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Light and the Structure of the Atom
What is light and how is it created? The creation or origin of light is directly related to the structure of atoms –
specifically where the electrons are around the nucleus. This in turn determines the characteristics of atoms and
how they react.
Light, more correctly defined as “visible light”, is one form of electromagnetic radiation - energy that travels
through space in waves at approximately 186,000 miles per second.
Other forms of electromagnetic radiation
include x-rays, infrared radiation (heat energy), gamma rays, microwaves and radio waves. All travel at the “speed
of light” or 186,000 miles per second and all travel in the form of waves. What are the characteristics of waves?
If you sit on a surfboard just offshore at the beach, you will find yourself bobbing up and down in the water. This is
due to energy being transferred from out in the ocean in towards the shore. This energy is being carried by the
water in the form of waves. If you have ever been pummeled by a breaking wave at the beach, you know that a lot
of energy has been transferred! As you bob up and down, you are riding different parts of the wave: when you go
up, you are on a peak or crest and when you go down, you are in a trough. The distance between two peaks or
between two troughs is called the wavelength of the wave. The number of peaks that pass by a given point (you!)
every second is called the frequency of the wave. How fast a given peak moves through the water is called the
speed of the wave. The speed, frequency and wavelength of a wave are related by the following equation:
speed = (frequency)
or using symbols:
c
=
X (wavelength)
(f)
X
()
If we are talking about light, c= 186,000 miles per second or about 3.0 x 10 8 meters per second (m/s). The
frequency of a wave has the units waves/second or hertz. The units of wavelength are in meters/wave. Using
this information, you can determine the length of any wave of electromagnetic radiation given the frequency of that
radiation. Let’s try one:
What is the wavelength of a wave transmitted by the FM radio station 100.5, the FOX? First, we know that the speed
of the waves is 3.0 x 108 m/s. On the FM band, 100.5 is the radio frequency and means 100.5 Megahertz or 100.5 x
106 hertz (waves/second).
Rearranging the above equation and solving for , gives us:
 = c = 3.0x108 m/s
f
100.5 x 106 wave/s
= 3.0 meters/wave, or the wavelength of the radiation being broadcast
The frequency of a wave is related to how much energy is used to generate it. Take a rope or a long spring and extend
it between 2 people. Move the spring to create a wave pattern. Count the number of waves between the ends of the
spring. Then shake the spring much harder and you will see more waves but a smaller distance between them. By
putting more energy into a wave, we increase the frequency and reduce the wavelength. In other words, the waves
with higher frequency (and shorter wavelengths) have more energy. In visible light, red light has a certain
characteristic wavelength that is longer than blue light. Their frequencies are therefore reversed: red light has a lower
frequency while blue light has a higher frequency. Blue light has higher energy than red light since its wavelength is
shorter (and its frequency higher). In fact, each color of light (or any other type of electromagnetic radiation) has its
own characteristic energy which is based on its wavelength and frequency. Our eyes are designed by nature to detect
different wavelengths of light which our brain translates into color. Our eyes are not designed to detect radiation
outside the visible light wavelengths. For instance, we cannot see x-rays or radio waves. Photographic film can
detect x-rays and a radio receiver can detect radio waves. X-rays have very short wavelengths (high frequencies) and
therefore have high energies – they can penetrate the body. Radio waves are the lowest energy radiation and therefore
have the longest wavelengths (lowest frequencies).
So why do we see colored light when we energize elements in the gas phase? Why do we see a different color for
each element? What is different about each element : The number of electrons and their arrangement in space. We
shall now begin to see how the emission of light helped to determine something of where electrons reside in the atom.
Quantized energy
In 1900, a German scientist named Max Planck wrote an equation to show this the relationship between energy and
frequency of electromagnetic radiation : E = (h) x (f) where E is the energy of a bit of light called a quantum. A
quantum is the smallest bit of electromagnetic radiation that can be emitted. It is also called a photon of light or
small “packet” of electromagnetic radiation.
The “h” in the above equation is a very small constant called
“Planck’s constant” and “f” is the frequency of the radiation. Through various experiments of Planck and Albert
Einstein, it came to be accepted that light has properties of particles as well as waves. Planck’s “quantum” idea
became the basis for the modern understanding of atomic structure. In the above equation, as the frequency of
radiation increases, its energy increases by the increment “h”. In other words, energy was not continuous, it was
quantized – only certain energies are allowed. Continuous energy and quantized energy can be likened to a ramp
versus a set of stairs connecting two levels of a building. The ramp is analogous to continuous energy – you can sit
at any position along the ramp and thus be at any elevation between the two levels. The stairs are analogous to
quantized or discrete energy – you can only sit at certain elevations between the two levels and nowhere in between.
You may sit only on the steps, not in between the steps. Only certain elevations are allowed.
Spectra of elements
So what does all this stuff about waves and light and Plancks have to do with chemistry? It had been known for many
years that when samples of elements were heated up or energized with electricity, they burned or glowed a certain
color, not the entire rainbow of colors like we see from white light. (Below)
Each element seemed to have its own characteristic color. If we energize a sample of hydrogen with electricity, we
see a light purple color and if we energize a sample of neon with electricity we see the characteristic bright orange
color that is so common in “neon signs”. If we pass this light through a prism, which separates the colors of light like
rain separates the colors of white light into a rainbow, we see not a rainbow of continuous colors but only certain,
sharp lines of color. We see discreet energy levels, not continuous energy levels. Only certain colors are seen, not
the whole rainbow. Why is this so? Between 1911 and 1913, the Danish scientist, Niels Bohr, tried to explain the
line spectrum of the element hydrogen which contains 5 and only 5 distinct lines of color, each with their own energy,
wavelength and frequency. Only 3 or 4 of the lines are bright enough to see, below. Starting at the left, violet at
410nm, blue at 434nm, green at 486nm and red at 656nm.
Bohr imagined hydrogen’s lone electron as orbiting around the nucleus just like planets orbit around the sun, but at a
fixed distance from the nucleus.
The energy of the electron is lowest when it is quite close to the nucleus and this state of the electron is called the
ground state of the atom.
When an atom gains extra energy ( through heating or electricity), the electron moves
farther away from the atom. There is a natural attraction of the negatively charged electron for the positively charged
nucleus so it follows that it would take energy to move the electron away from this desirable situation. Picture one
end of a rubber band pulled snug around a finger. The finger is the nucleus and the other end of the rubber band is the
electron. By stretching the rubber band, energy is added and one end of the band (the electron) is moved farther
away from the finger (the nucleus). This is called an excited state of the atom. If one now lets go of the rubber
band, it comes slamming back into the finger and the excess energy added a moment ago is released as heat on the
finger. The energy released depends on how much added energy was used to stretch the rubber band in the first place.
Bohr guessed that electrons in atoms had only certain allowed orbits, only certain distances from the nucleus. The
electron could therefore absorb only certain energies to take them to these fixed distances and when this excess energy
was released, only certain or quantized energies were released as light. This would explain why only certain colors
(and therefore certain wavelengths of light) were observed when a hydrogen atom was excited. The farther an
electron dropped back towards the nucleus, the more energy it would release and the shorter the wavelength of light
that would be observed. The violet line of the hydrogen spectrum was light of greater energy than the red line in the
spectrum because the electron had fallen much farther than it did in another hydrogen atom that released the red light.
All 5 lines are seen since billions of atoms are being excited to various but very limited degrees. So, had Bohr figured
it out? Could he predict the line spectra of other elements based on this idea of electrons jumping up and down
between only certain allowed orbits? He could not. He tried his theory with other atoms and it did not work. From
this analysis, it was determined that electrons do not move around the nucleus in circular orbits. In fact, it is still not
known just how the electrons move around the nucleus.
Electrons as waves
As mentioned previously, Einstein (and others) showed that electromagnetic radiation has properties of matter as
well as waves. This is known as the wave-particle duality for light. Einstein’s evidence came by way of explaining
the photoelectric effect for which he won the Nobel Prize in 1921. In 1924, the French scientist Lois de Broglie
wondered that since light, normally thought to be a wave, could have particle properties, could matter, specifically the
electron, normally thought to be a particle, have wave properties as well? He took Einstein’s famous equation
E=mc2, Planck’s equation E=hf, and the relationship between wave speed, frequency and wavelength c=f and
combined them algebraically to derive the equation:
=h
mc
If any velocity, v, is substituted for the speed of light, c, we get:
=h
mv
The calculated wavelength, , for an 11g ping pong ball traveling at 2.5 meters per second is 2.4 x 10 -32m.
This answer makes sense : With large objects traveling at slow speeds, the wavelengths are not able to be seen and
are so small they are unimportant. The wavelength calculated is much smaller than the shortest known wavelength of
gamma rays (10-11 m). If we use the mass of the electron traveling at 1 x 10 5 meters per second, we get a wavelength
of about 7.3 x 10-9m, which is about the same size as the radius of an atom. At this speed, the electron can “orbit” the
hydrogen nucleus over 3 million times in one second! It would appear that the electron is everywhere at once!
Treating the electron as a wave just might be the right way to handle this problem. But the question remained how
this could be applied to the atom.
If an electron really could exist as a wave inside the atom, where exactly was it? The German scientist Heisenberg
determined that it was impossible to experimentally determine both the position and the speed of the electron at the
same time. This became known as the Heisenberg Uncertainty Principle. It simply means that the electron is so
small and moving so fast, that the simple act of trying to measure its speed or position would change either quantity.
Trying to detect the electron by shining some type of wave at the electron would be energetic enough to move it and
thus change its position or speed. We can see that this principle would only apply to extremely small particles. If we
shine a flashlight at a truck in the dark, we can surely tell its position, or if we want to determine its speed by radar
(radio waves) we can do so. In each case, our measuring tool will not affect the speed or position of the truck; it is
too massive. So we were out of luck finding exactly where the electron is in the atom. And if we assumed it acts
like a wave, well, how does one tell the position of a wave?
The Austrian scientist, Erwin Schrodinger, pursued de Broglie’s idea of the electron having wave properties and it
seemed to him that the electron might be like a standing wave around the nucleus. A standing wave is like a string
stretched between 2 points and plucked, like a guitar string. The wave does not travel between the 2 points but
vibrates as a standing wave with fixed wavelength and frequency. There is a limitation on the number of waves that
will fit in between the two points. There must be a whole number of waves to be a standing wave; there cannot be,
for instance, a 2.3 waves. So, only certain, or allowed wavelengths (or frequencies) can be possible for a given
distance between the 2 points. The same could be said about the atom. At any given distance from the nucleus, only
a certain number of whole waves would “fit” around the nucleus and not overlap in between waves. For a given
circumference, only a fixed number of whole waves of specific wavelength would work. Most wavelengths would
not work and thus would not be observed.
This idea agreed very well with Bohr's idea of quantized energy levels: only certain energies and therefore,
wavelengths would be allowed in the atom. This explained why only certain colors (wavelengths) were seen in the
spectrum of the hydrogen atom. We are on to something! Schrodinger set out to make a mathematical model that
assumed the electron was a standing wave around the nucleus. His solutions to that model agreed not only with the
experimental evidence for hydrogen (as Bohr’s did too), but gave excellent results for all atoms when compared to
their actual spectrum.
Orbitals
I know some of you would want to see it, so here is the famous Schroedinger equation. No, I can’t solve it!
1 The mathematical description of the electrons is given by a wave function,
, (or a State Function),
which specifies the amplitude of the electron at any point in space and time. Wave functions are solution of
Schroedinger's equation. For a one-dimensional particle, the time-dependent Schroedinger equation can be
written,
Schrodinger’s equation requires calculus and is very difficult to solve, but the solution of the equation, when treated
properly, gives not the exact position of the electron (remember Heisenberg), but the probability of finding the
electron in a specific place around the nucleus. This most probable “place” is known as an orbital. An orbital is a
volume space around the nucleus that contains the electron 90% of the time. Realize this space is determined from
the solution of an equation and not from direct observation. Also, it does not describe an orbit. An orbital is very
different, but the concept of an orbit as being a fixed distance (and therefore a fixed energy) from the nucleus will help
us understand the idea of an orbital. To get an idea of what an orbital is, picture a string hanging from the ceiling in a
dark room. The string has a cage of sex attractant attached to the end. A firefly is let in and its light can be seen
periodically. If we record each flash of light on film over the period of a few hours, what would you expect to see on
the film? Where would most of the flashes be? Most would be very close to the sex attractant but we would also see
some flashes farther away, decreasing in number the farther the firefly got from the sex attractant. If we could look at
the multitude of flashes caught on film in 3 dimensions, we would see a sphere of flashes with greater density close to
the center of the sphere.
This is very much like the possible positions of the electron in an orbital. Most of the time, the negative electron will
be close to the positive nucleus, but sometimes, it will not. We cannot tell anything about when the electron (firefly)
occupied a certain point, but looking at the whole volume of probability (orbital) we can see where it is likely to be
found. If we draw a circle around 90% of the flashes, we have defined one type of orbital, in this case, a sphere.
This shape would be one solution to the Schrodinger equation for where to find the electron in a hydrogen atom.
Recall in Bohr’s model that each electron orbit had a certain energy associated with it and only certain orbits were
allowed, thus the energy levels of the hydrogen atom were quantized. We need to set up this same idea of
quantization for the orbital model of the hydrogen atom. To do this, we will define principal energy levels and label
them with integers n=1,2,3…… In the Bohr model, the larger “n” gets, the farther away the electron is from the
nucleus and the greater energy it has.
Where “n” = 1, the electron is in the ground state. In an orbital, the
principal energy level increases as the electron moves farther from the nucleus as well, but it moves from one orbital to
another not from one orbit to another. In the case of hydrogen, when the electron gains the right amount of energy, it
moves to an orbital with principal energy level 2. The principal energy level defines the energy (and therefore the
average distance from the nucleus) of the electron, but it does not specify the shape of the probability volume (the
orbital). This shape is defined by the energy sublevel and is also a consequence of Schrodinger’s equation. Each
principal energy level in an atom has the same number of sublevels as its principal energy level integer. The
following table summarizes these relationships:
Principal Energy Level
# of Sublevels (shapes)
1
1
(s)
2
2
(s,p)
3
3
(s,p,d)
4
4
(s,p,d,f)
5
5
(s,p,d,f,g)
Each sublevel defines the shape of the orbital where the electrons reside. The farther away from the nucleus an
electron gets, the more possible shapes the orbital has. Why do the number of sublevels increase as the principal
energy level increases? An analogy can be used to understand. Picture the nucleus as the performer on a stage in a
concert hall. People want to be as close to the performer as possible. There are only so many seats close to the
performer and these are right in front, on the floor. As one moves farther from the performer, there is more room for
more people and in different places around the stage. Some people are on the floor behind the front rows and some
are off to the side of the performer. As the distance from the stage gets still greater, there is more volume around the
performer for people to be, some still on the floor, some on the sides of the stage and even some in upper decks. The
same is true in the atom: Close to the nucleus, there is only so much room for electrons. As the distance from the
nucleus increases, so does the area around the nucleus where an electron may be found. These different places or
shapes are called the energy sublevels and are at about the same distance from the nucleus (performer), but in different
probability locations (floor, balcony, decks).
So, starting with the hydrogen atom, let us place the electrons around the nucleus in terms of the solution of
Schrodinger’s equation.
Electron Configurations
In its ground state, the one electron of hydrogen is in principal energy level 1. The only possible sublevel for this
principal energy level is the “s” sublevel which has a spherical shape (just like our firefly example). We say that
hydrogen’s electron is in the “1s” orbital.
If energy were applied to this electron, say from an electric current, it may move up to another place farther away from
the nucleus. Let’s say it moved up to principal energy level 2 in the “s” sublevel. It is now in the 2s orbital. When
that electron loses energy and drops back to its ground state in the 1s orbital, a bit of energy would be given off and
would be seen as a certain wavelength (energy, color) of light. If the same electron were REALLY energized and
moved up to principal energy level 3, in the “s” sublevel (the 3s orbital) when it dropped back down to ground state,
more energy would be released than before and we would see a bit of light with a shorter wavelength. It can be seen
that even though hydrogen has only one electron, it can move among many different orbitals. An orbital, then, is best
described not as a place where an electron is but a potential place for an electron. All electrons in all atoms absorb
and emit energy in this way. You can see that for atoms with more electrons, many more possible energy changes are
possible. Let’s now define the orbitals for other atoms besides hydrogen.
In the helium atom there are 2 electrons and both can fit in the 1s orbital. We say that the ground state electron
configuration for helium is 1s2. (Obviously, for hydrogen, this electron configuration would be 1s 1). At this point,
the 1s orbital is filled. We cannot fit more electrons so close together since they repel each other. We have filled the
front row at our concert hall. So, for the element lithium, which has 3 electrons, we must now move farther away
from the nucleus where there is more room. Since we are moving farther away, we go to the next allowed energy
level, principal energy level 2 where n=2. The first sublevel we will fill (remember there are 2 sublevels for principal
energy level 2) is again an “s” sublevel which, like the 1s obital, is also a sphere but a larger sphere since electrons are
farther away from the nucleus on average.
The cumulative ground state electron configuration for lithium is then 1s 22s1. We can always determine what atom
we are dealing with in an electron configuration by adding all the subscripts in an electron configuration. In this case,
the subscripts add up to “3” which is how many electrons lithium has. The next element, beryllium, has 4 electrons
and the last one will be in the 2s orbital giving a ground state electron configuration of 1s 22s2. It should be
mentioned here that the Pauli exclusion principal states that an orbital can hold a maximum of 2 electrons. This
rule arises from experimental data that shows that electrons are spinning on their axes, just like the earth is. This
spinning negative charge creates a magnetic field - the electron is like a tiny magnet. If 2 electrons occupy an orbital,
they have opposite spins and their magnetic fields cancel. An orbital cannot have 2 electrons with the same spin or
their magnetic fields would repel, thus a third electron in an orbital is never found.
So, where does the 5th electron in the element boron go? Principal energy level 2 has 2 sublevels and the “s”
sublevel is filled, so the “p” sublevel now will accept electrons. The “p” sublevel is actually made up of 3 separate
orbitals, each holding 2 electrons in shapes that looks like dumbbells. Each dumbbell is oriented along 3 different
axes (x,y,z) and is denoted px, py and pz.
These 3 dumbbell-shaped orbitals can hold a total of 6 electrons. The p x, py and pz distinctions are usually not used in
electron configurations. Ground state configurations for the next 6 elements are summarized below:
Boron
1s22s22p1
Carbon 1s22s22p2
Nitrogen 1s22s22p3
Oxygen 1s22s22p4
Fluorine 1s22s22p5
Neon
1s22s22p6
At this point, all of the possible places for electrons in the first 2 principal energy levels are filled. A total of 10
electrons can fit in these energy levels, 2 in energy level 1 and 8 in energy level 2. We must move farther from the
nucleus to place the next electron. Sodium has 11 electrons and its 11 th electron will fit into principal energy level 3,
in the “s” sublevel. Hopefully a pattern is emerging – we always begin a new principal energy level by putting
electrons in the “s” sublevel. The “s” sublevel of any given principal energy level has slightly lower energy (and is
thus closer to the nucleus) than its corresponding “p” sublevel. Again, we can fit 2 electrons into the 3s orbital which
fills it and we must move to the 3p orbitals where we can fit a total of 6 more electrons. So, starting with sodium, we
can write the ground state electron configurations for the next eight elements:
Sodium
1s22s22p63s1
Magnesium
1s22s22p63s2
Aluminum
1s22s22p63s23p1
1s22s22p63s23p2
Silicon
Phosphorus
1s22s22p63s23p3
Sulfur
1s22s22p63s23p4
Chlorine
1s22s22p63s23p5
Argon
1s22s22p63s23p6
You may remember that principal energy level 3 contains 3 sublevels or shapes s, p, and d. The d sublevel actually
consists of 5 separate orbitals holding 2 electrons each for a total of 10 electrons. These shapes have multiple lobes
and are oriented both between and along the x,y,z axes with the nucleus at the origin. As with the p orbitals, we
usually don’t differentiate between the electrons in each separate 5 d orbital, but put a total of 10 electrons in them.
Let’s summarize principal energy levels, sublevels and electron capacities to this point:
Principal Energy Level
Sublevels present (with total electron capacity in parentheses)
1
s (2)
2
s (2), p (6)
3
s (2), p (6), d (10)
4
s (2), p (6), d (10), f (14)
Note we have added the up to the 4th sublevel for principal energy level 4 which are called “f” orbitals. There are 7
separate orbitals in the “f” sublevel holding a total of 14 electrons. Which elements contain these electrons will be
discussed later.
Getting back to the electron configurations of the elements, it would make sense that after 18 electrons, the last of
which went into the 3p orbitals, the 19th would go into the 3d sublevel, but that does not happen. The electron
configuration for the next 3 elements is as follows:
Potassium
1s22s22p63s23p64s1
Calcium
1s22s22p63s23p64s2
Scandium
1s22s22p63s23p64s23d1
What is going on here? Why do we start to fill principal energy level 4, a higher energy level with electrons
supposedly farther away from the nucleus, before we fill the remainder of principal energy level 3 with electrons that
are thought to be closer to the nucleus? To answer this, we must realize that the principal energy levels
(n=1,2,3,…etc.) are average energies for all the sublevels contained within that principal energy level. Each of the
sublevels have slightly different energies with the “s” sublevel being the lowest, and the “p”, “d”, and “f” sublevels
having progressively greater energies. This causes some overlapping of energies between principal energy levels.
We can see from the following diagram that the 4s orbital has slightly lower energy than the 3d orbitals, so electrons
fill there first. Next, the 3d orbitals are filled and then the 4p orbitals.
Starting with potassium, the ground state electron configurations for the next 18 elements are as follows:
Potassium
1s22s22p63s23p64s1
Gallium
1s22s22p63s23p64s23d104p1
Calcium
1s22s22p63s23p64s2
Germanium
1s22s22p63s23p64s23d104p2
Scandium
1s22s22p63s23p64s23d1
Arsenic
1s22s22p63s23p64s23d104p3
Titanium
1s22s22p63s23p64s23d2
Selenium
1s22s22p63s23p64s23d104p4
Vanadium
1s22s22p63s23p64s23d3
Chlorine
1s22s22p63s23p64s23d104p5
Chromium
1s22s22p63s23p64s23d4
Argon
1s22s22p63s23p64s23d104p6
Manganese
1s22s22p63s23p64s23d5
Iron
1s22s22p63s23p64s23d6
Cobalt
1s22s22p63s23p64s23d7
Nickel
1s22s22p63s23p64s23d8
Copper
1s22s22p63s23p64s23d9
Zinc
1s22s22p63s23p64s23d10
As we get to elements with greater numbers of electrons, there is quite a bit of overlapping of orbitals between 2 and 3
different principal energy levels.
Without experience, it is difficult to determine the order in which the orbitals
will be filled. The diagram below, left, shows how this overlapping of orbital energies distorts our nice pattern we
started to see in the electron configurations. Use the diagram below, right, to determine the order of orbital filling,
starting from the bottom. Each box represents an orbital.
6d
5
f
d
f
p
4
d
s
p
3
d
s
p
2
s
p
s
Energy
1
(avg.
distance
from the
nucleus)
s
5f
7s
6p
5d
4f
6s
5p
4d
5s
4p
3d
4s
3p
3s
2p
2s
1s
Based on this order of adding electrons to atoms, which orbital will take the next electron? It must go into the “5s”
orbital, so the ground state electron configuration of the element rubidium is:
Rubidium
1s22s22p63s23p64s23d104p65s1
Now, this is becoming a lot of work writing down these ever-expanding electron configurations! The more electrons
we have in the atom, the longer the electron configuration. We have a method we can use to simplify writing these
configuration as we become more familiar with them. If we look closely, we notice that the electron configuration
for rubidium is the same as the previous element, argon, with a single 5s electron added on. For the electron
configuration of argon, let us simply write [Ar]. The simplified electron configuration for rubidium then becomes:
Rubidium
[Ar]5s1
We can do this for any element, BUT, we must use only noble gases in the brackets. I call this the noble gas
simplification. In this method of writing electron configurations, the last noble gas before we get to the element of
interest is the noble gas we put into the brackets. For instance, for the element aluminum we write
Aluminum
[Ne]3s23p1
Calcium
[Ar]4s2
and for calcium we write
We may NOT use any element in the brackets, only noble gases. This notation for writing electron configurations
helps us to highlight 2 different types of electrons in the atom. Those electrons in the brackets are called core
electrons. These electrons do not participate in chemical reactions. The electrons written after the noble gas in
brackets are called valence electrons. In many cases, “d” electrons will be present after the last noble gas, as in the
element manganese : [Ar]4s23d5. We typically do not consider “d” electrons as valence electrons and therefore a
more specific definition is needed: valence electrons are those electrons in the highest principal energy level.
These electrons are important because they are the ones that are gained, lost or shared in chemical reactions. For the
element aluminum, above, we see 2 electrons in the 3s orbital and 1 electron in the 3p orbital, so aluminum has a total
of 3 valence electrons. Using the same method, calcium has 2 valence electrons. If we look at the electron
configuration for manganese again:
Manganese
[Ar]4s23d5
We might then say that it has 2 valence electrons by one definition (highest
principal energy level) or 7 valence electrons by the other (electrons written after the last noble gas). In fact, both can
be true. For the transition metals, “d” electrons are present and they may or may not act as valence electrons; it
depends on the situation and it is not straight forward, so we will describe numbers of valence electrons only for
elements that are NOT transition metals.
It is very easy to determine an atom’s number of valence electrons in another way, from the periodic table. Look at
the following table to see that we can tell the number of valence electrons an element has by looking at the group
(vertical column) it belongs to on the periodic table:
Group number
Group’s electron
Configuration
Number of Valence
Electrons
Example
1
1
ns
1
sodium
2
ns2
2
magnesium
13
ns2p1
3
aluminum
14
2 2
ns p
4
silicon
15
ns2p3
5
phosphorus
16
2 4
6
sulfur
17
2 5
ns p
7
chlorine
18
ns2p6
8
argon
ns p
The number of valence electrons an element has will become useful when we talk about chemical bonding.
Electron configuratons and the periodic table
It will be helpful now to look at electron configurations also in the context of the periodic table. The periodic table
can be broken into “blocks” that show what the last electron added to the electron configuration is.
The alkali metal electron configurations (group 1) always end with “s 1” and the alkaline earth metals (group 2) always
end with “s2”. These 2 groups are know as “s block” elements. “P block” elements are all those in groups 13-18
and always end with 1 or more “p” electrons. For example, all the elements in group 13, beginning with boron, end
with “p1”. All of the elements in group 16, beginning with oxygen, end with “p 4”. The transition elements are called
“d block” elements and always end with 1 or more “d electrons”. For example, the all of the elements in group 3
beginning with scandium, all end in “d1”. The “f block” elements are those at the bottom of the periodic table that
we call the lanthanide and actinide groups. These elements’ electron configurations always end with one or more “f
electrons.”
It can be very useful to determine the last electron added (the outermost electron) to any element since this will always
be a valence electron. We can do this by looking at the periodic table and finding 2 things: the period number (row
number) and the block that the element is contained in. Let’s try this with the element calcium. From a periodic
table, we see it is in row (period) 4 and we see that it is in the “s” block. In fact calcium is the second element in the
“s” block, so the last electron is an “s2” electron. Since it is in period 4, the last electron added is 4s 2. Now try
finding the last electron added (the outermost electron) to the element iodine. We can see that it is in period 5 and in
the “p” block. It is the 5th element in the “p” block, so the last electron in iodine is 5p 5. One more example will show
a break in the trend we have set up. Find the last electron in the element nickel. We notice that it is in period 4 and it
is the 8th element in the “d” block. We would think that it’s last electron would be 4d 8, but in fact it is 3d8. Remember
that because of the orbital overlap we talked about earlier, the “d orbital” principal energy levels are always one behind
the “s” and “p” principal energy levels. As a result, its electron configuration is [Ar]4s23d8 and the last electron added
to nickel is a 3d8 electron. See the following periodic table for these last electrons in the electron configuration. A
few others are included so you can see the patterns.
Group
1
Group
THE PERIODIC TABLE
2
13
14
15
16
17
18
Last electron added in the electron configuration
Period
1
H
1s
He
1
1s2
2
Mg
3
4
5
6
3s
K
4s
1
Sc
2
1
3d
Ti
2
3d
Mn
Ni
5
3d
Ru
Rh
5
6
7
4d
I
Xe
5
4d
5p
Re
Au
1
5
9
7
4p6
4p
Cs
5d
Kr
4
3d
Tc
4d
Se
8
1
6s
Ne
2p6
3p4
Rb
5s
F
2p5
S
2
Ca
4s
O
2p4
5d
Hg
10
5d
Tl
1
6p
Pb
6p2
5p6
Hund’s Rule
Recall that the Pauli Exclusion Principle states that an orbital may hold a maximum of 2 electrons. Hund’s Rule
states that orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second
electron, and all electrons in singly occupied orbitals must have the same spin. So, what is this saying and why does
it matter? If we look at the box diagram, below for the element nitrogen, we see boxes representing orbitals and
arrows representing electrons. We add electrons from the bottom up, putting only 2 electrons in each box (one arrow
going up and one going down indicate electrons of opposite spin). When we get to the “2p” orbitals, we have 3
separate orbitals in which to place electrons and 3 electrons to place. How are they placed in the orbitals, each of
equal energy (distance from the nucleus)? One idea is to place 2 electrons in the first box and one in the second box.
Hund’s rule, however, says we should place one electron in each box before we start doubling up, so the box diagram
for nitrogen shows this. If we had one more electron to place (if we had the next element, oxygen), there would be 2
electrons in the first “2p” orbital. We can look at Hund’s Rule like a house with just as many bedrooms as children.
Each child likely wants his own room - they do not double up unless they have to. If a fourth child comes along,
then 2 must fit in one bedroom. The other box diagram, below, for Manganese, shows the same situation. There are
5 “d” orbitals and 5 electrons to place. One electron goes in each of the 5 “d” orbitals – two will not be placed in any
orbital until each has at least one electron.
Nitrogen
6d
5f
7s
6p
5d
4f
6s
5p
4d
5s
4p
3d
4s
3p
3s
2p

2s

1s


Manganese
6d
5f
7s
6p
5d
4f
6s
5p
4d
5s

4p
3d

4s

3p

3s

2p

2s

1s









So why is this such a big deal? Recall that electrons have a “spin” and therefore are like little magnets. If an element
has many unpaired electrons, a sample of it can become magnetic if all of the atoms in the sample are oriented
properly. We see this most commonly with the elements iron, cobalt and nickel. All three have unpaired electrons in
their “d” orbitals and if oriented properly, large samples of these elements can become a magnet. Most magnets you
are familiar with are made of iron.
Trends and the Periodic Table
Atomic radius
Now that we have a pretty good handle on electron configurations and their relationship to the periodic table, we can
look at a couple of trends that are important. The first one is atomic size or atomic radius. As we go down any
group on the periodic table, the atoms (and the ions they form when they gain or lose electrons) get larger.
Why? Because as we go down a group, we have electrons in higher and higher energy levels which are farther away
from the nucleus. The electron distance from the nucleus determines the size of the atom. If we go across a
period, however, the atoms get smaller. This is curious since as we go across a period, we are adding electrons, just
like we did going down a group. But, the electrons we are adding are all in the same principal energy level and
therefore not any farther away from the nucleus. At the same time, the number of protons are increasing as we go
across a period. This increases the positive charge in the atom which pulls the electrons in closer towards the
nucleus. So, as we go across a period on the periodic table, the atoms (and the ions they form when they gain or
lose electrons) get smaller.
Ionization Energy
When an atom gains enough energy to not just excite its electrons to higher energy levels, but to remove an electron
completely, it has absorbed the atom’s ionization energy. Remember when we discussed Bohr’s model of the atom
with a rubber band. As we pull the rubber band away from a finger, the electron is gaining energy. If we pull the
rubber band hard enough it may break free completely. If this happens, the atom we are modeling has become an ion.
We have given an atom its ionization energy. If we consider this ionization energy in relation to the elements on the
periodic table, we can also see some trends. As we go down a vertical column (a group or family), the valence
electrons are farther and farther away from the grip of the nucleus. It gets easier and easier to pull one electron away
to make an ion. So, we say that ionization energy decreases as we go down a group. As we go across a row of the
periodic table (a period), the electrons are not really any farther away from the nucleus since they are all in the same
principal energy level. But, the positive charge in the nucleus in increasing since more and more protons are being
added, so it becomes harder and harder to pull one electron away. So, we say that ionization energy increases as we
go across a period. This idea becomes important as we consider an atom’s reactivity. The easier it is to pull away
an electron from a metal atom, the more reactive the metal is and the more likely it will want to combine with a
nonmetal element to form a compound. Metals tend to want to lose electrons to form positive ions (cations) and
nonmetals tend to want to gain electrons to form negative ions (anions). This will be the basis for the next unit on
chemical bonding.
So, this long unit on light and where the electrons reside in the atom has given us the basis we need for describing how
and why atoms behave the way they do and the mechanism for atoms combining to form compounds.
Sort of semi-copyrighted by Steve Kemper, Twinkie Enterprises 2002