AP Chemistry - Atomic Structure and Periodicity
Electromagnetic Radiation
The picture of the atom that we have so far is that of a small dense nucleus containing protons and neutrons surrounded by electrons in the space around the nucleus. Although the nucleus determines the mass of the atom and also the number of electrons needed to give the atom a neutral charge, the nucleus does not play a role in chemical reactions.   When two or more atoms join together to form a compound the two nuclei stay relatively far apart.  Only the electrons in the outermost area of the atom come in close contact.  The chemical properties of an element are therefore determined by the electrons.  How the electrons are distributed is called the atoms's electronic configuration.   The clues that we have about how the electrons are arranged comes from a study of light emitted when the atoms are excited or energized. We must therefore learn a little about light itself.

Two forms of electromagnetic radiation that you have encountered are heat and visible light. These are not the only forms however and in chemistry we deal with the whole range of energies called the electromagnetic spectrum of which heat and light are only mere portions.

     Electromagnetic energy is energy carried through space or matter by means of waves. These waves are very much like the waves in water.  However what oscillates up and down in water waves is a physical substance called H2O.  What oscillates up and down in electromagnetic radiation is energy.  Each oscillation is called one cycle.  That is the wave going from peak to peak or trough to trough.  A successive series of these oscillations is called electromagnetic radiation or more popularly a light wave.  The number of cycles per second that pass or hit you are called the lights frequency.

      Frequency is identified by the Greek letter "v" pronounced "new".   Frequency can be used to describe other events. For example you go to school 5 days a week or you pay your cable TV bill once per month. Frequency describes how often an event occurs.  In the metric system, the unit of time is the second, so frequency is given as the unit "per second" which is 1/second or 1 second-1.

                                                            1 Hz = 1 s-1
 

Waves crashing on a beach may have a frequency of 1 Hz or 1 wave per second.  Paying your bills would have a frequency of  1 payment/month.
      The spaces between light waves are even.  The distance between peaks is called the wavelength and is symbolized by the Greek letter "  " which is pronounced "lambda". Wavelength is a distance and so the unit of measurement for wavelength is the meter.

If we multiply the wavelength by the frequency we get the velocity or speed of the light waves.
The speed of light is a constant known to be 3.0 x 108 m/s or 3.0 x 108 m.s-1.

Because the speed of light is an important physical constant it is designated by the sysmbol "c".

                                               c = 3.00 x 108 m.s-1

The speed of light =  the distance between each wave    X    the frequency of the waves.

                                                          OR

                                                c =  lambda  X  v


What does this concept mean?  Let's use a store analogy.  You are sent to the store with a fixed amount of cash, "c". You can buy 5 small cans for this amount or 2 large cans for the same amount.*

                      ie.   cash  =  number of cans  X  size of can

                            cash =  5small     OR          cash =  2   X    large


Do you see the implications here. Since we have a fixed constant, if the number of cans is a large number then the size must be correspondingly small. If the number of cans is a small number then the size of the cans must be correspondingly large.

*  For the sake of the economists we will assume that the amount of food in 5 small cans equals the amount of food in the 2 large cans and so there is no point in arguing about the economics of buying large versus small. For the sake of any environmentalists who worry so much about the amount of metal in 5 cans versus two that will eventually get sent to a landfill let me say that this was just an example question meant to illustrate a principle.


When it comes to light waves this means that if the wavelength is large, then the frequency must be small. If the wavelength is small then the frequency must be large.

                                        c = lambda X v   or          c =lambda v
Go to the Electromagnetism Frequency, Wavelength & Speed of Light Worksheet

 


Electromagnetic radiation comes in a large range of frequencies and wavelengths. The range is referred to as "the electromagnetic spectrum".  To give a few examples:  in the range of 104 to 1012 Hz the electromagnetic spectrum has a portion called radio waves. From 1012 to 1014 is the range called infrared.  From 1017 to 1019 we have what are called the X-rays.  Microwaves are part of the radio wave portion in the shorter wavelength portion of the radio waves.

Infrared radiation consists of the range of frequencies that can make molecules of most substances vibrate internally. An increase in internal vibration is measured by an increase in temperature

Of all these radiations, your eyes are able to sense only a very narrow band ranging from about 400 nm (violet)  to 700 nm (red).  This corresponds to 7.5 X 1014 to 4.3 X1014 Hz.   This narrow band is called the visible spectrum and consists of all the colours that can be seen from red through orange, yellow, green, blue, indigo and violet. White light is composed of all these colours in equal amounts.  Red light borders on the left with infrared (under red) and violet borders on the right with ultraviolet (above violet).

Following the rules in the last worksheet the radio waves with a frequency of 104 Hz would have the longest wavelength of 30,000 metres. As we go to the right the wavelengths get smaller and smaller. Microwaves with a frequency of 1010 Hz have a wavelength of 3 mm. X-rays with a frequency of 1017 Hz have wavelengths of 3 nm.  At the very end of the scale we have gamma and cosmic rays which have a frequency of 1019 Hz which means a wavelength of only 0.03 nm.
Go to the Electromagnetic Spectrum Worksheet

The Energy in a Light Wave
Why is it people will pay money to see reflections of light at a laser light show, or even spend time in a tanning booth yet they get paranoid when out on a hot sunny day because they fear skin cancer?   The answer lies in what they've been told. Visible light is harmless, tanning booth light is safe if used in moderation but intense direct sunlight can be harmful. Why is that?

In 1900,  Max Planck (1858-1947), a German physicist, coined the term "photons".  It seems that light can be thought of in two ways. Either as waves with troughs and peaks or as bundles of energy.  Anyone standing on a beach can attest to this.  Have you even been knocked over by a wave?  Max Planck proposed that electromagnetic radiation is emitted in tiny packets of energy which he called "photons".  Each photon pulses with a frequency, v, and travels at the speed of light.

Planck also proposed that photons with very high frequencies carried more energy than ones with lower frequencies.  What he actually said was "the energy of a radiation is proportional to its frequency."  Albert Einstein latter confirmed this and coined a new term, the quantum of energy.

                                      Energy of a photon(E) = hv

          where E = energy       v = frequency     h = Planck's constant = 6.63 X 10-34 J.s


Lets take a look at a particular event in everyday life,  photosynthesis in plants.  Photosynthesis is started when a plant absorbs light. It is the frequency of light that is important. Therefore different kinds of light will have different effects on the efficiency of how plants do photosynthesis. We know that plants grow best in blue light (it just happens to have one of the higher frequencies) and not as well in red light. Plants do not grow well in green light which is a middle frequency because plant pigments do not absorb green light. Plants in fact reflect green light, which is why plants appear green to us humans!

To sum up: the higher the frequency the more energy a photon has.  Since ultraviolet light has a higher frequency than infrared light, ultraviolet light photons each carry more energy than do infrared photons.  Infrared photons warm you, ultraviolet photons burn you, cosmic rays are so tiny and so energetic they pass through you before any damage can be done.
Go to the Energy in a Light Wave Worksheet

Atomic Line Spectra
The spectrum of electromagnetic radiation that we looked at in the last set of notes is called the "continuous spectrum" because it contains the light of all colours.  This spectrum is formed when the light from the sun, or any object is heated to a very high temperature.  (You have of course heard of metals being heated until they were white hot).  This light can then be spread out by passing it through a prism onto a screen. A rainbow is a continuous spectrum of visible light that has been spread out by tiny water droplets suspended in the air.

If we look at a pure gas like hydrogen or neon or anything else pure we do not get a continuous spectrum.  When an electric current discharge passes through the gas the electric current excites, or energizes the atoms of the gas.  The gas then releases this energy in the form of visible light as the atoms return to a lower energy state.  When a beam of this light is passed through a prism or a spectrometer we do not see a continuous spectrum.  Instead, only a few colours are observed and these are in a series of individual lines.  This series of lines is called the element's atomic spectrum.

Different elements produce different spectra. This different spectra are called the atomic spectra and are unique enough to be considered as characteristic as a fingerprint.

The equation E=hv showed the simple relationship between the frequency of light and its energy.  Atomic spectra show us that an atom produces only certain characterisitc frequencies and this means that there are only certain characteristic energy changes taking place inside the atom. For example, in the atomic spectrum of hydrogen, there is a red line.  That red line has a wavelength of 656 nm. If you do the math you'll see that the frequency is then 4.57 X 1014 Hz.   Using the Planck's constant equation it can be determined that each photon of this light carries 3.03 X 10-19 J of energy.  What is important here is that when hydrogen produces a red line in it atomic spectrum, its frequency is always 4.57 X 1014 Hz and the energy in each photon is always 3.03 X 10-19 J. It is always the same.  This tells us that when an atom is excited and then loses energy, not just any arbitrary amount is lost.  Only certain specific energy changes can occur, which means only certain specific frequencies of light are emitted.

In order to explain this we must use the following model.  In an atom, an electron can have only certain definite amounts of energy and no others. The electron is restricted to certain energy levels and must use only these levels.  We also say that the energy of the electron is quantized, meaning once again that the electron's energy in a particular atom can have only certain values and no others.

quantized - to have a certain specific quantity.

The energy of an electron in an atom can be compared to the potential energy of a ball on a staircase.  The ball can only come to rest on a step, and on each step it will have some specific amount of potential energy.  If the ball is raised to a higher step, then its potential energy will be increased as well.  When the ball drops to a lower step, its potential energy decreases. But the ball cannot stop between steps.  The ball can only rest at the specific energy levels specified by the steps.  So it is with the electrons in an atom.  The electron can only have energies corresponding to the set of electron energy levels in the atom.  When an atom is supplied with energy, as in a gas discharge tube, an electron is raised from a low-energy level to a higher one.  When the electron drops back, energy equal to the difference between the two levels is released and this energy gets emitted as a photon.  Because only certain energy jumps can occur, only certain frequencies can appear in the spectrum.

The Bohr Model of the Atom
The problem with finding out that electrons where capable of existing only at certain energy levels was coming up with a model to explain these levels.   In 1913 Neils Bohr (1885-1962), a Danish physicist, proposed a theoretical model for the hydrogen atom. He chose hydrogen because its atoms are the simplest, having only one electron about the nucleus, and because it produces the simplest spectrum with the fewest lines.  In his model, Bohr imagined the electron to move around the nucleus following fixed paths, or orbits, much as a planet moves around the sun. His model also restricted the sizes of the orbits and the energy that the electron could have in a given orbit.  The equation Bohr derived for the energy of the electron included a number of physical constants such as the mass of the electron, its charge, and Planck's constant. It also contained an integer, n, that Bohr called a quantum number. Each of the orbits could be specified by its value of n.

Bohr found that the electron had the least energy when n = 1. which corresponds to the first Bohr orbit. This lowest energy state is called the ground state. This orbit also brings the electron closest to the nucleus.

When the hydrogen atom absorbed energy, as it does in a gas discharge tube, the electron is raised from the orbit n = 1 to a higher orbit such as n = 2 or n = 3 or even higher.  Then when the electron drops back to a lower orbit, energy is emitted in the form of light. Since the energy of the electron in a given orbit is fixed, a drop from one particular orbit to another, say from n=2 to n=1, always releases the same amount of energy, and the frequency of light emitted because of this change in energy is always precisely the same.

Bohr's model of the atom was both a success and a failure.  It successfully predicted the frequencies of the lines in the hydrogen spectrum, so it seemed to be valid.  Nevertheless the model was a total failure when it tried to predict energy levels for atoms with more than one electron.  Still the theory held some validity and is still used to introduce students to the concept of orbital shells and the first quantum number "n".

The Quantum Numbers
The theory of quantum mechanics tells us that in an atom, the electrons are found in orbitals, and each orbital has a characteristic energy. Orbital means "small orbit".   We are interested in two properties of orbitals - their energies and their shapes. Their energies are important because we normally find atoms in their most stable states, which we call their ground states, in which electrons are at their lowest possible energies.

The Principal Quantum Number , n
The quantum number n is called the principle quantum number. You already know this as shell. The shell "K" has been given the value n = 1, the "L" shell has been given the value n = 2.
                                n       1    2    3    4   ...
                            shell      K    L   M   N  ...

The principle quantum number serves to determine the size of the orbital, or how far the electron extends from the nucleus.  The higher the value of n the further from the nucleus we can expect to find it.  As n increases so does the energy required as well because the further out from the nucleus you go the more energy the electron must have to stay in orbit.  Bohr's work took into account only this first principle quantum number. His theory worked for hydrogen because hydrogen just happens to be the one element in which all orbitals having the same value of n also have the same energy.  Bohr's theory failed for atoms other than hydrogen, however, because orbitals with the same value of n can have different energies when the atom has more than one electron.

The Secondary Quantum Number, l
      The secondary quantum number, l, divides the shells up into smaller groups of subshells called orbitals.  The value of n determines the possible values for l. For any given shell the number of subshells can be found by l = n -1.   This means that for n = 1, the first shell, there is only l = 1-1 = 0 subshells. ie. the shell and subshell are identical. When n = 2 there are two sets of subshells;  l = 1 and l = 0.  A number could be used to identify the subshell however to avoid confusion between the numerical values of n and those of l the l values are given a letter code.

                                         value of       0    1   2   3    4 .....
                             letter designation     s    p   d    f    g .....
 


To designate a particular subshell we write the number of the shell itself followed by the subshell designator.
                 n    l   This illustrates the relationship between "n" and "l".
                   1    s               the first shell has one orbital type associated with it.
                   2    s p            the second shell has two orbital types associated with it.
                   3    s p d         etc
                   4    s p d f
                   5    s p d f g

The principle quantum number describes size and energy, but the second quantum number describes shape. The subshells in any given orbital differ slightly in energy, with the energy in the subshell increasing with increasing l.  This means that within a given shell, the s subshell is lowest in energy, p is the next lowest, followed by d, then f, and so on. For example:

                                           4s < 4p < 4d < 4f --->  increasing energy


The Magnetic Quantum Number, ml
The third quantum number, ml, is known as the magnetic quantum number. It splits the subshells into individual orbitals.  This orbital describes how an orbital is orientated in space relative to other orbitals.  i.e. It gives 3D information. The first "s" subshell has a magentic number of  "1". The "p" subshell has a magnetic number of "3".  A simple numeric progression gives us:

                                        s    p   d     f     <---name of subshell
                                        1   3    5    7    <--- number of orbitals in that subshell
                                        2   6    10  14  <--- number of electrons that will fit into that subshell.*

*An orbital can hold two electrons total. It may hold none, one or two but never more than two.


The Spin Magnetic Number, ms
The fourth and final quantum number is used to indicate the orientation of the two electrons in each orbital. The values for ms are +1/2 and -1/2.   An atom is the most stable when its electrons have the lowest possible energy. Electrons get the lowest possible energy when they occupy the lowest possible energy orbitals available. But what determines how the electrons "fill" the orbitals?  Two electrons can fill each orbital. How can two electrons both with a negative charge, and therefore mutually repulsive stay together in the same orbital?

The concept of electron spin is based on the fact that electrons behave like tiny magnets. An electron spins about it axis much like a toy top. The revolving electrical charge generates a magnetic field. (The same effect makes electric motors and generators work.)  The electron can spin in two directions, either clockwise or counter-clockwise.  Using the Left Hand rule for magnetic fields the clockwise spinning electrons generate a north pole on top and a south pole on the bottom. The counter-clockwise spinning electrons generate a north pole on the bottom and a south pole on the top.

In 1925 an Autrian physicist, Wolfgang Pauli (1900-1958), expressed the importance of electron spin in determining electronic configurations. The Pauli exclusion principle states that no two electrons in the same atom may have identical values for all four quantum numbers.  This means that the two electrons that fill any particular orbital must have opposite spins.  What happens if an orbital contains only 1 electron?  Then its magnetic field is not cancelled out and it can be attracted to other outside magnetic fields.  Atoms having at least one an unpaired electron are paramagnetic and can be attracted to magnetic fields.  Atoms with no unpaired electrons are said to be diamagnetic and are not seen to be magnetic.

In general, the number of electrons in a shell is 2n2.

    shell       number of subshells    maximum number of electrons
      1                  1s                                         2
      2                  2s 2p                                    8
      3                  3s 3p 3d                             18
      4                  4s 4p 4d 4f                         32 

 
Electron Configurations
When creating electron configuration diagrams it is best to remember the following:
- Shells expand outwards with the K shell, n=1, closest to the nucleus.
- 's' subshells hold only 2 electrons in 1 orbital
- 'p' subshells hold 6 electrons in 3 orbitals
- 'd' subshells hold 10 electrons in 5 orbitals
- 'f' subshells hold 14 electrons in 7 orbitals
- each orbital can hold 0, 1 or 2 electrons but never more than 2.  (Pauli's Exclusion Principle)
- each electron is to be placed into the lowest possible energy orbital first. As lower levels fill then higher levels can be filled. (Aufbrau (Boiling) Principle)
- in the 'p' orbitals of which there are three of equal energy, each orbital gets one electron first.  Only when all three are full can you go back and fill in the orbitals with the second electron. 

Hund's law - When electrons are placed in a set of orbitals of equal energy, they are spread out as much as possible to give as many unpaired electrons as possible.   Hund's law also applies to the 'd' orbitals of which there are five and the 'f' orbitals of which there are seven the same rules apply.


Using the above rules we can predict which orbitals in an atom will have electrons and the number of electrons found in each orbital. This arrangement is called the atom's electronic structure or electron configuration.  Knowing how to predict an atom's electronic configuration is important because it is the arrangement of electrons that controls an atom's chemical properties. Specific examples follow:

Hydrogen (Z = 1)   A neutral atom has 1 electron. In its ground state the electron will occupy the lowest energy level and the lowest orbital in that energy level.  We use two methods to illustrate this. One is an orbital diagram the other is a form of chemical shorthand.
                            1s
              H          O        or     1s1

Let's take a look at helium. (Z=2)
                             1s
              He         O          or      1s2

Now let's take a look at Li (Z = 3)
                             1s      2s
              Li          O   O or       1s2 2s1

Now take a look at boron (Z = 5)
                             1s     2s         2p
              B           O  O  OOO        or      1s2 2s2 2p1

One final example before you get turned loose to do some yourself:   Ne (Z = 8)
                             1s     2s          2p
              Ne         O  O   OOO        or      1s2 2s2 2p6

Both the orbital diagram and shorthand have uses. The orbital diagram is best for showing how bonding takes place. While the shorthand method is used on the periodic table to show the electronic configuration of the outermost orbitals.

One last thing. The orbitals would seem to be filled in the following order:

                     1s  2s  2p  3s  3p  3d   4s   4p   4d   4f    5s etc.

BUT THIS IS NOT SO.


The electron order of filling is in fact:  1s  2s  2p  3s  3p  4s  3d   4p  5a   4d   5p and so on.
The order can be predicted using a periodic table as a reference or this simple chart:
 

                                7s   7p   7d   7f

                                6s   6p   6d   6f

                                5s   5p   5d   5f

                                4s   4p   4d   4f

                                3s   3p   3d

                                2s   2p

                                1s 
 

It can also be determined if you know how to read the periodic table.
For a visual diagram click here.
Go to the Electron Configuration Worksheet