what are atoms? what are their properties? · pdf file5.1 the atom has a structure elements...

What are atoms?What are their properties?Why are atoms important in chemistry?

What would happen if you took a piece of aluminum foiland tore it in half again and again? Then, when that pieceof aluminum became too small to hold, imagine that youcould keep cutting it in half again and again. Keepthinking of smaller and smaller pieces of aluminum.Could you keep cutting forever, or do you reach a limitthat is the smallest possible piece of aluminum? Theanswer to this question has far-reaching consequences.Either there is a smallest piece, which means thealuminum is made from tiny particles (atoms), or thealuminum is one smooth substance that can be cut in halfforever.

Over time, starting with the ancient Greeks, scientistsstruggled with this question, each building upon thework of others. Today we know that everything is madefrom atoms: There is a smallest piece of aluminum. Ourmodern view of the atom is the culmination of 2,500years of scientific thinking and experimentation. Ourunderstanding of the properties of the atom has led tomajor chemical discoveries that have improved our livesfrom medicine to energy.

132 A NATURAL APPROACH TO CHEMISTRY

Light, color, atoms, and electronsWhen you pass high-voltage electricity through a gas, it can light up. This is how aneon sign works. In the lab we use glass tubes filled with gas in a high-voltagepower supply.

Different elements give off noticeably different colors of light. The most interestingthing happens when you observe this light through a special lens called a diffractiongrating. You may know that “pure white” light is really an equal mixture of allcolors together. The light from a gas discharge tube is also a mixture of colors. Adiffraction grating separates the light into its component colors.

Do you notice how nitrogen and helium are different? Eachelement has its own unique line spectrum. In fact, the uniquepatterns of spectral lines are often called the “fingerprints” ofthe elements.

How are these line spectra different?Do the line spectra remind you of a barcode used at the checkout counter of a store? It is a good analogy!Line spectra contain information about the structure of each element just as barcodes contain informationabout product numbers. Compare the line spectra of helium, nitrogen, and oxygen. What differences do yousee? What similarities do you see?

• There are areas of the rainbow in which no color is emitted (black).• Nitrogen and oxygen have more lines than helium.• All three spectra are noticeably different.• Some of the lines are thicker than others.

The number of spectral lines is related to the number of electrons in each atom. Helium has two electronsand nitrogen has seven electrons. Could it be that nitrogen has more spectral lines because it has moreelectrons? In this chapter we will learn how to categorize atoms according to their electron structures in atable called the periodic table, which is the major reference document of chemistry.

To the eye, the lightfrom nitrogen gas lookspurple and heliumlooks pink. However,through the diffractiongrating, the purple andpink are not so simple!Instead of a singlecolor, the diffractiongrating shows us thatthe light is really manycolors. Each colorshows up as a verticalline in what chemistscall a line spectrum.

A NATURAL APPROACH TO CHEMISTRY 133

Section 5.1 The Atom Has a Structure

5.1 The Atom Has a Structure

Elements and compounds

In the previous chapters, we learned that ordinary matter is made of atoms of the 92naturally occurring elements. These atoms usually form compounds, such as salt (NaCl)or sodium bicarbonate (NaHCO3). Compounds explain how we get millions of types ofmatter from 92 elements, but 92 is still a relatively large number. Are the 92 differenttypes of atoms (i.e., the elements) made of even smaller things? The answer is yes.

Atoms are made from smaller particles called protons, neutrons, and electrons

How can three particles explain the universe?

This is an extraordinary fact! How can the incredible variety of matter in the universecome from only three particles? Think about making all the words in the dictionary withonly three letters or all the paintings in the world with only three colors. It may seemincredible, but it is true nonetheless. The atoms of all 92 elements (and more) are createdfrom three basic particles: electrons, protons, and neutrons. The beautiful variety ofnature arises from how the three particles come together in rich and complex ways.

Each elementis a uniquetype of atom

Before we delve into the depths of the atom, let’s review what we know. There are 92naturally occurring elements, plus 20 to 30 other elements that have been created in alaboratory. Each element represents a unique type of atom. For example, all oxygenatoms are similar to each other but different from carbon atoms or hydrogen atoms.


The beginning of atomic theory

Democritus (460–370 BC): the beginning of atomic theory

Democritus (460—370 BC) was an ancient Greek philosopher who proposed the ideathat you can’t divide something in half forever. He argued that eventually you must reachthe smallest indivisible part. He called this smallest piece of matter an atom. Democrituscorrectly deduced the existence of atoms, but he could go no further in discovering any oftheir properties. For the next 2,000 years atomism was an interesting idea, but there wasno good scientific evidence to support its truth or falsehood.

John Dalton (1768–1828) - first “modern” atomic theory

In 1808, John Dalton, an English school teacher, put together many ideas in his fourpostulates of the atomic theory. Dalton’s four postulates were a brilliant synthesis basedon what little evidence there was at that time. They remain true today.

1. All elements are made of tiny indivisible particles called atoms.2. All atoms of the same element are alike but different from atoms of every other ele-

ment.3. Chemical reactions rearrange atoms but do not create, destroy, or convert atoms from

one element to another.4. Compounds are made from combining atoms in simple whole number ratios.

Cathode rays In the mid 1800s it was discovered that highvoltage made a “glow” in a sealed glass tubefrom which most of the air had been pumpedout. In 1870, William Crookes invented a tubein which virtually all of the gas was removed.Now, the glow inside the tube disappeared, butthe glass at one end of the tube was glowing.Some kind of invisible ray was being emittedfrom the cathode end of the tube and striking the glass at the other end. These rays werecalled cathode rays, and a great debate occurred over their nature. Were they anotherkind of light? Were they a stream of particles?

J.J. Thomson (1856–1940) - the discovery of the electron

In 1897, J. J. Thomson wasfinally able to resolve thedebate. His experiments showedthat cathode rays were deflectedtoward a positively chargedplate and away from a nega-tively charged plate. Thomson deduced that cathode rays must benegative. He also found that they could be deflected by magnetic

fields. No ordinary ray of light would behave this way. He tried using different metals orstarting with the tube filled with different gases. None of those factors mattered. Healways got the same cathode rays, and they always were deflected in the same way.

High voltage electricity creating cathode rays inside a Crookes tube

Cathode rays deflected away from negative plate and toward positive plate

Thomson



The discovery of the nucleus

Cathode rays are electrons

Thomson’s discovery stunned the scientific world. Cathode rays were made of a streamof particles 2,000 times lighter than the lightest known atom (H)! How could there be aparticle smaller than an atom? Because Thomson always got the same cathode raysregardless of which metals he used for the electrodes in his Crookes tube, he named thenew particle an electron, and he proposed that electrons were inside all atoms.

The atommust have a structure inside

If electrons were inside atoms, then atoms could not be the most elementary particles ofmatter. Furthermore, electrons were negative and atoms were neutral, so there had to alsobe something positive inside atoms to cancel out the charge of the electrons. The searchwas on to discover the structure inside the atom.

Ernest Rutherford: the gold foil experiment

In 1910, Ernest Rutherford designed and carried out the crucialexperiments that provided the answer. Marie and Pierre Curie haddiscovered that uranium was radioactive and released energetic alphaparticles at high velocity. Alpha particles were positively charged andhad a mass about 8,000 times that of an electron. Rutherford devisedan experiment to shoot alpha particles through a thin gold foil andobserve what happened as they collided with gold atoms. He expectedmost of the alpha particles to be deflected a little as they crashedthrough the gold atoms.

Rutherford’s discovery of the atomic nucleus

Rutherford’s results were completely unexpected. Although most of the alpha particleswent straight through the gold foil with no deflection at all and a few were deflectedslightly off their original path, about 1 of every 20,000 reversed direction, bouncing backfrom the foil! Rutherford determined that atoms have nearly all their mass concentratedin a very tiny, very dense, positively charged nucleus. This was his reasoning:

1. The deflected alpha particles were repelled by something with a similar charge, so the nucleus must be positively charged.

2. Very few alpha particles were deflected, so it must be rare for one to come close to a nucleus. This meant the nucleus had to be tiny, about 1/10,000 the diameter of the atom.

3. The alpha particles were travelling at such high velocity that only something with significant mass could deflect them.

Rutherford


The interior of an atom

The big ideas The three most important ideas in this chapter are these:

1. Atoms are made of neutrons, protons, and electrons. The number of protons and elec-trons is always equal.

2. The number of protons determines the element. All atoms of hydrogen have one pro-ton, all atoms of helium have two, lithium has three, and so on.

3. Most of the properties of atoms are determined by their electrons. Atoms interact with each other via their electrons.

Of course, there are many interesting details! Electrons are quirky particles and theybehave in very strange ways, but that is what makes chemistry so interesting.

The nucleus Neutrons and protons make up the nucleus.The nucleus is at the center of the atom.There are no electrons in the nucleus, onlyprotons and neutrons. The nucleus isextremely small, even compared to an atom. Ifthe atom were the size of your classroom, thenucleus would be the size of a single grain ofsand in the center of the room!

Mass of protons, neutrons, and electrons

Look at the masses of the three particles. The masses are very small. The mass of a singleelectron in kilograms has 30 zeros between the decimal point and the first nonzero digit.More important are the relative masses. The proton and neutron are much more massivethan the electron. The protons and neutrons have essentially all the mass of the atom.

Mass and the nucleus

Most of an atom’s mass is concentrated in the nucleus.The number of electrons and protons is the same, butelectrons contribute very little mass. For example, acarbon atom has six protons, six electrons and sixneutrons. Of the carbon atom’s mass, 99.97% is in thenucleus and only 0.03% is electrons.

Particle Mass (kg) Charge (C) Relative mass Relative chargeProton 1.673×10–27 +1.602×10–19 1,835 +1

Neutron 1.675×10–27 0 1,837 0

Electron 9.109×10–31 1.602×10–19 1 –1

nucleus: the tiny dense core of an atom that contains all the protons and neutrons, measuring about 1/10,000 the diameter of the atom.



Atomic number and atomic mass

The atomic number

The atomic number of each element is the numberof protons in its nucleus. All atoms of the sameelement have the same number of protons in thenucleus. For example, every atom of helium has twoprotons in its nucleus. Every atom of carbon has sixprotons in its nucleus. The periodic table arranges theelements in increasing atomic number. Atomicnumber one is hydrogen with one proton. Atomicnumber 92 is uranium with 92 protons.

Neutrons act like glue

All protons have positive electric charge. That means they repel each other. So how doesthe nucleus stay together? The answer is neutrons. Think about neutrons as “glue”particles that help the nucleus stay together. Every element heavier than helium has atleast as many neutrons as protons in its nucleus.

Isotopes All atoms of the same element have the same number of protons in the nucleus. However,they do not necessarily have the same number of neutrons. Three different isotopes ofcarbon are found on Earth. Isotopes are atoms of the same element that have differentnumbers of neutrons in the nucleus.

The mass number

The most common isotope of carbon is carbon-12, written as 12C. A nucleus of 12Ccontains six protons (making it carbon) and six neutrons. The superscript “12” before thesymbol “C” tells you the mass number of the nucleus. The mass number is the totalnumber of protons plus neutrons. The two other isotopes of carbon are carbon-13 (13C)and carbon-14 (14C). These isotopes are carbon because they have six protons in thenucleus, but 13C has seven neutrons and 14C has eight neutrons.

Atomic mass unit (amu)

Because the mass of a proton is tiny by normal standards, scientists use atomic massunits (amu). One amu is 1.661 × 10–27 kg, or slightly less than the mass of a proton.

atomic number: the number of protons in the nucleus, unique to each element.isotopes: atoms or elements that have the same number of protons in the nucleus, but different number of neutrons.mass number: the total number of protons and neutrons in a nucleus.atomic mass unit (amu): a mass unit equivalent to 1.661 × 10–27 kg.


Average atomic mass

The average atomic mass may not be a whole number

Let’s examine the element lithium. Lithium hastwo isotopes that are found in nature. Lithium-6has three protons and three neutrons. Lithium-7 hasthree protons and four neutrons. The periodic tablelists the atomic mass of lithium as 6.94. How is thatpossible? Do lithium atoms have 0.94 neutrons?

Elements in nature contain a mix of isotopes

It is not possible to split a proton or a neutron in ordinary matter. Lithium atoms haveeither six or seven whole neutrons. The reason the atomic mass is 6.94 is that, on average,94 out of 100 atoms of lithium are 7Li and 6 out of 100 are 6Li. The average atomic massis 6.94 because of the mixture of isotopes. No lithium atom has a mass of 6.94 amu.

Radioactivity Not all isotopes exist in nature. For example, suppose scientists create a nucleus withthree protons and five neutrons. This would have an atomic number of 3, making itlithium. The mass number would be 8. Lithium-8 is unstable and quickly decays into twoatoms of helium instead! When an atomic nucleus decays or gives off energy, the processis called radioactivity. It means that the nucleus undergoes a spontaneous change calleddecay, often turning one element into a different element.

How many neutrons are in the nucleus of neon-21 (21Ne)?

Asked: Number of neutronsGiven: Mass number (21) and element (neon)Relationships: The mass number is the number of protons plus neutrons,

number of protons = atomic numberSolve: From the periodic table we find the atomic number of neon is 10. So,

there are 10 protons in the nucleus: 21 – 10 = 11 neutrons.Answer: There are 11 neutrons in a nucleus of neon-21.

radioactivity: a process by which the nucleus of an atom spontaneously changes itself by emitting particles or energy.decay: the process during which a nucleus undergoes spontaneous change.



The electron cloud

The electron cloud

Compared to protons and neutrons, electrons are muchlighter. This has the effect of making the electron muchfaster, with a much wider range than either protons orneutrons. Because electrons are so fast and light,scientists call the region outside the nucleus theelectron cloud. Think about a swarm of bees buzzing ina cloud around a beehive. It is not easy to preciselylocate any one bee, but you can easily see that, onaverage, the bees are confined to a cloud of a certainsize around the hive. On average, electrons areconfined to a similar cloud around the nucleus.

Drawing electrons

Electron orbit

Electrons are not really particles in the sameway a dust particle is a particle. Althoughelectrons have a definite mass, they do nothave a definite size. The matter in an electronspreads out over a relatively large volumewithin an atom. In early drawings of atoms,scientists represented electrons like tinyplanets in an orbit around the nucleus of theatom. Today we draw atoms with a tiny hardnucleus surrounded by a wispy electron cloud.

Electrons determine the size of atoms

The size of an atom is really the size of its electroncloud. When we talk about the size of atoms, whatwe really mean is how close atoms get to eachother. Unless the atoms are chemically bondedtogether, the electron cloud of one atom does notnormally overlap the electron cloud of another.

Except for mass, virtually every property of atoms is determined by electrons, including

size and chemical bondingThe electrons determine virtually everything about how one atom interacts with another. Forthis reason, most of chemistry will be concerned with electrons and their unusual organizationwithin atoms. The nucleus is buried deep inside, contributing mass, but not much else, as faras chemistry is concerned.

orbit: the imaginary path of an electron around the nucleus of an atom.


Electric charge

Comparing charge and mass

Charge is a difficult idea to grasp, so let’s start bycomparing mass and gravity with electric charge. Mass isa fundamental property of matter. Any two objects thathave mass attract each other through a force calledgravity. Mass is the property that determines an object’sresponse to the force of gravity. The more mass there is,the stronger the force of gravity.

Positive and negative

Electric charge is another fundamental property of matter. However, unlike mass, thereare two kinds of charge: positive and negative. Like gravity, there is a force that acts onelectric charge called the electromagnetic force. Unlike gravity, however, theelectromagnetic force can attract or repel.

The chargesof the three particles

The electric charge on a proton is what scientists define to be positive. The charge on anelectron is defined as negative. Neutrons are neutral and have zero charge. That meansthat two protons repel each other, and so do two electrons. Protons and electrons attracteach other. Neutrons feel no electromagnetic forces from either protons or electrons.

A complete atom has a charge of zero because the charge of the proton is exactly equal but opposite to the charge of the electron

Complete atoms have zero netcharge

The charges on the electron and theproton are exactly equal and opposite. Ifyou put a proton and an electron together,the total effective charge is zero. For thisreason, the charge on a complete atom isalways zero because a complete atomcontains the same number of protons aselectrons. For example, the positivecharge from six protons in a carbonnucleus is exactly cancelled by the sixelectrons in the electron cloud.



Forces in the atom

Why an atom stays together

The attractive electromagnetic force between protons in the nucleus and electrons is whatholds an atom together. The electromagnetic force between electrons is also what createschemical bonds between atoms, as we shall see. In fact, almost all of the chemistry welearn is driven by the electromagnetic force.

Forces in the nucleus

There is a force in the nucleus that is evenstronger than the electromagnetic force, butit does not affect chemistry directly. It iscalled the strong nuclear force and itattracts protons to protons, neutrons toneutrons, and protons and neutrons to eachother. If there are enough neutrons in thenucleus, the attractive strong nuclear forcecan overcome the repulsive electromagneticforce between protons. This is the reasonmost elements have equal numbers orslightly more neutrons than protons in thenucleus.

Electrons are both attracted and repelled

Let’s think about the electron cloud in anatom like carbon. Electrons have energy, sothey cannot just “fall in” to the nucleus, butthey must be constantly in motion. Each ofcarbon’s six electrons is attracted to thenucleus, but each is also repelled by all theother electrons! The combination of energywith attraction and repulsion is one reasonbehind the peculiar behavior of electrons inan atom.

Electrons are responsible for the chemicalbonds between atoms. When a watermolecule forms, the oxygen atom shareselectrons with two hydrogen atoms. Eachshared electron is a chemical bond. Themolecule has its bent shape because eight ofthe ten electrons in a water molecule repeleach other in four pairs. Two pairs areshared with hydrogen atoms and two pairsare not shared.


Ions

All matter contains charge

The fact that everything is made from atoms andatoms are made from electrically charged particlesmeans that everything, including you, is just a bigbundle of electric charge. This fact becomes moreobvious in the winter when you scuff your feetacross a carpet and get shocked by touching ametal doorknob. Static electricity and lightning areexamples of how we are made of, and aresurrounded by, electrically charged particles.

Neutral matter has equal positive and negative charge

If the numbers of electrons and protons in an atom are notequal, the atom will have an overall charge. Let’s considersodium as an example. Sodium has an atomic number of11, so that means all sodium atoms have 11 protons. Eachproton has a positive charge of +1. If these same atomshave 11 electrons, each with a –1 charge, then the –11charge from the electrons exactly cancels out the +11charge from the protons, and the atom is neutral.

Ions However, if there were only 10 electrons,then the total charge from the electronswould be –10 while the charge from theprotons would be +11. That means there isone proton that is not being cancelled out byan electron. This gives the atom an overallcharge of +1. Charged atoms are calledions. Whenever the numbers of protons andelectrons are not equal, an overall positiveor negative charge will occur, and an ionwill be formed. Ions can be single atoms orsmall molecules with an overall charge.

Ionic compounds

Positive and negative ions attract each other, just as protons and electrons do. The ioniccompounds we introduced in Chapter 4 are examples. Sodium ions (Na+) have one lesselectron and are attracted to chloride ions (Cl–), which have one extra electron. Theoverall compound, sodium chloride (NaCl), is electrically neutral because there are equalnumbers of sodium and chloride ions.

ion: an atom or a small molecule with an overall positive or negative charge as a result of an imbalance of protons and electrons.


Section 5.2 The Quantum Atom

5.2 The Quantum Atom

Why is it that the noble gases do not react?

Elements just before or just after the noble gases are very reactive

How do the chemical properties of the elements arisefrom the structure of atoms? We have seen thatelectrons are the components in atoms that are nearthe “surface” and interact with other atoms. Why is itthat the noble gases (helium, neon, argon, andkrypton) do not react with other elements or amongthemselves? Note that these elements have 2, 10, 18,and 36 electrons, respectively. The elementshydrogen, fluorine, chlorine and bromine have 1, 9,17, and 35 electrons. They have one fewer electronthan their respective noble gas group. These elementstend to form negative ions; they accept electronsfrom other atoms.The elements with one more electron than the noble gas group are lithium, sodium,potassium and rubidium with 3, 11, 19 and 37 electrons, respectively. These elementstend to form positive ions; they donate electrons to other atoms.

Some findings of quantum theory

The basic understanding of the electronic structure in the atom started around 1920 witha new theory called quantum theory. Championed by Niels Bohr, quantum theoryprovided a completely new way to look at things on the scale of atoms. Quantum theoryfinally gave us a way to understand why and how the elements make the bonds that theydo. Quantum theory makes the following statements about matter and energy on the scaleof atoms, and particularly about electrons in atoms.

1. On the scale of atoms, a particle of matter such as an electron is not solid but is smeared out into a wave over a region of space.

2. When electrons are confined in an atom, their wave properties force them into a pattern that minimizes their energy.

3. Each unique “place” in the pattern is called a quantum state, and each can hold one single electron.

4. Electrons are always found to be in one quantum state or another and are not found between states.

5. No two electrons can be in the same quantum state at the same time.Don’t worry if these statements seem quite strange. Quantum theory is accurate, but notintuitive.

quantum theory: a theory of physics and chemistry that accurately describes the universe on very small scales, such as the inside of an atom.quantum state: a specific combination of values of variables such as energy and position that is allowed by quantum theory.


Waves and particles

Our intuition is often wrong in the quantum world

The most basic idea of quantum theory is that our intuitive notion of a particle cannot beapplied to the tiny world of the atom. To most of us, a particle is a tiny speck of matterthat has a definite size, mass, and position, like a tiny ball. A ball-like particle can beeither here or there, but it cannot be in two places at the same time. The quantum theorytells us this intuition is wrong when things are as small as an atom. In the quantumworld, a particle is not like a tiny ball at all. Instead, the mass, size, and even the locationis spread out into a wave.

Heisenberg’s uncertainty principle

The fact that particles are “smeared out” into waves can be explained by Heisenberg’suncertainty principle. In 1927 Werner Heisenberg proposed that it is not possible to knowcertain parameters of a particle, such as its position and velocity, accurately at quantumscales. The better you determine one by experiment, the more you perturb the other andthereby increase its uncertainty. The quantum world is a world of statistics andprobability, instead of exact certainty.

Frequency The oscillations of a wave have frequency and wavelength. The frequency is thenumber of times per unit of time that any point on the wave goes back and forth. A lightwave has a very high frequency, 1012 times per second or more! A water wave mightoscillate one or two times per second.

Wavelength When a wave moves through space, the successive peaks (or valleys) are separated by adistance called the wavelength. The wavelength is the same from one peak to the next.Like the frequency, it is a characteristic of a particular wave. The wavelength of light isvery small, only 10–8 m or so.

frequency: the rate at which an oscillation repeats; one hertz (Hz) is a frequency of one oscillation per second.wavelength: the distance (separation) between any two successive peaks (or valleys) of a wave.



Planck’s constant

Wave energy increases with frequency

Waves in water carry energy, as anyone who has seen waves froma storm crashing on a beach can vividly remember. The same istrue of light waves and particle waves, such as electrons. Youmight intuitively think that the faster something oscillates, themore energy it has. You would be right! The energy carried by awave is proportional to how fast it oscillates, or its frequency. Highfrequency means faster oscillation and more energy.

A photon isthe smallest quantity of light energy

Before quantum theory, the ideas of “particle” and “wave” were distinct. Light was awave, and an electron was a particle. Today we know that an electron is also a matterwave, and light waves come in tiny bundles of energy called photons. A photon is like aparticle because it has a definite energy and moves with a certain speed and direction.However, a photon has no mass, just pure energy. You don’t see light as a stream ofphotons for the same reason you don’t see individual atoms. A small 3 W flashlight beamemits 1019 photons per second!

Planck’s constant

The scale at which the granular nature of matter and energy becomes evident isdetermined by Planck’s constant. Planck’s constant has the symbol h and a value of6.626 × 10–34 joule-seconds (J·s). The energy and wavelength of both electrons andphotons are calculated from Planck’s constant.

The connection among atoms, light, and electrons

In his 1924 Ph.D. thesis, Louis de Broglie proposed that thewavelength of a particle is inversely proportional to the square rootof its mass and energy. The de Broglie wavelength of an electron isvery small. If the electron had the same energy as green light(3.82 × 10–19 J), its de Broglie wavelength would be 7.94 × 10–10 m.This is the same size as an atom, which explains the closeconnection between light and the behavior of electrons in atoms.

Planck’s constant (h): the scale of energy at which quantum effects must be considered, equal to 6.626 × 10–34 joule-seconds (J·s).photon: the smallest possible quantity (or quanta) of light.


Electrons in the quantum atom

The wavelengthof an electron in an atom

Most of the properties of the elements are caused by what happens to the wavelength ofan electron when it is bound up inside an atom. To help understand this, consider a ballbouncing around in a box. At any instant, there is only one ball at one particular place inthe box. When the ball hits the walls of the box, it bounces off it.

Waves versus balls

A wave reflects when it hits a wall, just like a ball in a box.However, waves are very different from balls. A ball is only inone place, but a wave can occupy all the space in the box. So canits reflection! One ball plus one ball is two balls, but one waveplus another wave can add up to zero. If one wave is “up” whenthe other is “down,” then they cancel each other out! Whenaveraged over time, the only waves that survive in a box are theones whose wavelength fits the size of the box. All the othersinterfere with their own reflections and average out to zero.

The atom isa “box” for electrons

Now replace the box with an atom and let the wave be an electron. Electrons are “boxed”inside atoms by the attraction from the positive nucleus. The walls of the box are soft toan electron because the electron never hits a hard surface, but it needs more and moreenergy to get farther away from the nucleus. Given a limited amount of energy, anelectron is confined to be within a certain distance from the nucleus. This confinementacts just like a soft-walled box.

The key idea of the quantum atom

Here is the main idea of the quantum atom. Thewavelength of the electron must be a multiple of the“size” of the atom. If it is not, then the electron wavecancels with its own reflections over time. Thediagram shows three “allowed” electron waves andtwo that are “not allowed.” To be stable inside anatom, an electron must have one of the allowedwavelengths that exactly fits the size of the atom. Theelements differ because the “size” of the atomdepends on the strength of the attraction from thenucleus, which depends on the atomic number.



Quantum states

Consequences of restricting the electron wavelength

What does it mean to say that an electron can only have awavelength that matches the size of an atom? The mostimportant consequence comes from the relationshipbetween wavelength and energy. If you know the energyof an electron, then you also know its wavelength.Conversely, if the wavelength of the electron is fixed,you also fix its energy as well. Electrons inside atomscan only have specific energies that match thewavelengths they are allowed to have.

Quantization The restriction of energies to specific discrete values is called quantization. This is one ofthe most important consequences of quantum theory. An electron trapped inside an atomcannot have any value of energy. The electron can have only those specific values ofenergy that correspond to the allowed wavelengths.

We now have a way to define a quantum state. A quantum state is one of the allowedwavelengths in an atom. Because of the connection between wavelength and energy, eachquantum state has a specific energy. This is the key idea of the quantum atom.

Real quantum states

The details of real quantum states inside an atom are complicated for these reasons:

• Atoms are three dimensional, not simple boxes.• Besides charge and mass, electrons have a purely quantum property called spin.• Electrons repel each other, so in atoms with more than one electron, the size and

shape of the box depend on both the nucleus and the other electrons in the atom.Multiple states can havethe same wavelength

For example, because the electron wave can bealigned along any of the three coordinate axes(x, y, or z), there are three different quantumstates that have the same wavelength, andtherefore the same energy. This is a three-dimensional effect.


Orbitals

The origin ofs, p, d, and f

The allowed quantum states are grouped in a peculiar, yet historically interesting way.When scientists first started using spectroscopy to explore the elements, they noticed thatthe spectra of the metals (Li, Na, and K) had four characteristic groups of spectral lines.They named the groups sharp, principal, diffuse and fundamental, but they had no realidea what caused the differences among the four groups. Today we know each group isassociated with a quantum state in a particular shape. In deference to history, the fourtypes of shapes are known by the letters s, p, d, and f.

Orbitals Orbitals are groups of quantum states that have similar shapes in space. To understandwhat these shapes look like, consider the single electron in a hydrogen atom. With noother electrons to repel it, this electron has an equal chance to be at any angular positionaround the nucleus. Hydrogen’s lone electron is in an s orbital. The s orbitals arespherically symmetric, and each one can hold two electrons.

Why some orbitals have strange shapes

Carbon has six electrons. With this many electrons, repulsion between electrons changesthe shape of the electron cloud. The p orbitals are shaped like dumbbells along each ofthe three coordinate axes. The three p orbitals can hold six electrons all together. Thed orbitals are more elaborately shaped and can hold a total of 10 electrons.

Orbitals create 3-dimensional molecules

The three-dimensional shape of the orbitals represents the realthree-dimensional shape of the electron cloud. The orbital shapesare directly responsible for the three-dimensional shapes ofmolecules. Methane (CH4) is tetrahedral because of the way thes and p orbitals form chemical bonds between carbon andhydrogen.

orbital: group of quantum states that have similar spatial shapes, labeled s, p, d, and f.



Energy levels

The quantum states are grouped into energy levels

Since several quantum states have the same energy, the states are grouped into energylevels. The diagram below shows how the quantum states are arranged in the first fiveenergy levels. There is an even number of quantum states because they occur in spin-up/spin-down pairs. The first energy level has two quantum states. The second and thirdenergy levels have eight quantum states. The fourth and fifth levels have 18 states each.

The Pauli exclusion principle

Electrons confined to the same atom obey aquantum rule called the Pauli exclusionprinciple. The Pauli exclusion principlestates that two electrons in the same atom maynever be in the same quantum state. Electrons fillquantum states from the lowest energy to thehighest. Lithium, with three electrons, cannothave all three in the first energy level becausethere are only two quantum states (spin-up andspin-down). The third electron has to go into thesecond energy level.

Hund’s rule Electron-electron repulsion forces affect the wayelectrons are distributed in orbitals. According toHund’s rule, electrons with the same-spin mustoccupy a different equal-energy orbital, beforeadditional electrons with opposite spins canoccupy the same orbitals. Here we see how theelectrons of N and O are distributed in orbitals.

energy level: the set of quantum states for an electron in an atom that have approximately the same energy.Pauli exclusion principle: principle that states that two electrons in the same atom may never be in the same quantum state.


The periodic table

Rows correspond to energy levels

The rows of the periodic table correspond directly to the energy levels for electrons. Thefirst energy level has two quantum states. Atomic hydrogen (H) has one electron, andatomic helium (He) has two electrons. These two elements are the only ones in the toprow of the periodic table because there are only two quantum states in the first energylevel.

The second row The next element, lithium (Li), has three electrons. Lithium begins the second rowbecause the third electron goes into the second energy level. The second energy level haseight quantum states and there are eight elements in the second row of the periodic table,ending with neon. Neon (Ne) has 10 electrons, which exactly fill all the quantum states inthe first and second levels.

The third row Sodium (Na) has 11 electrons, and it starts the third row because the 11th electron goesinto the third energy level. The third row ends with the noble gas, argon, which has 18electrons. Eighteen electrons completely fill the third energy level.

Energy levels correspondto bonding properties

If you compare the energy level diagram with the periodic table, you find that all thenoble gases have completely filled energy levels. All the elements that tend to formnegative ions (F, Cl, and Br) have one electron less than a full energy level. All the alkalimetals that tend to form positive ions (Li, Na, and K) have one electron more than a fullenergy level. This is a strong clue that the energy levels are crucial to the chemicalproperties of the elements.


Section 5.3 Electron Configurations

5.3 Electron Configurations

Organizationof the energy levels

All the elements share a common organization for how the quantum states are groupedinto energy levels. Because each element has a different nuclear charge, the actualenergies of each level are unique to each element. However, the overall pattern is thesame for all the elements and determines the organization of the periodic table.

Electrons fill up lowest energy orbitals first

Every proton in the nucleus of an atom will attract one electron. Each of those electronsmust exist in one of the quantum states in the diagram. Like a ball rolling downhill, eachelectron settles into the lowest unoccupied quantum state.

Electrons settle into the lowest unfilled quantum states

How the first few elements fill the energy levels

Beginning the second row

Ending the second row

The first (and lowest) energy level holds twoelectrons. Hydrogen has one electron, so itbelongs in the first energy level. Helium hastwo electrons, and they completely fill thefirst energy level.

Lithium has three electrons. Two of lithium’selectrons go into the first energy level. ThePauli exclusion principle forbids lithium’sthird electron from occupying either of theoccupied states on the first energy level. Thethird one has to go into the second energylevel.

Fluorine has nine electrons. They fill all butthe last quantum state on the second energylevel. Neon has 10 electrons, which com-pletely fill the first and second energy levels.


Electron configuration

The principal quantum number

The principal quantum number (or quantum number) defines certain properties ofthe quantum states. The diagram below shows the first four quantum numbers and thequantum states associated with each. The quantum states are further divided into theorbital types s, p, d, and f. The key at the right shows how the quantum states fall intoenergy levels. Note that the energy level is not the same as the quantum number!

Electron configuration

The electron configuration is a quick way to describe howelectrons in an atom are distributed among the orbitals. Thefirst number is the principal quantum number. The letteridentifies the orbital, and the superscript is the number ofelectrons in that orbital. Quantum number 1 contains only asingle s orbital which can hold two electrons. Quantumnumber 2 can hold up to two “s” electrons and six “p”electrons for a total of eight.

ElementNumber of electrons

Electron Configuration

Description of electron locations

Hydrogen 1 1s1 One electron at the 1s level.

Helium 2 1s2 Two electrons at the 1s level

Lithium 3 1s22s1 Two electrons at the 1s level and one electron at the 2s level

Beryllium 4 1s22s2 Two electrons at the 1s level and two electrons at the 2s level

Boron 5 1s22s22p1 Two electrons at the 1s level, two electrons at the 2s level, and one electron at the 2p level

electron configuration: a description of which orbitals contain electrons for a particular atom.principal quantum number: a number that specifies the quantum state and is related to the energy level of the electron.


Section 5.3 Electron Configurations

Finding the electron configuration

Here is the complete list of orbitals and the filling order for all of the currently discoveredelements:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p

The table is arranged according to the structureof the atoms and orbitals

This order tells a chemist exactly how the electrons are structured in an atom. It mayseem somewhat random, but using the periodic table as your guide, there is a way toremember the orbital filling order. This is because the structure of the periodic table isactually based on the structure of the atoms. By understanding the connection betweenthe orbitals and the periodic table, we learn about both the structure of the atom and itsconnection to chemical and physical properties. First, let’s look at how the periodic tablewould be laid out if we didn’t place the rare earth elements below the table.

Finding the electron configurations

To find an electron configuration, start with the number of electrons (the atomic number).Use the chart below to find the largest number of electrons that is still less than theconfiguration you are trying to find. Subtract that number from the number of electronsyou have, and the remainder is the superscript on the unfilled orbital. For noble gases, thechart will give you the exact electron configuration.

Write the electron configuration for silicon (atomic number 14).

Solve: There are 14 electrons. The chart shows that 12 electrons fill up to 3s2. Therefore, the remaining 2 electrons must go into a 3p orbital, making the electron configuration 1s22s22p63s23p2.


5.4 Light and Spectroscopy

Visible light Light is a form of electromagnetic energy that comesmainly from electrons in atoms. If you are reading thisbook under a fluorescent light, then you are seeing theenergy levels in the atom right now! In fact, we “see”when the light that enters our eyes is absorbed byelectrons in molecules at the back of our eyes. Whenthese molecules absorb light, the cells that contain themsend electrical signals to your brain and you “see.”

The spectrum of visible light

Energy and color

The different colors of light come from the energies of different photons. Red is thelowest energy photon that humans can see. The highest visible energy is violet. All thecolors between red and violet form the visible spectrum. A spectrum is a representationof the different energies present in light. Since energy depends on frequency andwavelength, the colors of light also depend on frequency and wavelength. The spectrumoften specifies wavelength on the x axis. One nanometer (nm) is 10–9 meters.

White light isa mixture of colors

The white light from a lamp isactually a mixture of many differentcolors and energies. White lightfrom the Sun is not truly white. Youcan split white light into a spectrumof colors by using a prism. A devicethat splits light into its spectrum iscalled a spectrometer. Theseinstruments provided one of the firstand best clues to unraveling themystery of the structure of the atom.

spectrum: a representation of a sample of light into its component energies or colors, in the form of a picture, a graph, or a table of data.spectrometer: a device that measures the spectrum of light.


Section 5.4 Light and Spectroscopy

The electromagnetic spectrum

There are many types of light

The light that we can see (visible light) is really only a small subset of a much largerspectrum of electromagnetic energy. The full electromagnetic spectrum includeslower energies (radio and microwaves) and higher energies (ultraviolet and x rays).Many scientists use the word “light” loosely to mean the entire electromagneticspectrum. This includes radio waves, microwaves, x rays, and even gamma rays.

• Radio waves• Microwaves• Infrared• Visible light• Ultraviolet• X-rays• Gamma rays

Energy and frequency

The energy of a photon depends on its frequency andwavelength according to the Planck relationship E =hν. The Greek symbol ν (pronounced “nu”) is used torepresent frequency in hertz (Hz). Because photonenergies tend to be small (10–18 J), scientists define theelectron volt (eV) as 1.602 × 10–19 J. Electron voltsare also about the size of energy changes in an atom.For example, the difference between the second andthird energy levels in hydrogen is 1.89 eV.

electromagnetic spectrum: the complete range of electromagnetic waves, including visible light.electron volt: a unit of energy equal to 1.602 × 10–19 J.


The speed of light

The speed ofa wave is its frequency times its wavelength

Photons and other wavesmove one wavelength witheach oscillation. Since thenumber of oscillations persecond is the frequency, andone wavelength is the distancethe wave advances, the speedof a wave is its frequencymultiplied by its wavelength.This relation-ship allows us tocalculate the frequency if weknow the wavelength and viceversa.

The speedof light

Photons move very fast at a speed of 3 × 108 m/s, or 186,000 miles per second! This isthe ultimate speed limit in our universe. Nothing can move faster than light. The speedof light is so important it has its own special symbol, a lowercase letter c.

c is a constant The speed of light in a vacuum is a constant. That means it is the same for all frequenciesand wavelengths. In chemistry, the speed of light is very useful for converting betweenfrequency and wavelength. If you know the wavelength of light, then you can calculateits frequency from the speed of light.

The wavelength of red laser light is 652 nm. What is its frequency? How muchenergy does a photon of this light have in electron volts?

Asked: Frequency and energy

Given: λ = 652 × 10 –9 mRelationships: c = λν, E = hν

Solve:

Answer: Since 1 Hz=1/s, the frequency is 4.6 × 1014 Hz and the energy is 1.9 eV.

c λν therefore ν cλ--- 3 108m/s×

652 10 9– m×-------------------------------- 4.6 1014

×s

-------------------------- 4.6 1014/s×== = = =

E hν 4.136 10 15–× eV s⋅( ) 4.6 1014

× /s( ) 1.9 eV= = =

speed of light (c): a constant speed at which all electromagnetic radiation travels through a vacuum, including visible light; the speed of light in a vacuum is 299,792,458 m/s or approximately 3 × 108 m/s.


Section 5.4 Light and Spectroscopy

Interactions between light and matter

Experimenting with excited electrons

Light from an incandescent light bulb shows a continuous spectrum of colors. This tellsus that the atoms that produced the light can absorb and release any amount of energy.Light from pure hydrogen does something completely different. Instead of a continuousrainbow, we see a few very specific colors and nothing but darkness in between.

The spectrum tells us there are energy levels

The spectrum from hydrogen tells us that hydrogen atoms can only absorb and emit lightof very specific energies. It is like viewing the inner workings of a hydrogen atom. Thefact that the spectrum shows discrete colors tells us that electrons in the hydrogen atomcan only have discrete energies.

Interactions between matter and light

As a wave of light moves through matter, any electrons inside atoms oscillate in responseto the wave. On the atomic scale, two kinds of interactions can occur: absorption ornothing. If a photon is absorbed, another photon with the same energy may be reemitted.The scattering of light is actually a two-step process of absorption and reemission.

Electrons can get excited

Which of the two interactions occurs depends on how the energy of the photon comparesto the energy levels in the atom. If the photon energy matches a difference in the atom’senergy levels, the photon may be absorbed. If not, the photon typically passes rightthrough. If a photon passes through, we say that atom is transparent to that light.


Spectroscopy

Different elementshave different energy levels

Quantum theory tells us that any electron confined to a small space, like an atom, results inenergy levels. The specific energy levels depend on the strength of the force between thenucleus and the electrons. This depends on the number of protons in the nucleus, and onthe number of other electrons in the atom that might be shielding the attractive force fromthe nucleus. For this reason, the energy levels are different and unique for each element.

Each element has unique energy levels

Every element and compound has a unique spectrum

If the energy levels of electrons aredifferent for different elements, then thelight emitted from each element mustalso be unique. In fact, each elementemits a characteristic spectrum. Chem-ists refer to the emission spectrum asthe fingerprint of an element. Chemistrylaboratories identify elements andcompounds by their spectra.

Emission and absorption spectra

Atoms both emit and absorb light at the energiescorresponding to their energy levels. If white light ispassed through a sample of matter, some light will beabsorbed by the atoms in the sample. Not all light willbe absorbed. Only colors corresponding to specificenergy levels are strongly absorbed, resulting in darklines in a continuous spectrum. This is called anabsorption spectrum. Can you see the similaritiesbetween the absorption spectrum and emissionspectrum?

Spectroscopy Using spectra to analyze substances is called spectroscopy. Spectroscopy can tell youwhat elements produced the light being observed. Spectroscopy is a tool to find out whatdistant stars are made of, identifying unknown compounds at a crime scene, and evendiscovering forgeries. Right now, satellites are searching for water on Mars andastronomers are studying the composition of distant stars and galaxies by usingspectroscopy. Even the makeup of our own atmosphere and global scale environmentalresearch is done via satellites using spectroscopy.

spectroscopy: the science of analyzing matter using electromagnetic emission or absorption spectra.


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