Arrangement of Electrons in Atoms – Chapter 4

Quantum Numbers– aka Where is an electron located in an atom?


The main thing which distinguishes one atom from another is the number of protons in its nucleus (and the number of electrons in orbit around the nucleus).


Atoms are arranged on the periodic table according to their similar properties.  You can read the periodic table like a book, from left to right and down the “page”.  Each atom has one more proton and one more electron than the one before it.  Remember that the number of protons/electrons are indicated by the atomic number of the atom.  The mass number of an atom represents the number of protons PLUS the number of neutrons.


Chemists assign the position of electrons around the nucleus of an atom by giving them numbers as an address.  For example, a person can be found by his/her address:  101 Main St., San Clemente, CA 92167.  In your address is your street number, your street, your city, your state and your zip code.  Chemists use Quantum Numbers (there are four of them) n,l,m and s to describe the address of an electron.

Read pages 101-104 on the 4 quantum numbers

Principal Quantum Number (n):  As you know, atoms are surrounded by electrons in a series of “ringed orbits” known as energy levels.  While these levels are not exactly similar to planets revolving around the sun, that analogy will work for the time being (just realize that electrons are not EXACTLY like planets revolving around the sun). 

     The Principal Quantum Number (n) tells you how many electrons TOTAL can be held in any one energy level.  For any energy level, the number of electrons which can be held inside is 2n2.  For example, in the 1st energy level, there can be 2(1)2 = 2 electrons.  In the 2nd energy level, there can be 2(2)2 = 8 electrons.  Can you figure out how many electrons should be in the following energy levels:  3, 4, 5, 6, 7?

     The letter n represents the energy level of an electron in an atom.  So, if you know the numerical value for n, then you know in which energy level the electron is in (kind of like knowing what State a person is in – it helps narrow it down a little, but not completely).


Angular Momentum Quantum Number (l):    This quantum number represents the shape of the orbital in which the electron is held in the energy level.  Wow, that’s a mouthful!  Each energy level has some sublevels.  These sublevels contain the electrons and are classified by a number represented by the Second Quantum Number (l).

     One of these sublevels is called: s.  Another is called: p.  The others are d and f. 

  The letter (l) tells you which sublevel you are talking about: (see table 4-1 p. 102)

If l = 0 then you are talking about the s sublevel

If l = 1 then you are talking about the p sublevel

If l = 2 then you are talking about the d sublevel

If l = 3 then you are talking about the f sublevel

The s sublevel can hold 2 electrons

The p sublevel can hold 6 electrons

The d sublevel can hold 10 electrons

The f sublevel can hold 14 electrons

     All of the sublevels allow the electrons to surround the nucleus of an atom in a spherical shape.  However, each sublevel is made up of smaller parts (known as orbitals) which are different shapes – but when you put all of the orbital shapes together, you get essentially a sphere.

     The principal quantum number (n) also tells you how many sublevels are possible for an atom.  Whatever n is equal to is the number of sublevels you can have.  Therefore, an atom with an n=1 can have an s sublevel only.  An atom with an n=2 can have an s and a p sublevel.  An atom with an n=3 can have an s and a p and an d sublevel.  Mathematically speaking, the highest (l) value for any atom is (n-1).  Example:  Hydrogen has an (n=1).  So, (n-1 = 0) and then hydrogen can only have an s sublevel.

     This should make sense if only because as an atom gains energy levels, it gains space in which to put electrons.  With more open space, there is more room for more sublevels.

     Think of this sublevel as knowing what “city” an electron is in.


Magnetic Quantum Number (m):  Each sublevel is made up of smaller parts known as orbitals.  Each orbital can hold a maximum of two electrons. 

            In the s sublevel, there is one orbital.

In the p sublevel, there are three orbitals.

In the d sublevel, there are five orbitals.

In the f sublevel, there are seven orbitals.

If you remember that each orbital can hold two electrons, this should make some more sense.  Remember that s can hold 2 electrons, p can hold 6, d can hold 10 and f can hold 14.

     Look on page 101 to see what the s sublevel looks like and p. 103 for what the p sublevel looks like.  You should see that the s sublevel is a simple sphere.  But the p sublevel is broken up into three “figure 8” looking objects (called orbitals) along the x,y and z axis.  Notice that when you stick all of the p orbitals together you also get a sphere.  The 5 d orbitals are on p. 103 also.

     The third quantum number (m) tells you in which orbital an electron is in.

For the s sublevel, m= 0 (because there is only one orbital)

For the p sublevel, m= -1, 0 1 (because there are three orbitals)

For the d sublevel, m= -2, -1, 0, 1, 2 (because there are five orbitals)

For the f sublevel, m= -3, -2, -1,  0, 1, 2, 3 (because there are seven orbitals)

     Think of this quantum number as being the street upon which you live.


Spin Quantum number (s):  No two electrons can have the exact same set of quantum numbers.  With the quantum number (m) you can find the “street” of the electron, but more than one electron can live on that street.  This final quantum number will give us the exact street address of each electron.  The s quantum number represents the spin of an electron.  As two electrons occupy the same orbital, they must spin in opposite directions – either clockwise or counter-clockwise.

   The possible values for s are +1/2 and –1/2.


The order in which the sublevels fill:  Look on page 105 to see how the energy levels fill.  Copy the black vertical axis entitled “Energy”(fig. 4-16) which shows the order of energy levels filling; you will have to know the order in which the levels fill.  Remember the octet rule?  Notice that before the 4s sublevel, the 3s and 3p sublevels are filled.  That means that there are already 8 electrons in the 3rd energy level before the 4th energy level receives some electrons.

Periodic Law – Chapter 5

How the periodic table’s  design complements quantum theory


     Okay, now we know how to find where an electron is located in an atom.  But, how can we arrange atoms on the periodic table to group them in a useful way?  As it turns out, the most practical way to do it is to arrange elements both vertically and horizontally.


How the elements are arranged vertically:  Elements have similar properties if they have a similar electron configuration in their valence energy level.  As a result, we put the elements with the same number of valence electrons in the same vertical column. 

     For example, draw the electron configuration of the following elements (use arrows)






     What do you notice about these three elements which is similar?  Now try three others






      What do you notice about these three elements which is similar?  Where do you find these three elements in relation to each other on the periodic table?


     Elements in the same vertical column on the periodic table are said to belong to the same group or also known as a family.  Some of these groups have names.  The first column on the table are the Alkali metal family (the only exception is Hydrogen which is not a metal).  The second column are the Alkaline Earth metals.  The Chlorine group is called Halogens and the Helium group are called Noble gasses.  The elements in the center of the table are called Transition metals. The periodic table is broken up into s,p,d and f sublevels (fig 5-5 p. 129).


     You should also know that elements on the left side of the chart are called metals (with the exception of Hydrogen).  And, as the name says, they can do things like conduct electricity, they appear shiny (eg. metalic looking), and they tend to give up their electrons in chemical reactions.

     Elements on the right side of the chart are called non-metals and if you look at the periodic table on page 130-131, you will see an orange “staircase” line which defines the separation between metals and non-metals.  Notice that carbon, nitrogen and oxygen are non-metals (as is Hydrogen).  This is why humans are not metalic.  We care carbon based creatures made mainly of C, N, H, and O.  Non-metals gain electrons in a reaction.  Metals give away electrons in a reaction.  The orange elements are metalloids and you must memorize these elements.


Horizontal Grouping of Elements:  Basically, elements are grouped in horizontal rows according to atomic number.  As you read from left to right, the elements increase in atomic number by one.  This horizontal grouping is called the period of an atom.

     But you should also notice that all of the elements in the first period (H and He) have only one energy level.  All of the elements in the second row have 2 energy levels.  All of the elements in the third row have 3 energy levels….etc.

     But wait a minute…..  The transitional elements in the fourth row are filling their 3d energy level and sublevel.  What’s the deal?  The deal is the transitional elements in the fourth row have an outermost energy level #4.  The same is true for the Lantanide series down at the bottom of the chart.  They are really associated with the 6th period.  The Actinide series is associated with the 7th period.


Atomic radii:  Look on page 141 table 5-13 and you will see the trends in the size of an atoms as you look at the periodic table.  Typically, elements on the left hand side of the chart are bigger than on the right side.  Typically, elements at the bottom of the chart are bigger than elements on the top of the chart.  Why?

      Elements in the same period have the same number of energy levels.  An element like Lithium has two energy levels.  So does Fluorine.  But Fluorine has 9 protons in its nucleus pulling on the 7 electrons in the second energy level.  Lithium only has 3 protons pulling on its one electron in the second energy level.  The pull of those 9 protons is much greater than the pull of those 3 protons.  Therefore, Fluorine is a smaller atom than Lithium.  Atomic radii therefore decreases going left to right on the chart.

     As you go down the chart, the atoms get bigger just because they have more electrons in their energy levels.  (do sample problem 5-5 on p. 142)


Ionization energy trends on the Periodic Table:  Look on page 143 at figure 5-15 and you will see the ionization energy trends of the different elements.  Ionization energy is the amount of energy needed to make an atom let go of its outermost electron.  As you can probably tell, Noble gasses don’t want to give them up easy, but Alkali Metals do.

     Atoms on the left side of the chart have less than four electrons and therefore want to give up electrons (low ionization energy).  Atoms on the right side of the chart have more than four electrons and would rather gain electrons to get a full octet (therefore, they have a high ionization energy as they do not want to lose the electrons they currently have.)  Therefore, ionization energy increases as you go from left to right on the chart.

     As you go down the chart, the outermost electrons are further away from the pull of the central nucleus’ protons.  Therefore, it is easier to remove them and atoms at the bottom part of the chart have lower ionization energies than those at the top.  (do sample problem 5-6 on p. 146)


Ion radii:  Look on p. 149 and at Fig. 5-19.  An ion is a charged atom which has either lost electrons (making it positive) or gained electrons (making it negative).  Example:  The ion of Na is Na+1.  The ion of Mg is Mg+2.  The ion of Cl is Cl-1…etc.  You know many ions already.

     When an atom loses an electron, it is called a Cation and becomes Positive.  When an atom gains an electron, it is called an Anion and becomes Negative.

     As you go from left to right on the chart, the ion radii size will decrease for cations (atoms that lose electrons).  This is because as electrons are removed from their orbits, the protons left in the nucleus hold the electron cloud tighter.  (Example:  Na has 11 p and 11 e.  It gives away 1 e and then has 11 ps to pull on 10 e’s.  But, Mg has 12 p and 12 e.  It gives away 2 e’s and then has

12 ps to pull on 10 e’s.  Therefore, Mg is able to pull its electron cloud closer to it than Na.

      As you go from left to right on the chart, the ion radii size will decrease for anions (atoms that gain electrons).  This is because the ratio of electrons:protons is smaller on the right (example:  18 electrons: 17 protons for Cl-, but 18 electrons: 16 protons for S-2.  Sulfur’s 16 protons cannot hold those 18 electrons as close to its nucleus as can Cl with its 17 protons.

     As you go down the chart, ion radii size increases because there are more energy levels.


Electronegativity: Look on p. 151 figure 5-20.  Electronegativity is a measure of the ability of an atom to attract electrons.  As you go left to right on the chart, electronegativity increases (because in gaining 1 electron, Cl gets an octet, but it takes 2 electrons for S to become an octet.)  As you go down the chart, electronegativity decreases (because distance from nucleus increases)

(do sample problem 5-7 on p. 152)