the periodic table of elements2

by Anthony Carpi, Ph.D.

In 1869, the Russian chemist Dmitri Mendeleev first proposed that the chemical elements exhibited a "periodicity of properties." Mendeleev had tried to organize the chemical elements according to their atomic weights, assuming that the properties of the elements would gradually change as atomic weight increased. What he found, however, was that the chemical and physical properties of the elements increased gradually and then suddenly changed at distinct steps, or periods. To account for these repeating trends, Mendeleev grouped the elements in a table that had both rows and columns.

The modern periodic table of elements is based on Mendeleev's observations; however, instead of being organized by atomic weight, the modern table is arranged by atomic number (z). As one moves from left to right in a row of the periodic table, the properties of the elements gradually change. At the end of each row, a drastic shift occurs in chemical properties. The next element in order of atomic number is more similar (chemically speaking) to the first element in the row above it; thus a new row begins on the table.

For example, oxygen (O), fluorine (F), and neon (Ne) (z = 8, 9 and 10, respectively) all are stable nonmetals that are gases at room temperature. Sodium (Na, z = 11), however, is a silver metal that is solid at room temperature, much like the element lithium (z = 3). Thus sodium begins a new row in the periodic table and is placed directly beneath lithium, highlighting their chemical similarities.

Rows in the periodic table are called periods. As one moves from left to right in a given period, the chemical properties of the elements slowly change. Columns in the periodic table are called groups. Elements in a given group in the periodic table share many similar chemical and physical properties. The link below will open a copy of the periodic table of elements in a new window.

The Periodic Table of Elements
Electron Configuration and the Table
The "periodic" nature of chemical properties that Mendeleev had discovered is related to the electron configuration of the atoms of the elements. In other words, the way in which an atom's electrons are arranged around its nucleus affects the properties of the atom.

Bohr's theory of the atom tells us that electrons are not located randomly around an atom's nucleus, but they occur in specific electron shells (see our Atomic Theory II module for more information). Each shell has a limited capacity for electrons. As lower shells are filled, additional electrons reside in more-distant shells.

The capacity of the first electron shell is two electrons and for the second shell the capacity is eight. Thus, in our example discussed above, oxygen, with eight protons and eight electrons, carries two electrons in its first shell and six in its second shell. Fluorine, with nine electrons, carries two in its first shell and seven in the second. Neon, with ten electrons, carries two in the first and eight in the second. Because the number of electrons in the second shell increases, we can begin to imagine why the chemical properties gradually change as we move from oxygen to fluorine to neon.

Sodium has eleven electrons. Two fit in its first shell, but remember that the second shell can only carry eight electrons. Sodium's eleventh electron cannot fit into either its first or its second shell. This electron takes up residence in yet another orbit, a third electron shell in sodium. The reason that there is a dramatic shift in chemical properties when moving from neon to sodium is because there is a dramatic shift in electron configuration between the two elements. But why is sodium similar to lithium? Let's look at the electron configurations of these elements.

Group IA VIA VIIA VIIIA

Lithium Oxygen Fluorine Neon


Sodium

Electron Configurations for Selected Elements


As you can see in the illustration, while sodium has three electron shells and lithium two, the characteristic they share in common is that they both have only one electron in their outermost electron shell. These outer-shell electrons (called valence electrons) are important in determining the chemical properties of the elements.

An element's chemical properties are determined by the way in which its atoms interact with other atoms. If we picture the outer (valence) electron shell of an atom as a sphere encompassing everything inside, then it is only the valence shell that can interact with other atoms - much the same way as it is only the paint on the exterior of your house that "interacts" with, and gets wet by, rain water.


Lithium Sodium

An atom's valence shell
"covers" inner electron shells

The valence shell electrons in an atom determine the way it will interact with neighboring atoms, and therefore determine its chemical properties. Since both sodium and lithium have one valence electron, they share similar chemical properties.

Electron Configuration Shorthand:
For elements in groups labeled A in the periodic table (IA, IIA, etc.), the number of valence electrons corresponds to the group number. Thus Li, Na, and other elements in group IA have one valence electron. Be, Mg, and other group-IIA elements have two valence electrons. B, Al and other group-IIIA elements have three valence electrons, and so on. The row, or period, number that an element resides in on the table is equal to the number of total shells that contain electrons in the atom. H and He in the first period normally have electrons in only the first shell; Li, Be, B, and other period-two elements have two shells occupied, and so on. To write the electron configuration of elements, scientists often use a shorthand in which the element's symbol is followed by the element's electron shells, written as a right-hand parentheses symbol ")". The number of electrons in each shell is then written after the ) symbol. A few examples are shown below.

Element
Configuration Shorthand

Hydrogen
H )1e-

Lithium
Li )2e- )1e-

Fluorine
F )2e- )7e-

Sodium
Na )2e- )8e- )1e-


For further details, the table linked below shows the electron configurations of the first eleven elements.



Atomic structure animation table



Related Modules

Atomic Theory II



External Resources

• The Periodic Kingdom: A Journey into the Land of the Chemical Elements (Science Masters Series)

• Plutonium: A History of the World's Most Dangerous Element


• Other Recommended Products


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the periodic table of elements

Many of the same principles we learned in the last lesson (atomic structure) can be applied to the third element in the series, lithium. Lithium has 3 protons in its nucleus and an atomic number = 3. To keep these protons stable and glued together, lithium normally has 4 neutrons in its nucleus. Recall that in a neutral atom the number of protons equals the number of electrons, so a neutral lithium atom will have 3 electrons spinning around it. When we look at the atomic structure of lithium though, we see a significant difference between it and the 1st two elements discussed in the last lesson. Lithium's 3rd electron spins at a different level (called a shell) than the 1st two electrons.
A Lithium Atom has 2 electron shells
This 3rd electron is forced to spin around the nucleus in a second electron shell because of the repulsive forces between the 3 negatively charged electrons. Just as 2 positively charged protons repel each other if they are brought too close together, so will negatively charged electrons repel each other. No neutral particles exist however to help hold electrons together in their shells (neutrons only exist in the nucleus). When an electron will not fit into an existing level because of repulsive forces between negative charges, the atom will work around this problem by adding the electron to a new shell, more distant from the nucleus than the existing shell (or shells).

In other words, electron shells have a limited capacity for electrons. As you might expect, the farther an electron shell is from the nucleus, the larger it is. You can calculate the total capacity of an electron shell using the formula 2n2, where n equals the number of the electron shell. For example, for the 1st electron shell n = 1 and 2 x 12 = 2, telling us that the capacity of the 1st shell is 2 electrons as we have already seen. For the 2nd shell (n = 2) and 2 x 22 = 8. For an atom to fill its 2nd electron shell, it would need 10 electrons: 2 to fill the 1st shell and 8 to fill the 2nd. The 3rd shell has a total capacity of 2 x 32 = 18 electrons. But things get a bit tricky here. Electron shells actually have sublevels. The first sublevel (the s sublevel) holds 2 electrons. The second, p, sublevel holds 6. The third, d, sublevel holds 10. After levels 3s and 3p are filled, electron shell #3 acts as if it has reached capacity with only 8 total electrons. In other words, in an atom with 20 electrons (which is the element calcium, Ca) the first 2 electrons are located in the 1st shell, the next 8 in shell #2, the following 8 in shell #3 and the remaining 2 electrons are located in shell #4.

As you can see, at this point atomic theory begins to get complicated. Just as we saw in the last lesson that the electron is not a simple particle but a more complex wave, here we find that filling electron shells is not as simple as stacking books on a shelf. This is because at the atomic level things are just plain wierd. Particles travel through time and space like something out of a bad Star-Trek re-run. It all boils down to something called quantum theory. We'll try to keep things as simple as possible, but if you would like, you can learn more about atomic structure and quantum theory using some of the links listed at the bottom of this page.

By convention there is color,
by convention sweetness,
by convention bitterness,
but in reality there are atoms and space.
-Democritus (400 BC)

Why does this matter? What significance do electron shells have on the fact that "you'd rather be fishing"? As it turns out, the reason hydrogen atoms stick to oxygen atoms to form the water in the fish pond depends on electron structure. Actually, just about everything depends on electron structure. The chemical properties of an atom will depend on the number of electrons in the atom's outermost (or valence) electron shell. Thus lithium behaves more similarly to hydrogen than it does to helium because both lithium and hydrogen have 1 electron in their outermost shell. The atoms can be arranged according to their electron structure and chemical properties. This is where we encounter the Periodic Table of Elements.

The Periodic Table of Elements (or the Periodic Table for short) was first proposed by a Russian chemist named Dmitri Mendeleev in 1871. A modern version of the Table appears below. Atoms are ordered by their atomic number in the Periodic Table. The Table is set up so as to indicate the number of electron shells in each atom and the number of valence electrons (electrons in the outermost shell) in the atom. As you descend rows in the Table, the number of electron shells in the atom increases. For example, hydrogen (H) in the 1st row has 1 shell, lithium (Li) in the 2nd row has 2 shells, sodium (Na) 3 shells, etc. As you read the Table from left to right in any one row, the number of valence electrons increases. For example, hydrogen has 1 electron (in the first shell). Helium (He), the 2nd element in the first row, has 2 electrons (thus filling its valence shell). Let's look at lithium (Li) again. From the atomic number we know that Li has 3 electrons. From its position on the Periodic Table (and from our discussion above) we know that Li has 1 valence electron: 2 electrons fill Li's 1st shell and 1 orbits in the second shell. From its position on the Table we know that berylium (Be) has 2 valence electrons in its 2nd shell. Can you predict the structure of the next element, Boron (B)?

Each element in the Table below is linked to information on Chris Heilman's Pictorial Periodic Table. To return to this page hit the 'Back' button on your web browser.

The Periodic Table of Elements
1
H
1.01 IIA Atomic number
Symbol
Atomic mass Metals
Transition Metals
Metalloids
Nonmetals

He
4.00
3
Li
6.94 4
Be
9.01 5
B
10.81 6
C
12.01 7
N
14.01 8
O
16.00 9
F
19.00 10
Ne
20.18
11
Na
22.99 12
Mg
24.31

--------------------------------------------------------------------------------
13
Al
26.98 14
Si
28.09 15
P
30.97 16
S
32.06 17
Cl
35.45 18
Ar
39.95
19
K
39.10 20
Ca
40.08 21
Sc
44.96 22
Ti
47.90 23
V
50.94 24
Cr
52.00 25
Mn
54.94 26
Fe
55.85 27
Co
58.93 28
Ni
58.71 29
Cu
63.55 30
Zn
65.38 31
Ga
69.72 32
Ge
72.59 33
As
74.92 34
Se
78.96 35
Br
79.90 36
Kr
83.80
37
Rb
85.47 38
Sr
87.62 39
Y
88.91 40
Zr
91.22 41
Nb
92.91 42
Mo
95.94 43
Tc
(98) 44
Ru
101.07 45
Rh
102.91 46
Pd
106.4 47
Ag
107.87 48
Cd
112.40 49
In
114.82 50
Sn
118.69 51
Sb
121.75 52
Te
127.60 53
I
126.90 54
Xe
131.30
55
Cs
132.91 56
Ba
137.34 57
La*
138.91 72
Hf
178.49 73
Ta
180.95 74
W
183.85 75
Re
186.21 76
Os
190.2 77
Ir
192.22 78
Pt
195.09 79
Au
196.97 80
Hg
200.59 81
Tl
204.37 82
Pb
207.2 83
Bi
208.96 84
Po
(209) 85
At
(210) 86
Rn
(222)
87
Fr
(223) 88
Ra
226.03 89
Ac*
(227) 104
Rf
(261) 105
Db
(262) 106
Sg
(263) 107
Bh
(262) 108
Hs
(265) 109
Mt
(266) 110
Uun
(269) 111
Uuu
(272) 112
Uub
(277) 113
Uut
(282)
*Lanthanide series: 58
Ce
140.11 59
Pr
140.91 60
Nd
144.24 61
Pm
(145) 62
Sm
150.36 63
Eu
151.96 64
Gd
157.25 65
Tb
158.92 66
Dy
162.50 67
Ho
164.93 68
Er
167.26 69
Tm
168.93 70
Yb
173.04 71
Lu
174.97
*Actinide series: 90
Th
232.04 91
Pa
231.04 92
U
238.03 93
Np
237.05 94
Pu
(244) 95
Am
(243) 96
Cm
(247) 97
Bk
(247) 98
Cf
(251) 99
Es
(252) 100
Fm
(257) 101
Md
(258) 102
No
(259) 103
Lr
(260)



Using the Table row and group numbers to predict the number of valence electrons in an atom works reasonably well for the metals, metalloids and nonmetals (see the color legend above). However, with the transition metals our simplified explanation of valence electrons begins to break down and quantum theory is needed to explain behavior. We will limit our discussion to the metals, metalloids and nonmetals. In our simplified approach to atomic structure, you can predict the number of valence electrons in an atom by ignoring the transition metals and counting from left to right in group A of the Periodic Table. Thus, elements in group IA have 1 valence electron, elements in group IIA have 2, IIIA have 3 valence electrons, etc. If you are having trouble visualizing this, an abbreviated Periodic Table (with the transition metals removed) can be viewed by clicking below.



For those interested, some links to other resources have been included below.

A Practice Test on Atomic Structure
More in-depth information on the structure of the atom:
The Atomic Model: an interesting summary of developments in atomic theory
The Physics 2000 Quantum Zone: very cool, but not for the faint of heart
The Particle Adventure: quarks, muons, universal forces and more
Electron Orbital Shapes: that says it all
Portrait of an Atom: an interesting artistic rendition of atomic structure

Hydrogen: a proton surrounded by an electron cloud

hydrogen atom

atomic structure

atoms were particles of elements, substances that could not be broken down further. In examining atomic structure though, we have to clarify this statement. An atom cannot be broken down further without changing the chemical nature of the substance. For example, if you have 1 ton, 1 gram or 1 atom of oxygen, all of these units have the same properties. We can break down the atom of oxygen into smaller particles, however, when we do the atom looses its chemical properties. For example, if you have 100 watches, or one watch, they all behave like watches and tell time. You can dismantle one of the watches: take the back off, take the batteries out, peer inside and pull things out. However, now the watch no longer behaves like a watch. So what does an atom look like inside?
Atoms are made up of 3 types of particles electrons , protons and neutrons . These particles have different properties. Electrons are tiny, very light particles that have a negative electrical charge (-). Protons are much larger and heavier than electrons and have the opposite charge, protons have a positive charge. Neutrons are large and heavy like protons, however neutrons have no electrical charge. Each atom is made up of a combination of these particles. Let's look at one type of atom:

A neutron walked into a bar and
asked how much for a drink.
The bartender replied,
"for you, no charge."
-Jaime - Internet Chemistry Jokes

The atom above, made up of one proton and one electron, is called hydrogen (the abbreviation for hydrogen is H). The proton and electron stay together because just like two magnets, the opposite electrical charges attract each other. What keeps the two from crashing into each other? The particles in an atom are not still. The electron is constantly spinning around the center of the atom (called the nucleus). The centrigugal force of the spinning electron keeps the two particles from coming into contact with each other much as the earth's rotation keeps it from plunging into the sun. Taking this into consideration, an atom of hydrogen would look like this:
A Hydrogen Atom

Keep in mind that atoms are extremely small. One hydrogen atom, for example, is approximately 5 x 10-8 mm in diameter. To put that in perspective, this dash - is approximately 1 mm in length, therefore it would take almost 20 million hydrogen atoms to make a line as long as the dash. In the sub-atomic world, things often behave a bit strangely. First of all, the electron actually spins very far from the nucleus. If we were to draw the hydrogen atom above to scale, so that the proton were the size depicted above, the electron would actually be spinning approximately 0.5 km (or about a quarter of a mile) away from the nucleus. In other words, if the proton was the size depicted above, the whole atom would be about the size of Giants Stadium. Another peculiarity of this tiny world is the particles themselves. Protons and neutrons behave like small particles, sort of like tiny billiard balls. The electron however, has some of the properties of a wave. In other words, the electron is more similar to a beam of light than it is to a billiard ball. Thus to represent it as a small particle spinning around a nucleus is slightly misleading. In actuality, the electron is a wave that surrounds the nucleus of an atom like a cloud. While this is difficult to imagine, the figure below may help you picture what this might look like:

Hydrogen: a proton surrounded by an electron cloud


While you should keep in mind that electrons actually form clouds around their nucleii, we will continue to represent the electron as a spinning particle to keep things simple.
In an electrically neutral atom, the positively charged protons are always balanced by an equal number of negatively charged electrons. As we have seen, hydrogen is the simplest atom with only one proton and one electron. Helium is the 2nd simplest atom. It has two protons in its nucleus and two electrons spinning around the nucleus. With helium though, we have to introduce another particle. Because the 2 protons in the nucleus have the same charge on them, they would tend to repel each other, and the nucleus would fall apart. To keep the nucleus from pushing apart, helium has two neutrons in its nucleus. Neutrons have no electrical charge on them and act as a sort of nuclear glue, holding the protons, and thus the nucleus, together.

A Helium Atom

As you can see, helium is larger than hydrogen. As you add electrons, protons and neutrons, the size of the atom increases. We can measure an atom's size in two ways: using the atomic number (Z) or using the atomic mass (A, also known as the mass number). The atomic number describes the number of protons in an atom. For hydrogen the atomic number, Z, is equal to 1. For helium Z = 2. Since the number of protons equals the number of electrons in the neutral atom, Z also tells you the number of electrons in the atom. The atomic mass tells you the number of protons plus neutrons in an atom. Therefore, the atomic mass, A, of hydrogen is 1. For helium A = 4.

Ions and Isotopes
So far we have only talked about electrically neutral atoms, atoms with no positive or negative charge on them. Atoms, however, can have electrical charges. Some atoms can either gain or lose electrons (the number of protons never changes in an atom). If an atom gains electrons, the atom becomes negatively charged. If the atom loses electrons, the atom becomes positively charged (because the number of positively charged protons will exceed the number of electrons). An atom that carries an electrical charge is called an ion. Listed below are three forms of hydrogen; 2 ions and the electrically neutral form.

H+ : a positively charged hydrogen ion H : the hydrogen atom H- : a negatively charged hydrogen ion


Neither the number of protons nor neutrons changes in any of these ions, therefore both the atomic number and the atomic mass remain the same. While the number of protons for a given atom never changes, the number of neutrons can change. Two atoms with different numbers of neutrons are called isotopes. For example, an isotope of hydrogen exists in which the atom contains 1 neutron (commonly called deuterium). Since the atomic mass is the number of protons plus neutrons, two isotopes of an element will have different atomic masses (however the atomic number, Z, will remain the same).

Two isotopes of hydrogen

Hydrogen
Atomic Mass = 1
Atomic Number = 1 Deuterium
Atomic Mass = 2
Atomic Number = 1


If you would like to explore the interaction of protons and electrons further, the University of Colorado's Physics 2000 site has an interesting experiment posted on line. At the Electrical Force page, you can place an electron next to a proton and see how the electron moves. You can even try to build your own atom (and see how difficult it is)!

An atom is the smallest building block of matter. Atoms are made of neutrons, protons and electrons. The nucleus of an atom is extremely small in comparison to the atom. If an atom was the size of the Houston Astrodome, then its nucleus would be the size of a pea.

* Introduction to the Periodic Table
* Charges in the Atom
* Atomic Models and the Quantum Numbers
* Determining Electron Configuration

Introduction to the Periodic Table
Scientists use the Periodic Table in order to find out important information about various elements. Created by Dmitri Mendeleev (1834-1907), the periodic table orders all known elements in accordance to their similarities. When Mendeleev began grouping elements, he noticed the Law of Chemical Periodicity. This law states, "the properties of the elements are periodic functions of atomic number." The periodic table is a chart that categorizes elements by "groups" and "periods." All elements are ordered by their atomic number. The atomic number is the number of protons per atom. In a neutral atom, the number of electrons equals the number of protons. The periodic table represents neutral atoms. The atomic number is typically located above the element symbol. Beneath the element symbol is the atomic mass. Atomic mass is measured in Atomic Mass Units where 1 amu = (1/12) mass of carbon measured in grams. The atomic mass number is equal to the number of protons plus neutrons, which provides the average weight of all isotopes of any given element. This number is typically found beneath the element symbol. Atoms with the same atomic number, but different mass numbers are called isotopes. Below is a diagram of a typical cells on the periodic table.

There are two main classifications in the periodic table, "groups" and "periods." Groups are the vertical columns that include elements with similar chemical and physical properties. Periods are the horizontal rows. Going from left to right on the periodic table, you will find metals, then metalloids, and finally nonmetals. The 4th, 5th, and 6th periods are called the transition metals. These elements are all metals and can be found pure in nature. They are known for their beauty and durability. The transition metals include two periods known as the lanthanides and the actinides, which are located at the very bottom of the periodic table. The chart below gives a brief description of each group in the periodic table.
Group 1A

* Known as Alkali Metals
* Very reactive
* Never found free in nature
* React readily with water

Group 2A

* Known as Alkaline earth elements
* All are metals
* Occur only in compounds
* React with oxygen in the general formula EO (where O is oxygen and E is Group 2A element)

Group 3A

* Metalloids
* Includes Aluminum (the most abundant metal in the earth)
* Forms oxygen compounds with a X2O3 formula

Group 4A

* Includes metals and nonmetals
* Go from nonmetals at the top of the column to metals at the bottom
* All oxygen form compounds with a XO2 formula

Group 5A

* All elements form an oxygen or sulfur compound with E2O3 or E2S3 formulas

Group 6A

* Includes oxygen, one of the most abundant elements.
* Generally, oxygen compound formulas within this group are EO2 and EO3

Group 7A

* Elements combine violently with alkali metals to form salts
* Called halogens, which mean "salt forming"
* Are all highly reactive

Group 8A

* Least reactive group
* All elements are gases
* Not very abundant on earth
* Given the name noble gas because they are not very reactive

Charges in the Atom
The charges in the atom are crucial in understanding how the atom works. An electron has a negative charge, a proton has a positive charge and a neutron has no charge. Electrons and protons have the same magnitude of charge. Like charges repel, so protons repel one another as do electrons. Opposite charges attract which causes the electrons to be attracted to the protons. As the electrons and protons grow farther apart, the forces they exert on each other decrease.

Atomic Models and the Quantum Numbers
There are different models of the structure of the atom. One of the first models was created by Niels Bohr, a Danish physicist. He proposed a model in which electrons circle the nucleus in "orbits" around the nucleus, much in the same way as planets orbit the sun. Each orbit represents an energy level which can be determined using equations generated by Planck and others discussed in more detail below. The Bohr model was later proven to be incorrect, but provides a useful model for building an explanation.

The "accepted" model is the quantum model. In the quantum model, we state that the electron cannot be found precisely, but we can predict the probability, or likelihood, of an electron being at some location in the atom. You should be familiar with quantum numbers, a series of three numbers used to describe the location of some object (like an electron) in three-dimensional space:

1. n: the principal quantum number, an integer value (1, 2, 3...) that is used to describe the quantum level, or shell, in which an electron resides. The principal quantum number is the primary number used to determine the amount of energy in an atom. Using one of the first important equations in atomic structure (developed by Niels Bohr), we can calculate the amount of energy in an atom with an electron at some value of n:

En = -
Rhc

n2
where:
R = Rydberg constant, a value of 1.097 X 107 m-1
c = speed of light, 3.00 X 108 m/s
h = Planck's constant, 6.63 X 10 -34 J-s
n = principal quantum number, no unit

For example, how much energy does one electron with a principal quantum number of n= 2 have?

En = -
Rhc

n2
or
En = -
(1.097x107 m-1 ∗ (6.63x10-34 J•s)∗(3.0x108 m•s-1)

22
= 5.5x10-19 J

You might ask, well, who cares? In addition to the importance of knowing how much energy is in an atom (a very important characteristic!), we can also derive, or calculate, other information from this energy value. For example, can we see this energy? The table below suggests that we can. For example, suppose that an electron starts at the n=3 level (we'll call this the excited state) and it falls down to n=1 (the ground state). We can calculate the change in energy using the equation:

ΔE = hv = RH
1

ni2
-
1

nf2


Where:
ΔE = change in energy (Joules)
h = Planck's constant with a value of 6.63 x 10-34 (J-s)
ν is frequency (s-1)
RH is the Rydberg constant with a value of 2.18 x 10-18J.
ni is the initial quantum number
nf is the final quantum number

Using the equation below, we can calculate the wavelength and the frequency of the energy. The wavelength and the frequency give us information about how we might "see" the energy:

vλ = c
Where:
ν = the frequency of radiation (s-1)
λ = the wavelength (m)
c = the speed of light with a value of 3.00 x 108 m/s in a vacuum

Speed of light = 3.00E+08
Rydberg constant = 2.18E-18
Planck's constant = 6.63E-34

Excited state, n = 3 4 5
Ground state, n = 2 2 2
Excited state energy (J) 2.42222E-19 1.363E-19 8.72E-20
Ground state energy (J) 5.45E-19 5.45E-19 5.45E-19
ΔE = -3.02778E-19 -4.09E-19 -4.58E-19
ν = 4.56678E+14 6.165E+14 6.905E+14
λ(nm) = 656.92 486.61 434.47

2. l ("el", not the number 1): the azimuthal quantum number, a number that specifies a sublevel, or subshell, in an orbital. The value of the azimuthal quantum number is always one less than the principal quantum number n. For example, if n=1, then "el"=0. If n=3, then l can have three values: 0,1, and 2. The values of l are typically not identified as "0, 1, 2, and 3" but are more commonly called by their historic names, "s, p, d, and f", respectively. Since the quantum numbers were discovered through the study of light and lines on an electromagnetic spectra, chemists identified the lines by their quality: sharp, principal, diffuse and fundamental. The table below shows the relationship:

Value of l Subshell designation
0 s
1 p
2 d
3 f

3. m: the magnetic quantum number. Each subshell is composed of one or more orbitals. In the study of light, it was discovered that additional lines appeared in the spectra produced when light was emitted in a magnetic field. The magnetic quantum number has values between -l and +l. When l =1, for example, m can have three values: -1, 0, and +1. Because you know from the chart above that the subshell designation for l =1 is "p", you now know that the p orbital has three components. In your study of chemistry, you will be presented with px, py, and pz. Notice how the subscripts are related to a three-dimensional coordinate system, x, y, and z. The chart below shows a summary of the quantum numbers:

Principal Quantum Number (n) Azimuthal Quantum Number (l) Subshell Designation Magnetic Quantum Number (m) Number of orbitals in subshell
1 0 1s 0 1
2 0
1 2s
2p 0
-1 0 +1 1
3
3 0
1
2 3s
3p
3d 0
-1 0 +1
-2 -1 0 +1 +2 1
3
5
4 0
1
2
3 4s
4p
4d
4f 0
-1 0 +1
-2 -1 0 +1 +2
-3 -2 -1 0 +1 +2 +3 1
3
5
7

Chemists care about where electrons are in an atom or a molecule. In the early models, we believed that electrons move like billiard balls, and followed the rules of classical physics. The graphic below attempts to show that earlier models thought that we could identify the exact path, position, velocity, etc. of an electron or electrons in an atom:

A more accurate picture is that the electron(s) reside in a "cloud" that surrounds the nucleus of the atom. This concept is shown in the graphic below:

Chemists are interested in predicting the probability that the electron will be at some particular part of this cloud. The cloud is better known as an orbital, and comes in several different types, or shapes. Atomic orbitals are known as s, p, d, and f orbitals. Each type of atomic orbital has certain characteristics, such as shape. For example, as the graphic below shows, an s orbital is spherical in shape:

On this graph, the horizontal (x) axis represents the distance from the nucleus in units of a0, or atomic units. The value of a0 is 0.0529 nanometers (nm). The vertical (y) axis represents the probability density. What you should notice is that as the electron moves farther away from the nucleus, the probability of its being found at that distance decreases. In other words, the electron prefers to hang around close to the nucleus.

The three graphics below show some other orbitals. The first graph (top left) is of a "2s" orbital. Each "s" orbital can hold two electrons in its cloud. Notice how there is a relatively high probability of an electron being near the nucleus, then some space where the probability is close to zero, then the probability increases substantially at some distance from the nucleus. The graphic at the top right shows a "2p" atomic orbital. Orbitals that are "p" orbitals can hold up to six (6) electrons in their cloud. Notice its "dumbbell" or "figure of eight" shape. At the bottom left is a "3s" orbital. Again, notice its spherical shape. Finally, at the bottom right, is a "3p" orbital.


Determining Electron Configuration
One of the skills you will need to learn to succeed in freshman chemistry is being able to determine the electron configuration of an atom. An electron configuration is basically an account of how many electrons there are, and in what orbitals they reside under "normal" conditions. For example, the element hydrogen (H) has one electron. We know this because its atomic number is one (1), and the atomic number tells you the number of electrons. Where does this electron go? The one electron of hydrogen goes into the lowest energy state it possibly can, which means it will start at "level" one and goes into "s" orbitals first. We say that hydrogen has a "[1s1]" electron configuration. Looking at the next element on the Periodic Table --helium, or He -- we see it has an atomic number of two, so two electrons. Since " s" orbitals can hold up to two electrons, helium has an electron configuration of "[1s2]".

What about larger atoms? Let's look at carbon, with an atomic number of 6. Where do its 6 electrons go?

* First two: 1s2
* Next two: 2s2
* Last two: 2p2

We can therefore say that carbon has the electron configuration of "[1s22s22p2]".

The table below shows the subshells, the number of orbitals, and the maximum number of electrons allowed:

Subshell Number of Orbitals Maximum Number
of Electrons
s 1 2
p 3 6
d 5 10
f 7 14

The Abridged (shortened) Periodic Table below shows the electron configurations of the elements. Notice for space reasons we sometimes leave off a portion of the electron configuration. For example, look at argon (Ar), element 18. The table below shows its electron configuration as "[3s23p6]" (remembering that "p" orbitals can hold up to six (6) electrons). Its actual electron configuration is:

Ar = [1s22s22p63s23p6]

Sometimes you will see the notation: "[Ne]3s23p6", which means to include everything that is in neon (Ne, 10) plus the stuff in the "3"-level orbitals.

Try It Out

1. What is the frequency of infrared radiation that has a wavelength of 1.25 x 103 nm?

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