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Pauli Exclusion Principle

An orbital can hold 0, 1, or 2 electrons only, and if there are two electrons in the orbital, they must have opposite (paired) spins. Therefore, no two electrons in the same atom can have the same set of four Quantum Numbers. 

incorrect;electrons must spn in opposite directions

correct; the electrons have opposite spins 

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. 

atom	orbital box diagram
B	1s	2s	2p
C	1s	2s	2p
N	1s	2s	2p
O	1s	2s	2p
F	1s	2s	2p
Cl	1s	2s	2p	3s	3p
Mn	1s	2s	2p	3s	3p	4s

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. 

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.