CHM 1020--Chemistry for Liberal Studies--Fall 2000

Chapter 3  Atomic Structure 

Dalton postulated an atom that was a “hard structureless sphere”, something that was not divisible into something simpler.  He held to this notion even in spite of later evidence that suggested some elements were made of diatomic molecules.  Common gaseous elements such as oxygen, nitrogen, hydrogen, chlorine, are actually O2, N2, H2, and Cl2, for example.  He refused to believe that.

But other evidence was accumulating in the early part of the 19th century that indicated there must be some sub-structure to atoms.  One was in the discovery of electricity, and the observations that passing electric currents through substances could cause chemical change.  A few weeks after the Italian scientist Volta discovered the battery, Nicholson and Carlisle, carried out the decomposition of water to hydrogen and oxygen by passing an electric current through it.  This was in 1800, three years before Dalton stated his atomic theory.  The British chemist Humphry Davy and his student Michael Faraday proceeded to experiment with electric current, discovering a number of new elements.  Passing an electric current through molten salts, such as potassium hydroxide and sodium hydroxide, produced the highly reactive metals potassium and sodium.  This process of splitting compounds into elements with an electric current was known as electrolysis. (Figure 3.3)

Faraday postulated that the current was carried in the molten salts by charged atoms which later were called ions.  In an electrolytic cell, the positive electrode is called the anode, and the ions attracted to it are called anions.  Anions therefore carry a negative charge.  The negative electrode is called a cathode, and the ions attracted to it are called cations.  Cations therefore carry a positive charge.  By measuring the mass of an element produced by a given amount of current, one can get a mass to charge ratio that was proportional to the known relative atomic weights measured by other means. 

Towards the end of the 19th century, experiments with higher voltage electrical sources established that electrical current could actually flow in a vacuum, provided sufficient gas was removed from the vacuum tube.  It was established using barriers in the tube that something was flowing from the negative electrode (the cathode) to the positive electrode.  (Figure 3.4) This something was called a cathode ray, and experiments designed to study the nature of the cathode ray by the English physicist Joseph Thomson established the nature of the particles in this “ray”.  (See Figure 3.5).  They are negatively charged, and by measuring the extent of their deflection in a magnetic field it could be determined that mass to charge ratio was much smaller (about 1/2000) than that of the lightest then known substance, hydrogen.  This observation strongly suggested one was dealing with a particle much smaller than an atom.  The particles in the cathode ray later were named electrons.

 A slight variation on the cathode ray experiments by a German scientist named Eugen Goldstein, in which he used cathodes with perforations, and detected positive ions that were streaming toward the cathode but passing through the perforations.  (See Figure 3.6).  These ions had mass to charge ratios equivalent to the relative masses of the elements in the tube.  Another strange observation was made here, however.  When neon atoms were in the discharge tube, there were three types of particles, with relative mass to charge ratios of 20, 21,and 22.  If these ions were charged neon atoms, this meant that atoms of a single element were not all identical in mass (one of Dalton’s tenets which had to be modified).  We now call atoms of the same element with different masses isotopes, and we will see shortly an explanation for their existence. 

Therefore atoms are not indivisible.  They can be broken down into a small negatively charged particle, an electron, and a positive ion.  Thus another of Dalton’s tenets had to be modified. 

One can deduce a great deal from dealing with ratios, such as the ratios of reacting substances in a chemical reaction or the mass to charge ratios in the various electrical experiments.  A clever experiment just after the turn of the century provided us with a measure of the size of the charge on the electron, allowing us to actually calculate the size of its mass and therefore the mass of various ions.  This is the oil drop experiment of Robert Millikan.  (See Figure 3.7).  Tiny oil droplets are sprayed into a chamber and aquire a negative charge of static electricity.  The mass of an individual particle can be measured by the rate at which it settles in the chamber by the pull of gravity.  A positively charged plate placed at the top of the chamber can attract the droplets upward, opposing the pull of gravity.  The voltage required to just arrest the fall of the particle will give the mass to charge ratio of the particle, and combining this value with the mass determined by the rate of fall allows the calculation of the charge.  The charges so measured were all multiples of a single value, which we now know represents the charge on the electron, and which we represent simply as –1. 

 (We might think of this discovery as sort of an atomic theory for electrical charge.  The atomic theory says that matter comes in discrete units called atoms.  This observation tells us that there is a “smallest unit” of electrical charge—the size of the charge on the electron).

 With this discovery of the electron, Thomson developed a revised model of the atom, a model in which electrons were stuck in the atom like raisins in a plum pudding, and his model was called the pudding model.


Other observations around the turn of the century produced other problems with Dalton’s theory. 

 The first Nobel prize in physics was awarded in 1901 to the German scientist named Wilhelm Roentgen.  While studying the effect of cathode rays on substances, he discovered a new kind of ray, called an x-ray, which could travel through walls, and which when passing through his hand onto a film could produce an image of the bones in his hand.  This discovery caused quite a public stir.  The discovery of rays that could penetrate clothing raised great privacy issues.  It was know that the rays could not pass through heavy metals such as lead, and lead lined underwear became a popular item.

 Interestingly, the discovery of x-rays, and experiments designed to study this phenomenon, lead to an even more interesting discovery.  It was know that some chemicals when exposed to strong sunlight would produce a fluorescence, a glow of a different wavelength of light.  You have probably all seen examples of this when certain minerals are exposed to ultraviolet light (“black light”).  A Frenchman, Henri Becquerel, was studying this phenomenon to see if x-rays could be produced by fluorescence.  He would expose minerals to sunlight while the mineral was placed on an envelope containing photographic film.  If x-rays were produced, they should produce an image of the mineral on the film.

 It was a cloudy day in Paris one day, and Becquerel put aside his minerals and x-ray film in the drawer without carrying out the experiment.  For some reason, he later developed the film, and found the image of the mineral exposed on the film!.  Something was being emitted by the mineral (a compound of uranium) that passed through the envelope and exposed the film.  Further studies showed this to be a characteristic of uranium, and the phenomenon became known as radioactivity, the spontaneous emission of radiation from certain unstable elements.

 Becquerel shared the 1906 Nobel prize in physics with Marie and Pierre Curie, who following up on Becquerel’s discovery were able to isolate other radioactive elements radium and polonium.  After her husband's death in a traffic accident, Marie Curie continued her work with radioactive elements, and she won the 1911 Nobel prize in chemistry, the first person for 50 years to win two prizes. 

 Ultimately, three types of radioactivity were characterized. 










0 (1/1837)




 The charge and charge to mass ratio could be determined by experiments with electrical plates and photographic film, as in Figure 3.9.  The particles causing exposure of X-ray film in Becquerel’s experiments were the alpha particles.

 Ernest Rutherford, a New Zealander who worked in Cambridge, England, used these particles to study the nature of matter.  He devised a way to create a beam of alpha particles from a sample of radioactive mineral, and he and his students proceeded to study how bombarding various types of matter with these “rays” affected the matter.  One of his more famous experiments was that of bombarding thin gold foil with the alpha particles.  (See Figure 3.10)

Most of the particles went through the gold foil.  This was remarkable at first glance, because gold was known to consist of atoms with a relative mass of 197, and in the solid the atoms were presumably touching one another.  So shooting alpha particles, mass 4, at the gold atoms is a bit like shooting marbles at a wall made of bowling balls.

 The second astonishing thing, though, was that some of the particles actually did bounce back, and some were deflected at various angles.  This is known as Rutherford’s alpha particle scattering experiment.

Rutherford deduced that for most of the particles to pass through the gold atoms, most of the gold atoms must be made of empty space.  But for some to be deflected, the mass of the gold must be contained in a very small region at the center of the atom called the nucleus.  (See Figure 3.11) While an atom has a size of about 10-10 m, the diameter of the nucleus is about 10‑14 m, about 1/10,000 the size.  If the atom is the size of Campbell Stadium, the nucleus is about the size of the coin tossed at the beginning of a football game.

 For the nucleus to repel the positively charged alpha particle, it must be positively charged.  According to Rutherford, then, the space around the nucleus must be taken up by the very light, negatively charged, electrons.  The characteristic thing about the atom of an element was therefore not its atomic mass, but its nuclear charge, also called its atomic number.  Rutherford visualized these electrons spinning around the nucleus much as planets spin around the sun, hence his model of the atom was called the “planetary model”.   


The smallest nucleus was that of hydrogen, with a mass of 1 and a charge of plus 1.  Therefore, the hydrogen atom consisted this nucleus and one electron surrounding it.  The nucleus of the hydrogen atom is called a proton.

Discovery of another elementary particle by Chadwick, one of Rutherford’s students, allows us to develop a rather simple model for the atom.  Chadwick discovered the neutron, which has a mass of 1, equivalent to the proton, but lacks an electrical charge.

 The alpha particle, then, would be composed of two protons, imparting the 2 positive charges and 2 mass units, and 2 neutrons, adding 2 mass units for a total of 4.  If the alpha particle picks up in addition two electrons, it becomes a helium atom. 

Therefore, according to Rutherford, the nucleus of atoms contain protons and neutrons.  The protons give a positive charge to the nucleus, and the number of protons determines the atomic number of the element, which is the important variable to its identity.  The neutral atom contains enough electrons around the nucleus to balance the charge.  An ion is created when an electron is taken away (forming a positive ion) or is added (forming a negative ion).  Isotopes are explained by atoms that have the same number of protons, and hence the same atomic number, but different numbers of neutrons, and therefore different masses.

 We can easily summarize this atomic structure in the symbolism we use for the elements as follows:

                   A       q


                   Z       n


          A = mass number = n + p
          Z = atomic number = p = e
          q = charge = p-e
          n = number of atoms in unit

The mass number is the atomic mass rounded to the nearest whole number.  If you examine atomic weights, you will find some that are very near whole numbers, some that are not.  One reason for deviation from whole numbers is the the fact that the atomic weights are averages for a mixture of isotopes.  A given isotope will have a mass near a whole number but will deviate by a small amount for a reason we will see in the next chapter.

 Fill in the following table to see how one describes a given atom or ion in terms of this sub-atomic particle model: 

Atom or ion

# of protons

# of neutrons

# of electrons


























The next step in our model development comes from studies of the way that light interacts with atoms.

If we put compounds in flames, they produce colors which are characteristic of the elements in the compounds. 

Demo with flame tests

 See figures 3.13 and 3.17.

 If the light from these flames is passed through a prism that separates the light into its component wavelengths, we see characteristic line spectra illustrated in Figure 3.17.  Niels Bohr used these line spectra, and the wavelength of the various lines, as experimental evidence to support a slightly revised planetary model.

 To understand Bohr’s argument, we need to diverge a little bit and talk about light as a form of energy called electromagnetic radiation.  Unfortunately, your textbook does not take any space to this topic. 

As light passes through space it disturbs the electrical and magnetic fields of space.  This disturbance gives it the property of a wave, just as the surface of a lake is disturbed.

Wavelength x frequency = velocity,       or ln=c

C is the velocity of light, which in a vacuum is 3.00 x 108 ms-1.

Visible light spans from l of 400 nm to 700 nm.

Spectrum of rainbow:  ROY G. BIV (700nm®400nm)

 Slightly longer wavelengths are the infrared;  slightly shorter is the ultraviolet.

 Known spectrum extends from l of 10-14 m to 104 m as follows:

Cosmic rays—gamma rays—X-rays—UV—visible—infrared—microwaves—TV—radio.  . 

Frequencies vary from 1022 Hertz to 104 Hertz.  (AM radio frequencies are in kilohertz; FM frequencies are in megahertz) 

Do some conversions:   

Wavelength of WFSQ signal (88.9 MHz) 

 Frequency of blue light at 680 nm. 


Quantum theory:  sort of an atomic theory for energy.  Idea that energy comes in definite packages called quanta, and that atoms exist only in discrete energy states.  A quantum of electromagnetic radiation is considered to be a particle called a photon.

 Particle-wave duality seems to our senses to be a contradiction in terms.  Yet not only does electromagnetic radiation seem to behave that way, matter at the very tiny level of electrons and below also behaves that way.   

Through a combination of experiments by Max Planck and Albert Einstein, we can put a quantitative figure on this particle, and relate the particle and energy properties of light.  The basic relationship is:

                    E = hn   (or the counterpart  E = hc/l).

 h = Planck’s constant, which has the value 6.63 x 10-34 Js

 When you consider the energy required to do something to a molecule, we can show that microwave and infrared radiation only have enough energy to enhance the motions (vibrations) of molecules.  Infrared radiation is radiant heat, and associated with motions in molecules.  When one gets to ultraviolet light, then the energy per quantum begins to be enough to lead to breakage of chemical bonds in molecules.  That is why from UV to cosmic radiation, the photons are considered hazardous.

 You can explore these relationships further at this web site.

With this understanding of the nature of light, let us return to Bohr’s model of the hydrogen atom.  Most of his quantitative work was with the simplest atom, hydrogen.  He suggested that in the planetary model of hydrogen, in which an electron circled the nucleus in an orbit, there were only certain discrete orbits allowed, and each had a particular energy.  (The further the electron from the nucleus, the higher its energy, because it takes work to pull the negatively charged electron from the positively charged nucleus).  (This was a break from classical physics, which had shown that a moving charge radiates energy, and if the electron behaved that way it would lose energy and collapse into the nucleus).

The allowed orbits constituted energy levels.  When hydrogen is put in a flame, all the atoms are excited, and electrons are promoted to higher energy levels.  They don’t remain there for long, but fall back to the lower levels, ultimately coming to the lowest, most stable level, called the ground state.  As the electrons drop from a high to a lower energy level, they give off a particle of electromagnetic radiation with the energy corresponding to the difference in energy levels in the atom.  Therefore by calculating the energies of the photons in the line spectrum, Bohr could calculate the energy differences in the levels of the hydrogen atom, and develop a picture of these allowed energy levels for the electron in hydrogen.

 Bohr used classical mechanics to calculate the kinetic and potential energy an electron would have in a certain set of defined orbits.  He had to assume that some orbits are stable, and could have only certain definite energy values defined by the relationship: 

                   E = -2.18 x 10-18J x 1/n2,  where n =1, 2, 3, 4, 5, etc.

 When an electron drops from energy level 2 (-2.18 x 10-18J/4) to energy level 1 (-2.18 x 10-18J/1), the difference in energy is released as a quantum of light with the energy E2 – E1, which determined its frequency and wavelength. 

The wavelengths of light emitted by excited hydrogen, in both the ultraviolet, the visible, and the infrared regions of the spectrum, corresponded with very high precision and accuracy (five to six significant figures) to those calculated by Bohr. 

In spite of this almost perfect fit between theory and experiment, there were some serious shortcomings of Bohr's theory:

1.  There was no rationale for why the particular orbits he chose should be stable, while others wouldn't be.
2.  The orbit of one electron would be flat.  The hydrogen atom is spherical.
3.  The calculations didn't work for other atoms.  Nor could some additional lines seen when hydrogen is placed in a magnetic field be explained.

Last lecture we described Bohr's model for the hydrogen atom in which the electron was assumed to be traveling around the nucleus in a circular orbit.  Only certain orbits were allowed, and Bohr could calculate the kinetic and potential energy of the electron in these specific orbits using classical laws of physics with the known mass and charge of the electron.  The energies of the orbits so calculated were precisely (to 5 significant figures) those that would produce the emission spectrum of hydrogen, where each line in the spectrum represents a quantum of energy emitted as the electron falls from a higher energy orbit to a lower energy one.

We also pointed out there were problems with the Bohr model: 

1.  There was no rationale for why the particular orbits he chose should be stable, while others wouldn't be.
2.  The orbit of one electron would be flat.  The hydrogen atom is spherical.
3.  The calculations didn't work for other atoms.  Nor could some additional lines seen when hydrogen is placed in a magnetic field be explained.

Nevertheless, using Bohr's notion of discrete stable orbits, scientists began to recognize from studies in other elements that electrons seemed to be found in discrete energy levels called shells, which correspond roughly to Bohr's orbits in relative energies.  Furthermore, the number of electrons that could be in a particular shell seemed to be related to the level of the shell by the formula 2n2, where n is the shell level.  Thus shell n = 1 could have only 2 electrons, n = 2 could have 8 electrons, n = 3 could have 18 electrons, etc.  And these simple numerical relationships began to reflect the periodicity of the periodic chart.

Bohr's model, along with the work of Planck and Einstein, had provided two intellectual breakthroughs.  First, the idea that energy comes in discrete packets.  This is sort of an "atomic theory for energy".  These packets are called "quanta" or "photons".  The second was the notion that classical laws of physics did not necessarily hold at the atomic scale.  For some reason, electrons could move in certain stable paths without emitting radiation.

Further advancement required another intellectual breakthrough.  And there are many names associated with it.  Central to it was a suggestion by a French physicist Louis de Broglie, that just as light has a dual nature—wave and particle—matter also has a dual nature and has wave properties.  But the wave properties are recognizable for very small particles of matter such as the electron.  Just as a violin string vibrates with a one-dimensional standing wave pattern, an electron constrained to a small space must exist in standing wave patterns, except that the wave patterns are three-dimensional instead of one-dimensional.  The "wavelength" of a vibrating string is some integral multiple of the length of the string, because the ends are tied down and don't vibrate.

(l= 2L/n, where L = length of string, n = 1, 2, 3, etc).


Three dimensional waves are not so easily visualized, but they can be described by mathematical equations.  The stable "orbits" are explained in terms of stable standing wave patterns, and the equations describing each pattern is therefore referred to as an "orbital". 

These equations, developed in different forms by Erwin Schrodinger and Paul Dirac, could be used to calculate the energy the electron would have in any particular stable standing wave, but could not trace a "path" for the electron.  In fact, another scientist at the time, Werner Heisenberg, recognized that it should be impossible to trace an exact path for a particle as small as an electron, because any attempt to measure that path would disturb it.  This principle is known as the "Uncertainty Principle":  it is not possible to describe exactly both the energy and position of an electron.  The more accurately the position is known, the more uncertain will be the position.

 So what we are left with is a "probable" distribution of the electron, sort of a time average snapshot, as if you left a camera shutter open and photographed a bee as it flits around a flower collecting the pollen.  Such probability distributions, we sometimes call them "electron clouds" give us the only physical picture we can use in thinking about the properties of electrons.

From the mathematical equations it turns out that there are several distinct classes of orbitals, each with a characteristic shape.  There are four classes that concern us, and they are called s, p, d, and f, respectively. 

The orbitals are organized in shells, corresponding roughly to the electron shells of the Bohr model, and in the hydrogen atom the energy of each shell is the same as that calculated by Bohr assuming the electrons traveled in circular orbits.  But in this picture, the shells have subshells, consisting of the different orbital types. 

There are rules as to the number of subshells in each shell.  Each shell can have n2 subshells.  Therefore there is one in the first shell, four in the second shell, nine in the third shell, and sixteen in the fourth shell.  The pattern is summarized in the following table. 

Shell (n)

# of orbitals

Orbital types














Your textbook describes the shapes of the simplest orbitals.  The s orbital is spherical in shape, while the p orbital is shaped a bit like a dumbbell.  (See Figure 3.21)  In case you are interested, I have links to some web sites that give you much more graphical detail to help visualize these orbital shapes.  Note that some orbitals have nodes, or positions in space where the electron does not reside.  These nodes in a three dimensional wave are like the points in a violin string that do not vibrate. 

Each orbital has a distinct name.  The 1s, 2s, 3s, 4s, etc orbitals are all spherical.  They differ in their energy, and their average distance from the nucleus.  The 2p, 3p, 4p, etc orbitals also differ in energy and average distance from the nucleus.  But within a shell, the orbitals have the same energy but differ in their orientation in space.  So we have 2px, 2py, and 2pz orbitals, referring to a coordinate reference frame.

 In the hydrogen atom, the "ground state" has one electron in the lowest energy orbital, the 1s orbital.  Excitation leads to promotion of this electron to a higher orbital.  Putting hydrogen in a magnetic field causes the energies of the orbitals to vary slightly according to their orientation, which explains the additional spectral lines found under these conditions.

 What about the rest of the elements?  Our model expands this picture with two additional assumptions referred to as principles.  The Aufbau Principle (building up) stipulates that the orbital states of other elements are the same as those for hydrogen, though the energies will be different reflecting the different sized charges on the nucleus and the presence of additional electrons around the nucleus.  As one adds additional electrons, one simply adds them into the "available" orbital with lowest energy.  But what about availability?  The second principle, called the Exclusion Principle (stated by Wolfgang Pauli) limits each orbital to only two electrons. 

(Why two electrons, and not one or three?  Electrons have a property called "spin".  Imagine a tiny top spinning.  It can spin clockwise or counter-clockwise.  The electron can have a "+" spin or a "-" spin.  Electrons like to form pairs, with one spinning in each direction.  So electrons can "pair up" in an orbital provided they have opposite spins.)

One more point to be made.  As the nuclear charge increases and electrons are added, the energy levels of the shells change.  The first shell gets lower in energy, for example, because of the increased attraction to the nucleus.  But the relative energies of the subshells also changes.  In any given shell, the s orbitals have slightly lower energies than the p orbitals, which have lower energies than the d orbitals, etc.  This differentiation is a result of the different shapes of the orbitals, and therefore different ways they are affected by nuclear charge.  The energies of the shells actually begin to overlap, so that 3d orbitals are more energetic than 4s orbitals, 4d than 5s, etc. 

 As we fill in this order, we begin to see the periodic repetition in electron configuration that is evident in the periodic repetition of chemical properties indicated by the periodic chart.  Consider the following energy level diagram.


The table below illustrates the order with which electrons are added to the orbital diagram above. 





H = 1s
He = 1s2
Li = 1s22s
Be = 1s22s2
B = 1s22s22p
C = 1s22s22p2
N = 1s22s22p3
O = 1s22s22p4
F = 1s22s22p5
Ne = 1s22s22p6
Na = 1s22s22p63s
Mg = 1s22s22p63s2
Al = 1s22s22p63s23p
Si = 1s22s22p63s23p2
P = 1s22s22p63s23p3
S = 1s22s22p63s23p4
Cl = 1s22s22p63s23p5
Ar = 1s22s22p63s23p6
K = 1s22s22p63s23p64s
Ca = 1s22s22p63s23p64s2

 So we can correlate the orbital filling with the periodicity of the periodic chart.  Elements that line up under one another in groups we say belong to the same family with very similar chemical properties.  They also have similar electron configurations in the outer shell of electrons. 

In Chapter 5 we will have a more detailed discussion of the properties of these various families, and the relationship of the electronic structure to those properties.  

We will skip Chapter 4, but you may be interested in reading it on your own.

Return to Dr. Light's Class Index Page     
 Comments or questions, mail to:
© 2000 Florida State University