electrons) Valence electron Shell L (8 electrons) Shell M (18 electrons) Nucleus 29 FIGURE 2–4 Copper atom. The valence electron is loosely bound
33Section2.1AtomicTheoryReviewCoulomb'sLawTheforcebetween chargeswas studiedbytheFrenchscientistCharlesQ1Coulomb(1736-1806).Coulombdeterminedexperimentallythattheforcebetween two charges Q, and Q, (Figure 2-5) is directly proportional to the02product of their charges and inversely proportional to the square of the dis-(a) Like chargestancebetweenthem.Mathematically,Coulomb's law statesrepel102F= A(2-1) [newtons, N]where Q,and Qare the charges in coulombs,r is the center-to-center spac-ing between them in meters, and k = 9 × 10°. Coulomb's law applies toaggregates of charges as in Figure 2-5(a) and (b), as well as to individualelectronswithintheatomasin (c).As Coulomb's law indicates, force decreases inversely as the square of(b) Unlike chargesdistance; thus, if the distance between two charges is doubled, the forceattractdecreases to (/2)2 = /4 (i.e., one quarter) of its original value. Because ofthis relationship,electrons in outer orbits are less strongly attracted to theElectronnucleus than those in inner orbits; that is,they are less tightly bound to thenucleus than those closeby.Valenceelectrons arethe least tightly bound andOrbitwill, if they acquire sufficient energy,escapefrom their parent atomsFree Electrons(c) The force of attractionThe amount of energy required to escape depends on the number of electronskeeps electrons in orbitinthevalence shell.Ifanatomhas onlyafewvalenceelectrons,onlyasmallamountofadditional energyisneeded.Forexample,forametal likecopperFIGURE2-5Coulomblawforcesvalenceelectronscangain sufficientenergyfromheatalone(thermal energy)evenatroomtemperature,toescapefromtheirparentatomsandwanderfromatom toatomthroughout the material as depicted in Figure 2-6.(Note thatthese electrons do not leavethe substance,they simplywanderfromthevalence shell of one atom to thevalence shell of another.Thematerial there-foreremains electricallyneutral.)Suchelectrons arecalledfreeelectrons.Incopper, there are of the order of 1023 free electrons per cubic centimeter atroomtemperature.As we shall see,it is thepresence of this largenumberoffreeelectronsthatmakescoppersuchagood conductorof electriccurrent.OnFIGURE2-6Randommotionoffreethe otherhand, if thevalence shell isfull (ornearlyfull),valence electrons areelectrons in a conductor.muchmoretightlybound.Suchmaterialshavefew (if any)freeelectronslonsAsnoted earlier,whenapreviouslyneutral atomgains orloses an electron,itacquires a net electrical charge. The charged atom is referred to as an ion. Ifthe atom loses an electron, it is called a positive ion; if it gains an electron, itis called a negative ion.Conductors,Insulators,and SemiconductorsThe atomic structure of matter affects how easily charges, i.e.,electronsmove through a substance and hence how it is used electrically.Electrically,materialsareclassifiedasconductors,insulators,or semiconductors
Coulomb’s Law The force between charges was studied by the French scientist Charles Coulomb (1736–1806). Coulomb determined experimentally that the force between two charges Q1 and Q2 (Figure 2–5) is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, Coulomb’s law states F k Q r 1Q 2 2 [newtons, N] (2–1) where Q1 and Q2 are the charges in coulombs, r is the center-to-center spacing between them in meters, and k 9 109 . Coulomb’s law applies to aggregates of charges as in Figure 2–5(a) and (b), as well as to individual electrons within the atom as in (c). As Coulomb’s law indicates, force decreases inversely as the square of distance; thus, if the distance between two charges is doubled, the force decreases to (1 ⁄2) 2 1 ⁄4 (i.e., one quarter) of its original value. Because of this relationship, electrons in outer orbits are less strongly attracted to the nucleus than those in inner orbits; that is, they are less tightly bound to the nucleus than those close by. Valence electrons are the least tightly bound and will, if they acquire sufficient energy, escape from their parent atoms. Free Electrons The amount of energy required to escape depends on the number of electrons in the valence shell. If an atom has only a few valence electrons, only a small amount of additional energy is needed. For example, for a metal like copper, valence electrons can gain sufficient energy from heat alone (thermal energy), even at room temperature, to escape from their parent atoms and wander from atom to atom throughout the material as depicted in Figure 2–6. (Note that these electrons do not leave the substance, they simply wander from the valence shell of one atom to the valence shell of another. The material therefore remains electrically neutral.) Such electrons are called free electrons. In copper, there are of the order of 1023 free electrons per cubic centimeter at room temperature. As we shall see, it is the presence of this large number of free electrons that makes copper such a good conductor of electric current. On the other hand, if the valence shell is full (or nearly full), valence electrons are much more tightly bound. Such materials have few (if any) free electrons. Ions As noted earlier, when a previously neutral atom gains or loses an electron, it acquires a net electrical charge. The charged atom is referred to as an ion. If the atom loses an electron, it is called a positive ion; if it gains an electron, it is called a negative ion. Conductors, Insulators, and Semiconductors The atomic structure of matter affects how easily charges, i.e., electrons, move through a substance and hence how it is used electrically. Electrically, materials are classified as conductors, insulators, or semiconductors. Section 2.1 ■ Atomic Theory Review 33 Electron Orbit (a) Like charges repel (b) Unlike charges attract (c) The force of attraction keeps electrons in orbit Q1 F F Q2 r FIGURE 2–5 Coulomb law forces. FIGURE 2–6 Random motion of free electrons in a conductor.
34Chapter2VoltageandCurrentConductorsMaterials through which charges move easily are termed conductors. Themostfamiliarexamplesaremetals.Goodmetal conductorshavelargenum-bers of free electrons that are able to move about easily.In particular, silver,copper,gold,andaluminum areexcellent conductors.Ofthese,copperisthemost widelyused.Not only is it an excellent conductor, it is inexpensive andeasilyformedintowire,makingitsuitableforabroadspectrumofapplica-tions ranging from common house wiring to sophisticated electronic equip-ment. Aluminum, although it is only about 60% as good a conductor as cop-per, is also used, mainly in applications where light weight is important,such as in overhead power transmission lines. Silver and gold are too expen-sivefor general use.However, gold, because it oxidizes less than other mate-rials,isused in specialized applications;forexample,some critical electricalconnectors use it because it makes a more reliable connection than othermaterials.InsulatorsMaterials that do not conduct (e.g., glass, porcelain, plastic, rubber, and soon)are termed insulators.The covering on electric lamp cords, for example,is an insulator.Itis used toprevent thewires fromtouching and toprotectusfrom electric shock.Insulators do not conduct because they have full or nearly full valenceshells and thus their electrons are tightly bound.However, when highenough voltage is applied, the force is so great that electrons are literally tornfrom their parent atoms,causing the insulationto break down and conduc-tion to occur.In air,you see this as an arc orflashover.In solids, charredinsulation usually results.SemiconductorsSilicon and germanium (plus a few other materials) have half-filled valenceshells and are thus neither good conductors nor good insulators.Known assemiconductors,theyhave uniqueelectrical properties that make themimportanttotheelectronics industry.Themostimportantmaterial is siliconIt isused to maketransistors, diodes,integrated circuits,and other electronicdevices.Semiconductorshavemadepossiblepersonal computers,VCRs,portable CD players,calculators,and a host ofotherelectronic products.Youwillstudy them in great detail in your electronics courses.IN-PROCESS1. Describe the basic structure of the atom in terms of its constituent particles:LEARNINGelectrons, protons, and neutrons. Why is the nucleus positively charged? WhyCHECK1is theatomas a whole electricallyneutral?2. What are valence shells? What does the valence shell contain?3.DescribeCoulomb'slawand useittohelpexplainwhyelectrons farfromthenucleus are loosely bound.4. What are free electrons? Describe how they are created, using copper as anexample.Explain what rolethermal energy plays in theprocess.5.Briefly distinguish between a normal (i.e.,uncharged) atom, a positive ion,and a negative ion
Conductors Materials through which charges move easily are termed conductors. The most familiar examples are metals. Good metal conductors have large numbers of free electrons that are able to move about easily. In particular, silver, copper, gold, and aluminum are excellent conductors. Of these, copper is the most widely used. Not only is it an excellent conductor, it is inexpensive and easily formed into wire, making it suitable for a broad spectrum of applications ranging from common house wiring to sophisticated electronic equipment. Aluminum, although it is only about 60% as good a conductor as copper, is also used, mainly in applications where light weight is important, such as in overhead power transmission lines. Silver and gold are too expensive for general use. However, gold, because it oxidizes less than other materials, is used in specialized applications; for example, some critical electrical connectors use it because it makes a more reliable connection than other materials. Insulators Materials that do not conduct (e.g., glass, porcelain, plastic, rubber, and so on) are termed insulators. The covering on electric lamp cords, for example, is an insulator. It is used to prevent the wires from touching and to protect us from electric shock. Insulators do not conduct because they have full or nearly full valence shells and thus their electrons are tightly bound. However, when high enough voltage is applied, the force is so great that electrons are literally torn from their parent atoms, causing the insulation to break down and conduction to occur. In air, you see this as an arc or flashover. In solids, charred insulation usually results. Semiconductors Silicon and germanium (plus a few other materials) have half-filled valence shells and are thus neither good conductors nor good insulators. Known as semiconductors, they have unique electrical properties that make them important to the electronics industry. The most important material is silicon. It is used to make transistors, diodes, integrated circuits, and other electronic devices. Semiconductors have made possible personal computers, VCRs, portable CD players, calculators, and a host of other electronic products. You will study them in great detail in your electronics courses. 34 Chapter 2 ■ Voltage and Current 1. Describe the basic structure of the atom in terms of its constituent particles: electrons, protons, and neutrons. Why is the nucleus positively charged? Why is the atom as a whole electrically neutral? 2. What are valence shells? What does the valence shell contain? 3. Describe Coulomb’s law and use it to help explain why electrons far from the nucleus are loosely bound. 4. What are free electrons? Describe how they are created, using copper as an example. Explain what role thermal energy plays in the process. 5. Briefly distinguish between a normal (i.e., uncharged) atom, a positive ion, and a negative ion. IN-PROCESS LEARNING CHECK 1
35Section2.2TheUnitof Electrical Charge:TheCoulomb6. Many atoms in Figure 2-6 have lost electrons and are thus positively charged,yet the substance as a whole is uncharged.Why?(Answersareattheendof thechapter)2.2The Unit of Electrical Charge:The CoulombAs noted in the previous section,the unit of electrical charge is the coulomb(C). The coulomb is defined as the charge carried by 6.24 × 10i8 electrons.Thus, if an electrically neutral (i.e., uncharged) body has 6.24 × 1018 elec-trons removed, it will beleft witha netpositivecharge of 1 coulomb,i.e.Q=1C.Conversely,if anuncharged bodyhas6.24X 1018electrons added,it will have a net negative charge of 1 coulomb, ie., Q = -1 C. Usually,however, we are more interested in the charge moving through a wire. In thisregard, if 6.24 × 1018 electrons pass through a wire, we say that the chargethatpassedthroughthewireisIC.Wecan nowdeterminethechargeononeelectron.It is Q=1/(6.24×1018) = 1.60 × 10-19 C.EXAMPLE2-1An initiallyneutral bodyhas1.7μCof negative chargeremoved. Later, 18.7 × 1ol electrons are added. What is the body's finalcharge?Solution Initially the body is neutral,ie,Qimitia =0 C.When 1.7μC ofelectrons isremoved,thebodyis leftwitha positivecharge of 1.7μC.Now,18.7×10electrons areadded back.This isequivalent to1coulomb18.7×10l*electronsX=0.3μC6.24×1018electronsof negativecharge.The final chargeon thebodyisthereforeQ,=1.7μC0.3 μC = +1.4 μC.Togetan ideaof howlargea coulomb is,we can useCoulomb's law.Iftwochargesof 1coulombeachwereplacedonemeterapart,theforcebetweenthemwouldbe(1 C)(1 C)F=(9×10°)=9 × 10°N,ie.,about1 million tons!(1 m)21. Positive charges Q, =2 μC and Q,=12 μC are separated center to center byPRACTICEPROBLEMS110 mm.Compute the force between them.Is it attractiveor repulsive?2.Two equal charges are separated by 1 cm.If the force of repulsion betweenthem is 9.7X 10-2N,what is their charge?What may the charges be,bothpositive, bothnegative,or one positive and one negative?3. After 10.61 X 1013 electrons are added to a metal plate, it has a negativecharge of 3μC.What was its initial charge in coulombs?Answers:1.2160N,repulsive;2. 32.8nC,both(+)orboth (-);3. 14 μC (+)
6. Many atoms in Figure 2–6 have lost electrons and are thus positively charged, yet the substance as a whole is uncharged. Why? (Answers are at the end of the chapter.) 2.2 The Unit of Electrical Charge: The Coulomb As noted in the previous section, the unit of electrical charge is the coulomb (C). The coulomb is defined as the charge carried by 6.24 1018 electrons. Thus, if an electrically neutral (i.e., uncharged) body has 6.24 1018 electrons removed, it will be left with a net positive charge of 1 coulomb, i.e., Q 1 C. Conversely, if an uncharged body has 6.24 1018 electrons added, it will have a net negative charge of 1 coulomb, i.e., Q 1 C. Usually, however, we are more interested in the charge moving through a wire. In this regard, if 6.24 1018 electrons pass through a wire, we say that the charge that passed through the wire is 1 C. We can now determine the charge on one electron. It is Qe 1/(6.24 1018) 1.60 1019 C. Section 2.2 ■ The Unit of Electrical Charge: The Coulomb 35 EXAMPLE 2–1 An initially neutral body has 1.7 mC of negative charge removed. Later, 18.7 1011 electrons are added. What is the body’s final charge? Solution Initially the body is neutral, i.e., Qinitial 0 C. When 1.7 mC of electrons is removed, the body is left with a positive charge of 1.7 mC. Now, 18.7 1011 electrons are added back. This is equivalent to 18.7 1011 electrons 0.3 mC 1 coulomb 6.24 1018 electrons of negative charge. The final charge on the body is therefore Qf 1.7 mC 0.3 mC 1.4 mC. To get an idea of how large a coulomb is, we can use Coulomb’s law. If two charges of 1 coulomb each were placed one meter apart, the force between them would be F (9 109 ) (1 ( C 1 ) m (1 ) 2 C) 9 109 N, i.e., about 1 million tons! PRACTICE PROBLEMS 1 1. Positive charges Q1 2 mC and Q2 12 mC are separated center to center by 10 mm. Compute the force between them. Is it attractive or repulsive? 2. Two equal charges are separated by 1 cm. If the force of repulsion between them is 9.7 102 N, what is their charge? What may the charges be, both positive, both negative, or one positive and one negative? 3. After 10.61 1013 electrons are added to a metal plate, it has a negative charge of 3 mC. What was its initial charge in coulombs? Answers: 1. 2160 N, repulsive; 2. 32.8 nC, both () or both (); 3. 14 mC ()