Chapter 7 schrodinger2003

.The Onset of Quantum theory: by Dr. Robert D. Craig, Ph.D.

In 1934, Schrödinger lectured at Princeton University; he was offered a permanent position there, but did not accept it (just like “Will Hunting!!!)

•!

What does this remind You of???

Let’s begin

I Claim . . . . .

Today’s Agenda

• More on Schrodinger (Who was He?• Use other power point for history@@@• More about his Cat!• More Quantum numbers• Hund’s Rule • Pauli Exclusion principle• Aufbah principle

We all make final together-2 questions

I have a sample with me!!!!

. Dr Poget – said you may see him!

• Dr Poget is free after this class-in office!!• Would like to here from students after this

class!

Much of what we know now!!!Gold nanoparticles

.• In 1934, Schrödinger lectured at Princeton University; he was offered a permanent position there, but did not accept it (just like “Will Hunting!!!)

• Let’s look at what was going on at the time!

A SECOND ORDER DIFFERENTIAL EQUATION

FOR OUR PURPOSES

• Principle quantum number (n)Azimuthal quantum number (l)Magnetic quantum number (m)Spin quantum number (s)

LITHIUM SYSTEM

• Electron 1: N =1, L=0, Ml= 0 , Ms = +1/2• Electron 2: N =1, L=0, Ml= 0 , Ms = -1/2• Electron 3: N =2, L=0, Ml= 0 , Ms = +1/2

Pauli Exclusion Principle

• Pauli Exclusion Principle• The second major fact to keep in mind is the

Pauli Exclusion Principle which states that no two electrons can have the same four quantum numbers. The first three (n,l, and ml) may be similar but the fourth quantum number must be different. We are aware that in one orbital a maximum of two electrons can be found and the two electrons must have opposing spins.

Pauli Exclusion Principle

• That means one would spin up ( +1/2) and the other would spin down (-1/2). This tells us that each subshell has double the electrons per orbital. The s subshell has 1 orbital that can hold to 2 electrons, the p subsheel has 3 orbitals that can hold up to 6 electrons, the d subshell has 5 oribtals that hold up to 10 electro

BERYLLIUM

• Electron 1: N =1, L=0, Ml= 0 , Ms = +1/2• Electron 2: N =1, L=0, Ml= 0 , Ms = -1/2• Electron 3: N =2, L=0, Ml= 0 , Ms = +1/2• Electron 4: N =2, L=0, Ml= 0 , Ms = +1/2

BORON

• Electron 1: N =1, L=0, Ml= 0 , Ms = +1/2• Electron 2: N =1, L=0, Ml= 0 , Ms = -1/2• Electron 3: N =2, L=0, Ml= 0 , Ms = +1/2• Electron 3: N =2, L=0, Ml= 0 , Ms = +1/2• Electron 3: N =2, L=1, Ml= 0 , Ms = +1/2

BORON

• Because the 1s and 2s orbitals are filled the fifth electron has to be assigned to a p-orbital

Elements 3A to 8A- p block

Carbon is sp3 hybridized

CARBON –IS THE MOST INTERESTINGlast time!!!

• Electron 1: N =1, L=0, Ml= 0 , Ms = +1/2• Electron 2: N =1, L=0, Ml= 0 , Ms = -1/2• Electron 3: N =2, L=0, Ml= 0 , Ms = +1/2• Electron 4: N =2, L=0, Ml= 0 , Ms = +1/2• Electron 5: N =2, L=1, Ml= 1 , Ms = +1/2• Electron 6: N =2, L=1, Ml= -1 , Ms = +1/2

Some thing interesting now happens

Orbitals mix to lower energy

• An explaination is that the s and 3 p atomic orbitals have "mixed" to form 4 new hybrid orbitals

Lower energy system-all ns2 np2 elements can do this

SO –IS NITROGEN- ns2 nsp3it follows Hunds rule

• Hund's rule: every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin

Nitrogen

• Electron 1: N =1, L=0, Ml= 0 , Ms = +1/2• Electron 2: N =1, L=0, Ml= 0 , Ms = -1/2• Electron 3: N =2, L=0, Ml= 0 , Ms = +1/2• Electron 4: N =2, L=0, Ml= 0 , Ms = +1/2• Electron 5: N =2, L=1, Ml= 1 , Ms = +1/2• Electron 6: N =2, L=1, Ml= 0 , Ms = +1/2• Electron 7: N =2, L=1, Ml= -1 , Ms = +1/2

Nitrogen

• . Atoms at ground states tend to have as many unpaired electrons as possible.

As far apart as possible and lined up

• When visualizing this processes, think about how electrons are exhibiting the same behavior as the same poles on a magnet would if they came into contact;

• as the negatively charged electrons fill orbitals they first try to get as far as possible from each other before having to pair up.

Example

• If we look at the correct electron configuration of Nitrogen (Z = 7), a very important element in the biology of plants: 1s2 2s2 2p3

In ammonia-the molecular shape is

Oygen

• Oxygen (Z = 8) its electron configuration is: 1s2 2s2 2p4

• Oxygen has one more electron than Nitrogen and as the orbitals are all half filled the electron must pair up

The Aufbau Process

• Aufbau comes from the German word "Aufbauen" which means "to build". When writing electron configurations, we are building up electron orbitals as we proceed from atom to atom.

• However, there are some exceptions to this rule

*Examples

• If we follow the pattern across a period from B (Z=5) to Ne (Z=10) the number of electrons increase and the subshells are filled.

• Here we are focusing on the p subshell in which as we move towards Ne, the p subshell becomes filled.

In order

• B (Z=5) configuration: 1s2 2s2 2p1

• C (Z=6) configuration:1s2 2s2 2p2

• N (Z=7) configuration:1s2 2s2 2p3

• O (Z=8) configuration:1s2 2s2 2p4

• F (Z=9) configuration:1s2 2s2 2p5

• Ne (Z=10) configuration:1s2 2s2 2p6

Aufbah order

True picture is orbital levels adjust themselves- due to sheilding

Rules for Assigning Electron Orbitals

• The order of levels filled would look like this: • 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f,

5d, 6p, 7s, 5f, 6d, and 7p

Exceptions to Electron Configuration Trends

• The reason these exceptions occur is because some elements are more stable with less electrons in some subshells and more electrons within others. A list of the exceptions to the Aufbau process can be found below

Period 4:

• Chromium: Z:24 [Ar] 3d54s1

• Copper: Z:27 [Ar] 3d104s1

Chromium:

• Chromium: Z:24 [Ar] 3d54s1

Copper

• Copper: Z:27 [Ar] 3d104s1

• Example: In the following configuration, • Cu: [Ar]4s23d9, copper's d shell is just one

away from stability, and therefore, one electron from the s shell jumps into the d shell: [Ar]4s13d10. This way, the d shell is full, and is therefore stable, and the s shell is half full, and is also stable.

The more stable configurationthis is less stable!!

Most stable configurations####

• Chromium has a configuration of [Ar]4s13d5,• The stability rule applies to atoms in the same

group as chromium and copper.• If one of these atoms has been ionized, that is,

it loses an electron, it will come from the s orbital rather than the d orbital.

• the configuration of Cu+ is [Ar]4s03d10.

Loss of outer electrons

• If one of these atoms has been ionized, that is, it loses an electron, it will come from the s orbital rather than the d orbital. For instance, the configuration of Cu+ is [Ar]4s03d10. If more electrons are removed, they will come from the d orbital

Magnetism

On final

• The spin of an electron creates a magnetic field (albeit ridiculously weak), so unpaired electrons create a small magnetic field. Paired electrons have opposite spin, so the magnetic fields cancel each other out, leading to diamagnetism.

3 terms on final

• Diamagnetism is actually a very weak repulsion to magnetic fields. All elements have diamagnestism to some degree. It occurs when there are pair electrons.

• Paramagnetism is an attraction to external magnetic fields. It is also very weak. It occurs whenever there is an unpaired electron in an orbital.

• Ferromagnetism is the permanent magnetism that we encounter in our daily lives. It only occurs with three elements: iron (Fe), nickel (Ni), and cobalt (Co).

Period 5:

• Niobium: Z:41 [Kr] 5s1 4d4

• Molybdenum: Z:42 [Kr] 5s1 4d5

• Ruthenium: Z:44 [Kr] 5s1 4d7

• Rhodium: Z:45 [Kr] 5s1 4d8

• Palladium: Z:46 [Kr] 4d10

Writing Electron Configurations

• When writing the electron configuration we first write the energy level (the period) then the subshell to be filled and the superscript, which is the number of electrons in that subshell. The total number of electrons as mentioned before is the atomic number, Z. Using the rules from above, we can now start writing the electron configurations for all the elements in the periodic table.

Methods

• There are three main methods used to write electron configurations: orbital diagrams, spdf notation, and noble gas notation. Each method has its own purpose and each has its own drawbacks.

Orbital Diagrams

• As seen in some examples above, the orbital diagram is a visual way to reconstruct the electron configuration by showing each of the separate orbitals and the spins on the electrons. This is done by first determining the subshell (s,p,d, or f) then drawing in each electron according to the stated rules above.

Example

• Electron configuration for aluminum. • If we look at the periodic table we can see

that its in the p-block as it is in group 13. Now we shall look at the orbitals it will fill: 1s, 2s, 2p, 3s, 3p. We know that aluminum completely fills the 1s, 2s, 2p, and 3s orbitals because mathematically this would be 2+2+6+2=12.

Example

• The block that the atom is in (in the case for aluminum: 3p) is where we will count to get the number of electrons in the last subshell (for aluminum this would be one electron because its the first element in the period 3 p-block).

Aluminum system

• From this we can construct the following:• Note that in the orbital diagram

• Note that in the orbital diagram• Note that in the orbital diagram, the two

opposing spins of the electron can be seen. This is why it is sometimes useful to think about electron configuration in terms of the diagram

Filling orbitals: In action

• http://en.wikibooks.org/wiki/General_Chemistry/Filling_Electron_Shells

Electron Notation using spdf

• 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d1

Electron Notation using spdf

• This is a much simpler and efficient way to portray electron configuration of an atom. A logical way of thinking about it is that all we have to do is to fill orbitals as we move across a period and through orbital blocks

Electron Notation using spdf

• As we move across we simply count how many elements fall in each block. We know that yttrium is the first element in the fourth period d-block, thus this corresponds to one electron in the that energy level. To check our answer we would just add all the superscripts to see if we get the atomic number. In this case 2+2+6+2+6+2+10+6+2+1= 39 and Z=39 thus we have the correct answer.

Electron Notation using spdf

• Example• Vanadium (V, Z=23) lies in the transition metals

at the four period in the fifth group. The noble gas before it is argon, (Ar, Z=18) and knowing that vanadium has filled those orbitals before it, we will use argon as our reference noble gas. We denote the noble gas in the configuration as the symbol, E, in brackets: [E] configuration:

• Vanadium, V: [Ar] 4s2 3d3

.

Electron Configurations of Ions

• Writing electron configurations for ions, whether it be cation or anion, is basically exactly the same as writing them for normal elements. All the same rules apply, except you must take into account the gained or lost electrons. For instance, when Potassium (K) loses an electron it becomes K+ and has the noble gas configuration of [Ar].

electron configuration

• K ([Ar]4s1) --> K+([Ar]) + e-

Therefore, the electron configuration for the K+ ion is simply [Ar]

• When an atom, such as Chlorine (Cl) gains an electron, it becomes Cl- and also has the electron configuration of [Ar].

• Cl ([Ne]3s23p5) + e- --> Cl- ([Ar])Yet again, the electron configuration is [Ar]

• For more complex ionic electron configurations, such as an ion from the transition metals, the answer isn't always a noble gas. Take Iron (Fe). The most common irons for Iron are Fe2+ and Fe3+. Lets focus on Fe2+.

• Fe ([Ar]3d64s2) --> Fe2+ ([Ar]3d6) - 2e-

Here Iron loses two electrons. So thats two less electrons to fill orbitals. When you backtrack

two electrons in Fe's original electron configuration you get [Ar]3d6 as Fe2+'s new configuration

• When writing the electron configuration for ions, treat it like any normal element. Just remember to simply add or subtract the gained or lost electrons when filling out shells.

7.4 an 7.5

• Finish electron config of ions

•Put power point in portal for home work•Give problems to collect

monday

Sec 7.5

• Atomic properties and periodic trends

H.W

• 7.3, 7.6, 7.7, 7.11, 7.17, 7.19****• Please sytop here

For next week

• 7.37, 7.40***• 7.43,m7.44,

AGO TO TEXT BOOK

• 3 topics

• Atomic radius• Ionic radius• Ionization energy