Quantum Theory Schrodinger Heisenberg PC1144/PC1144%20Lectures/lecture16.ppt 206%20presentation.ppt.

Quantum Theory

Schrodinger Heisenberg

http://staff.science.nus.edu.sg/~PC1144/PC1144%20Lectures/lecture16.ppt

http://www.colby.edu/chemistry/CH141F/Chapter%206%20presentation.ppt

The Quantum Mechanical Model

• Energy is quantized. It comes in chunks.

• A quanta is the amount of energy needed to move from one energy level to another.

• Since the energy of an atom is never “in between” there must be a quantum leap in energy.

• Schrodinger derived an equation that described the energy and position of the electrons in an atom

08

2

2

2

2

2

2

2

2

Eh

m

zyx

• Heisenberg Uncertainty Principle---it is impossible to know both the exact position and momentum of an object at the same time.

• Can’t know position if e- is moving.

• Can’t know momentum if e- is not moving.


• Has energy levels for electrons.

• Orbits are not circular.

• It can only tell us the probability of finding

an electron a certain distance from the nucleus.


• The atom is found inside a blurry “electron cloud”

• A area where there is a chance of finding an electron.

• Draw a line at 90 %


Schrodinger’s Quantum #’s• (n) Principal quantum #

n = 1, 2, 3 … -1

– the energy level of the electron.

– Formula: 2(n)2 = # of electrons per energy level

• (l) Azimuthal or Secondary quantum #l = 0,1, 2, (n-1)

– the sublevels or shape within an energy level.

– s,p,d,f (names of sublevels)

– s,p,d, & f each have a unique shape.

Quantum #’s (cont.)• (ml) magnetic quantum #

ml = +l .. 0 .. –l (2l +1) = total orbitals– regions where there is a high probability of finding

an electron– each orbital can hold 2 e-

• (ms) spin quantum #ms = +1/2 or –1/2

– in each orbital there can be up to 2 electrons spinning in opposite directions.

– Clockwise +1/2 Counter clockwise –1/2

Quantum Numbers

n Principle n = 1, 2, 3, 4 … (-1)

l Azimuthal l = 0, 1, 2, 3 … (n-1)

m l Magnetic m l = +l ..+2,+l, 0,. –l, -2.. -l

ms Spin ms = +1/2 or –1/2

s p d f

Arrangement of Arrangement of Electrons in AtomsElectrons in Atoms

Arrangement of Arrangement of Electrons in AtomsElectrons in Atoms

Electrons in atoms are arranged asElectrons in atoms are arranged as

LEVELS (n)LEVELS (n)

SUBLEVELS (l)SUBLEVELS (l)

ORBITALS (mORBITALS (mll))

Energy LevelsEnergy LevelsEnergy LevelsEnergy Levels

• Each energy level has a number Each energy level has a number called thecalled the PRINCIPAL QUANTUM PRINCIPAL QUANTUM NUMBER, nNUMBER, n

• Currently n can be 1 thru 7, because Currently n can be 1 thru 7, because there are 7 periods on the periodic there are 7 periods on the periodic tabletable

Energy LevelsEnergy LevelsEnergy LevelsEnergy Levelsn = 1n = 1

n = 2n = 2

n = 3n = 3

n = 4n = 4

Orbitals and the Orbitals and the Periodic TablePeriodic Table

• Orbitals grouped in s, p, d, and f orbitals Orbitals grouped in s, p, d, and f orbitals (sharp, proximal, diffuse, and fundamental)(sharp, proximal, diffuse, and fundamental)

s orbitalss orbitalsp orbitalsp orbitals

d orbitalsd orbitals

f orbitalsf orbitals

• 1 s orbital for every energy level

• Spherical shaped

• Each s orbital can hold 2 electrons

• Called the 1s, 2s, 3s, etc.. orbitals.

s orbitals

1s2s

3s

p orbitals• Start at the second energy level

• 3 different directions

• 3 different shapes

• Each can hold 2 electrons

d orbitals• Start at the third energy level

• 5 different shapes

• Each can hold 2 electrons

f orbitals

• Start at the fourth energy level

• Have seven different shapes

• 2 electrons per shape

f orbitals

Summary

s

p

d

f

# of orbitals

Max electrons

Starts at energy level

1 2 1

3 6 2

5 10 3

7 14 4

Number of Electrons that can be held in each orbital

• s = 2 e-

• p = 6 e-

• d = 10 e-

• f = 14 e-

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

Electron Configurations• The way electrons are arranged in atoms.• Aufbau principle- electrons enter the lowest

energy first.– This causes difficulties because of the overlap of orbitals

of different energies.

• Pauli Exclusion Principle- at most 2 electrons per orbital - different spins

• Hund’s Rule- When electrons occupy orbitals of equal energy they don’t pair up until they have to .

Electron Configuration

• Let’s determine the electron configuration for Phosphorus (P)

• Need to account for 15 electrons

• The first to electrons go into the 1s orbital

• Notice the opposite spins

• only 13 more

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The next electrons go into the 2s orbital

• only 11 more

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The next electrons go into the 2p orbital

• only 5 more

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The next electrons go into the 3s orbital

• only 3 more

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The last three electrons go into the 3p orbitals.

• They each go into seperate shapes

• 3 upaired electrons

• 1s22s22p63s23p3

The easy way to remember

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2

• 2 electrons

Fill from the bottom up following the arrows

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2

• 4 electrons


1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

• 12 electrons


1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2

• 20 electrons


1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2 3d10 4p6

5s2

• 38 electrons


1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2 3d10 4p6

5s2 4d10 5p6 6s2

• 56 electrons


1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2 3d10 4p6

5s2 4d10 5p6 6s2

4f14 5d10 6p6 7s2

• 88 electrons


1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2 3d10 4p6

5s2 4d10 5p6 6s2

4f14 5d10 6p6 7s2

5f14 6d10 7p6 • 108 electrons

Effective Nuclear Charge•Electrostatic repulsion between negatively charged electrons

•Influences the energies of the orbitals.

•The effect of repulsion is described as screening or shielding.

•The combined effect of attraction to the nucleus and repulsion from other electrons gives an effective nuclear charge, Zeff, which is less than that of the ‘bare’ nucleus.

+++

++

Zeff = Z - S

# Protons# Shielding electrons

Periodicity of Effective Nuclear Charge

H1.00

He1.65

Li1.30

Na2.20

K2.20

Rb2.20Cs

2.20Ba

2.85

Sr2.85

Ca2.85

Mg2.85

Be1.95

B2.60

Al3.50Ga

5.00

In5.00Tl

5.00Pb

5.65

Sn5.65

Ge5.65

Si4.15

C3.25

N3.90

P4.80As

6.30

Sb6.30Bi

6.30Po

6.95

Te6.95

Se6.95

S5.45

O4.55

F5.20

Cl6.10Br

7.60

I7.60At

7.60Rn

8.25

Xe8.25

Kr8.25

Ar6.75

Ne5.85

Z* on valence electrons

EffectiveEffective Nuclear Charge, Nuclear Charge, ZZeffeff

• Atom Zeff Experienced by Electrons in Valence Orbitals

• Li +1• Be +2• B +3• C +4• N +5• O +6• F +7

Increase in Increase in ZZeffeff across a across a

periodperiod

Electron ConfigurationsA list of all the electrons in an atom (or ion)

• Must go in order (Aufbau principle)

• 2 electrons per orbital, maximum

• We need electron configurations so that we can determine the number of electrons in the outermost energy level. These are called valence electrons.

• The number of valence electrons determines how many and what this atom (or ion) can bond to in order to make a molecule

1s1s22 2s 2s22 2p 2p66 3s 3s22 3p 3p66 4s 4s22 3d 3d1010 4p 4p66 5s 5s22 4d 4d1010 5p 5p66 6s 6s22 4f 4f1414…… etc.etc.

Electron Configurations

2p4

Energy LevelEnergy Level

SublevelSublevel

Number of Number of electrons in electrons in the sublevelthe sublevel

1s1s22 2s 2s22 2p 2p66 3s 3s22 3p 3p66 4s 4s22 3d 3d1010 4p 4p66 5s 5s22 4d 4d1010 5p 5p66 6s6s22 4f 4f1414…… etc.etc.

Let’s Try It!

• Write the electron configuration for the following elements:

H

Li

N

Ne

K

Zn

Pb

Shorthand Notation

• A way of abbreviating long electron configurations

• Since we are only concerned about the outermost electrons, we can skip to places we know are completely full (noble gases), and then finish the configuration

Shorthand Notation

• Step 1: Find the closest noble gas to the atom (or ion), WITHOUT GOING OVER the number of electrons in the atom (or ion). Write the noble gas in brackets [ ].

• Step 2: Find where to resume by finding the next energy level.

• Step 3: Resume the configuration until it’s finished.

Shorthand Notation• Chlorine

– Longhand is 1s2 2s2 2p6 3s2 3p5

You can abbreviate the first 10 electrons with a noble gas, Neon. [Ne] replaces 1s2 2s2 2p6

The next energy level after Neon is 3So you start at level 3 on the diagonal rule (all

levels start with s) and finish the configuration by adding 7 more electrons to bring the total to 17

[Ne] 3s2 3p5

Practice Shorthand Notation

• Write the shorthand notation for each of the following atoms:

Cl

K

Ca

I

Bi

Valence ElectronsValence ElectronsValence ElectronsValence ElectronsElectrons are divided between core and Electrons are divided between core and

valence electronsvalence electronsB 1sB 1s22 2s 2s22 2p 2p11

Core = [He]Core = [He] , , valence = 2svalence = 2s22 2p 2p11

Br [Ar] 3dBr [Ar] 3d1010 4s 4s22 4p 4p55

Core = [Ar] 3dCore = [Ar] 3d1010 , , valence = 4svalence = 4s22 4p 4p55

Rules of the GameRules of the GameRules of the GameRules of the GameNo. of valence electrons of a main group No. of valence electrons of a main group

atom = Group numberatom = Group number (for A groups) (for A groups)

Atoms like to either empty or fill their outermost Atoms like to either empty or fill their outermost level. Since the outer level contains two s level. Since the outer level contains two s electrons and six p electrons (d & f are always in electrons and six p electrons (d & f are always in lower levels), the optimum number of electrons lower levels), the optimum number of electrons is eight. This is called the is eight. This is called the octet rule.octet rule.

Keep an Eye On Those Ions!

• Electrons are lost or gained like they always are with ions… negative ions have gained electrons, positive ions have lost electrons

• The electrons that are lost or gained should be added/removed from the highest energy level (not the highest orbital in energy!)


• Tin

Atom: [Kr] 5s2 4d10 5p2

Sn+4 ion: [Kr] 4d10

Sn+2 ion: [Kr] 5s2 4d10

Note that the electrons came out of the highest energy level, not the highest energy orbital!


• Bromine

Atom: [Ar] 4s2 3d10 4p5

Br- ion: [Ar] 4s2 3d10 4p6

Note that the electrons went into the highest energy level, not the highest energy orbital!

Try Some Ions!• Write the longhand notation for these:

F-

Li+

Mg+2

• Write the shorthand notation for these:

Br-

Ba+2

Al+3

Exceptions to Electron Configuration

Exceptions to the Aufbau Principle

• Remember d and f orbitals require LARGE amounts of energy

• If we can’t fill these sublevels, then the next best thing is to be HALF full (one electron in each orbital in the sublevel)

• There are many exceptions, but the most common ones are

d4 and d9

For the purposes of this class, we are going to assume that ALL atoms (or ions) that end in d4 or d9 are exceptions to the rule. This may or may not be true, it just depends on the atom.


d4 is one electron short of being HALF full

In order to become more stable (require less energy), one of the closest s electrons will actually go into the d, making it d5 instead of d4.

For example: Cr would be [Ar] 4s2 3d4, but since this ends exactly with a d4 it is an exception to the rule. Thus, Cr should be [Ar] 4s1 3d5.

Procedure: Find the closest s orbital. Steal one electron from it, and add it to the d.


OK, so this helps the d, but what about the poor s orbital that loses an electron?

Remember, half full is good… and when an s loses 1, it too becomes half full!

So… having the s half full and the d half full is usually lower in energy than having the s full and the d to have one empty orbital.


d9 is one electron short of being full

Just like d4, one of the closest s electrons will go into the d, this time making it d10 instead of d9.

For example: Au would be [Xe] 6s2 4f14 5d9, but since this ends exactly with a d9 it is an exception to the rule. Thus, Au should be [Xe] 6s1 4f14 5d10.

Procedure: Same as before! Find the closest s orbital. Steal one electron from it, and add it to the d.

Orbitals fill in order

• Lowest energy to higher energy.

• Adding electrons can change the energy of the orbital.

• Half filled orbitals have a lower energy.

• Makes them more stable.

• Changes the filling order

Write these electron configurations

• Titanium(Ti) - 22 electrons

• 1s22s22p63s23p64s23d2

• Vanadium(V) - 23 electrons 1s22s22p63s23p64s23d3

• Chromium(Cr) - 24 electrons

• 1s22s22p63s23p64s23d4 is expected

• But this is wrong!!

Chromium is actually

• 1s22s22p63s23p64s13d5

• Why?

• This gives us two half filled orbitals.

• Slightly lower in energy.

• The same principal applies to copper.

Copper’s electron configuration

• Copper has 29 electrons so we expect

• 1s22s22p63s23p64s23d9

• But the actual configuration is

• 1s22s22p63s23p64s13d10

• This gives one filled orbital and one half filled orbital.

• Remember these exceptions

Quantum Theory Schrodinger Heisenberg PC1144/PC1144%20Lectures/lecture16.ppt 206%20presentation.ppt.

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