quantum-numbersand electronic configuation.ppt

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BASIC CONCEPTS OF QUANTUM MECHANICS

• ELECTRONS EXIST IN AREAS OUTSIDE THE

NUCLEUS. THESE AREAS ARE CALLED ENERGY LEVELS. YOU MIGHT HAVE HEARD OF THEM BEFORE AS “SHELLS”. THERE ARE NUMEROUS ENERGY LEVELS AT WHICH THE ELECTRON CAN BE FOUND, EACH AT A PROGRESSIVE HIGHER

ENERGY.

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BASIC CONCEPTS OF QUANTUM MECHANICS

• AN ORIGINAL ATOMIC THEORY PROPOSED BY NEILS BOHR IN THE EARLY 20TH CENTURY SUGGESTED THAT ELECTRONS

CIRCLE THE NUCLEUS OF ATOMS IN ORBITS SIMILAR TO THE PATHS OF THE PLANETS AROUND THE SUN.

• A MOST IMPORTANT CONCEPT OF MODERN QUANTUM

THEORY IS HOWEVER, THAT ELECTRONS DO NOT MOVE IN ORBITS ABOUT THE NUCLEUS OF THE ATOM !!

THE ENERGY LEVELS OF ATOMS ARE NOT ORBITS FOR ELECTRONS. THEY ARE AREAS OF HIGH PROBABILITY OF FINDING ELECTRONS.

ELECTRON ORBITS !!

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+

The Bohr model of the atom is a planetary

model where the electrons move in distinct orbits about

the nucleus.

Each orbit represents an energy level or

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A probability model of the

atom.

Areas of high probability

of finding electrons exist but no distinct orbits

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BASIC CONCEPTS OF QUANTUM MECHANICS

(CONT’D)

• WHEN ENERGY (HEAT, ELECTRICITY, ETC.) IS ADDED TO AN ATOM, THE ELECTRONS WITHIN THE ATOM JUMP TO HIGHER ENERGY LEVELS. • WHEN THE ELECTRONS FALL BACK TO THEIR

ORIGINAL ENERGY LEVEL, THEY RELEASE THE ENERGY THAT THEY ABSORBED IN THE FORM OF LIGHT.

• THEREFORE, IN ORDER TO UNDERSTAND THE ELECTRONIC STRUCTURE OF THE ATOM WE MUST FIRST UNDERSTAND THE NATURE OF

LIGHT ITSELF! _{WAVES &}

ORBITALS IRWIN SCHROEDINGER

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USING OUR KNOWLEDGE OF LIGHT TO

UNDERSTAND ELECTRONIC STRUCTURE IN ATOMS

• RECALL FROM OUR PREVIOUS INFORMATION:

WHEN ATOMS ABSORB ENERGY, ELECTRONS JUMP TO HIGHER ENERGY LEVELS. WHEN THEY FALL BACK TO THEIR ORIGINAL ENERGY LEVELS, THAT ABSORBED ENERGY IS RELEASED AS LIGHT.

ANALYZING THIS EMITTED LIGHT ALLOWS US TO DISCOVER THE ELECTRONIC STRUCTURE OF THE ATOM!

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LIGHT PARTICLES, PLANCK AND PHOTONS

• PARTICLES OF LIGHT ARE CALLED “PHOTONS”. THESE ARE “PACKAGES” OF LIGHT ENERGY.

• MAX PLANCK WAS FIRST TO DISCOVER THE

RELATIONSHIP BETWEEN THE WAVE NATURE OF LIGHT AND ITS PARTICLE NATURE.

• HE FOUND THAT THE ENERGY CONTENT OF LIGHT WAS DIRECTLY RELATED TO THE FREQUENCY OF THE LIGHT WAVE.

• THE EQUATION THAT MEASURES ENERGY AS A FUNCTION OF FREQUENCY IS:

ENERGY = A CONSTANT x FREQUENCY E = h x  WERE h IS A CONSTANT CALLED

PLANCK’S CONSTANT (6.63 x 10-34 JOULES SEC / PHOTON)

PHOTONS

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LIGHT PARTICLES, PLANCK AND PHOTONS

• IN ADDITION TO LIGHT VERY HIGH VELOCITY

SUBATOMIC PARTICLES (SUCH AS

ELECTRONS) ALSO HAVE OBSERVEABLE

WAVE PROPERTIES. THE WAVELENGTH OF

THESE PARTICLE CAN BE CALCULATED USING

THE DEBROGLIE EQUATION:

•



= h / m x v WHERE h = PLANCK’S CONSTANT

(6.63 x 10-34 JOULE SEC/ PHOTON)

m = MASS IN KILOGRAMS

v = VELOCITY IN METERS / SEC

iiIF YOU’RE MOVIN’ YOU’RE

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LIGHT PARTICLES, PLANCK AND PHOTONS

(CONT’D)

• SAMPLE PROBLEM:

ALL MOVING OBJECTS HAVE WAVELENGTHS EVEN EVERYDAY OBJECTS, HOWEVER LARGE MASS

PARTICLES EXHIBIT VERY SHORT WAVELENGTHS.

FOR EXAMPLE: WHAT IS THE WAVELENGTH OF A 60 Kg RUNNER WHO IS MOVING AT 10 METERS / SECOND?



= h / m x v,



= (6.63 x10

-34

) / (60 x 10)



= 1.11 x 10

-36

METERS

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What are Quantum Numbers?

Quantum number are a set of four values that define the energy state of an electron in an atom.

Quantum number values are designated as n, l, m and s (s is often written as m_s)

n is called the principal quantum number and ranges from 1, 2, 3, etc. (also refers to the energy level or shell

l represents the orbital type and depends on n. It ranges from 0 through n – 1. It often called the azimuthal

quantum number

m depends on l. It ranges from – l thru 0 to + l. It defines the orbital orientation in space and is call the magnetic

quantum number.

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

S

phere around the nucleus

T

he one tells you that the electron is

in the orbital closest to the nucleus



S

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

S

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

A

t the first energy level there is only the 1s

orbital, after the second energy level there

are 2p orbitals



L

ook like dumbbells



I

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ENERGY LEVEL

MAX # OF ELECTRONS

1

2

8

3

18

4

32

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Quantum numbers may be view as an electrons address. Just like your address, each has its own distinct set of values.

For example in order to receive a letter, the address must contain state and zip, city, street and name. No other person has

the exact same set of information. It is similar for electrons. They each have their own address, n, l, m, and s.

NO TWO ELECTRON IN AN ATOM CAN HAVE THE EXACT SAME SET OF QUANTUM NUMBERS.

QUANTUM NUMBERS ARE ASSIGNED TO EACH EACH ELECTRON USING THE RULES PREVIOUSLY

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Orbital types defined by the azimuthal quantum number

l = 0

s type orbital

l = 1

p type orbital

l = 2

d type orbital

One orientation

Three orientations

Five orientations

l = 3

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Assigning Quantum Numbers to Atoms

n l m s

atom

H (1 e-) ₁

Lowest possible n value 0

Lowest possible l value (n – 1)

0

Lowest possible m value (-l > 0 > +l)

-½

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Assigning Quantum Numbers to Atoms

n l m s

atom

He (2 e-) ₁ ₀ ₀ _-½

1 0 0 +½

This time we can use the same n, l and m values as the first electron and still get a different set of values by changing

s to = + ½

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n l m s

atom

Li (3 e-) ₁ ₀ ₀ _-½

1 0 0 +½

This time we must change n to 2 otherwise we will duplicate the first or second set of numbers.

Following the rules we get the set shown. Notice that when we change n we again start at the lowest possible

values for l, m and s.

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Assigning Quantum Numbers to Atoms

n l m s

atom

Be (4 e-) ₁ ₀ ₀ _-½

1 0 0 +½

2 0 0 -½

This time we can use the same n, l and m values as the third electron and still get a different set of values by changing

s to = + ½

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n l m s

atom

B (5 e-) ₁ ₀ ₀ _-½

1 0 0 +½

2 0 0 -½

2 0 0 +½

This time we must change l to 1 otherwise we will duplicate the first or second set of numbers.

Following the rules we get the set shown. Notice that when we change l we again start at the lowest possible

values for m and s.

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Assigning Quantum Numbers to Atoms

n l m s

atom

C (6 e-) ₁ ₀ ₀ _-½

1 0 0 +½

2 0 0 -½

2 0 0 +½

2 1 -1 -½

2 1 0 -½

This time we can use the same n and l values as the fourth electron and still get a different set of values by changing

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n l m s

atom

N (7 e-) ₁ ₀ ₀ _-½

1 0 0 +½

2 0 0 -½

2 0 0 +½

2 1 -1 -½

2 1 0 -½

m to + 1

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Assigning Quantum Numbers to Atoms

n l m s

atom

N (7 e-) ₁ ₀ ₀ _-½

1 0 0 +½

2 0 0 -½

2 0 0 +½

2 1 -1 -½

2 1 0 -½

m to – 1 and s to + ½

2 1 + 1 -½

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Assigning Quantum Numbers to Atoms n l m s

atom

O (8 e-) 1 0 0 -½

1 0 0 +½

2 0 0 -½

2 0 0 +½

2 1 -1 -½

2 1 0 -½

m to – 1 and s to + ½

2 1 + 1 -½

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Assigning Quantum Numbers to Atoms n l m s

atom

F (9 e-) 1 0 0 -½

1 0 0 +½

2 0 0 -½

2 0 0 +½

2 1 -1 -½

2 1 0 -½

m to 0

2 1 + 1 -½

2 1 - 1 +½

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Assigning Quantum Numbers to Atoms n l m s

atom

Ne (10 e-) 1 0 0 -½

1 0 0 +½

2 0 0 -½

2 0 0 +½

2 1 -1 -½

2 1 0 -½

m to + 1

Energy level 2 is now complete. We are at the end of period (row) 2 on the Periodic Table

2 1 + 1 -½

2 1 - 1 +½

2 1 0 +½

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Assigning Quantum Numbers to Atoms n l m s

atom

Na (11 e-) 1 0 0 -½

1 0 0 +½

2 0 0 -½

2 0 0 +½

2 1 -1 -½

2 1 0 -½

2 1 + 1 -½

2 1 - 1 +½

2 1 0 +½

2 1 + 1 +½

3 0 0 -½

This time we must change n to 3 otherwise we will duplicate one of the first thru tenth set of numbers.

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Quantum Number Summary

n =1 l = 0 m = 0 s = + ½ or – ½

n =2 l = 0

l = 1

m = - 1 m = 0 m = + 1

s = + ½ or – ½

n =3 l = 0

l = 1

l = 2

m = -2 m = - 1 m = 0 m = + 1 m = +2

s = + ½ or – ½

n =4 l = 0

l = 1 l = 2

l = 3

m = - 3 m = -2 m = - 1 m = 0 m = + 1 m = +2

m = + 3

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For larger atom the assignment of quantum numbers must continue following the rules until the number of electrons corresponding to the particular atom is reached.

Writing quantum number for a particular electron can be made easier by translation a spectroscopic

notation into a quantum number set. For example a 4s2 can be translated as

n = 4 , s means l = 0 and therefore m must be 0. s can be – ½ or + ½

A 3p2 can be translated as

n = 3 , p means l = 1 and therefore m must be. -1, 0 or + 1

s can be – ½ or + ½

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Basic Principle:

electrons occupy

lowest energy levels

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Electron spin

How could an orbital hold two electrons _{without electrostatic repulsion?}

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1

s

value of energy level

sublevel no. of

electrons

spdf NOTATION

for H, atomic number = 1

Orbital Box Notation

Arrows show electron

spin

(+½ or -½)

ORBITAL BOX NOTATION

for He, atomic number = 2

1s

2

1s





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E xample:

Determine the electron configuration and orbital notation for the ground state neon atom.

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Hund’s Rule –

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Rules for Filling Orbitals

Bottom-up

(Aufbau’s principle)

Fill orbitals singly before doubling up

(Hund’s Rule)

Paired electrons have opposite spin

(Pauli exclusion principle)

Basic Principle:

electrons occupy

lowest energy levels

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Identify examples of the following principles:

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Examples

● Aluminum:

1s22s22p63s23p1 [Ne]3s23p1

● Calcium:

1s22s22p63s23p64s2

[Ar]4s2

● Nickel:

1s22s22p63s23p64s23d8

[Ar]4s23d8

{or [Ar]3d8_4s2_}

● Iodine:

[Kr]5s2_4d10_5p5 _{_or_[Kr]_4d10_5s2_5p5_}

● Astatine (At):

[Xe]6s24f145d106p5

{or [Xe]4f145d106s26p5}

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s

p

n = 2 s

d

p _{n = 3}

f

s

d

p n = 4

s

n = 1

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Phosphorus

Symbol: P

Atomic Number: 15

Full Configuration: 1s2_2s2_2p6_3s2_3p3

Valence Configuration: 3s23p3

Shorthand Configuration: [Ne]3s2_3p3

                 

1s 2s 2 p

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n

= principal quantum number

 _{electron’s energy depends principally on this}

l

= azimuthal quantum number

 _{for orbitals of same}_n_,_l_{distinguishes different shapes} (angular momentum)

m

l = magnetic quantum number

 for orbitals of same n & l, m_l distinguishes different orientations in space

m

s = spin quantum number

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E nergy level Sublevel # of orbitals/sublevel

n

= 1 1s (l = 0) 1 (m_l has one value)

n

= 2 2s (l = 0) 1 (m_l has one value)

2p (l = 1) 3 (m_l has three values)

n

= 3 3s (l = 0) 1 (m_l has one value) 3p (l = 1) 3 (m_l

has three values) 3d (l = 2) 5 (m_l has five values)

n = principal

quantum number (energy)

l = azimuthal

quantum number

(shape)

m_l = magnetic

quantum number (orientation

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s

orbitals p orbitals d orbitals f orbitals

l = 0 l = 1 l = 2 l = 3

m_l = 0 ml = -1, 0, 1 ml = -2, -1, 0, 1, 2 ml=-3,-2,-1,0,1,2,3

An s

subshell A p subshell A d subshell An f subshell

One s orbital Three p orbitals Five d orbitals Seven f orbitals

For n=1

l=0 an s subshell (with 1 orbital)

For n=2

l=0,1 an s subshell and a p subshell (with 3 orbitals)

For n=3

l=0,1,2 an s subshell, a p subshell, a d subshell (with 5 orbitals)

For n=4

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1s2

2s22p6 3s23p63d10 4s24p5 [Ar]

3d104s24p5 [Ar] = “noble gas core”

[Ar]3 d10 = “pseudo noble gas core”

(elect rons that tend not to react)

Atom’s reactivity is determined by valence electrons

valence e’s in Br

:

4s

2

4p

5

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Examples ●

Sulfur: 1s22s22p63s23p4 or [Ne]3s23p4

valence electrons: 3s2_3p4

●

Strontium: [Kr]5s2

valence electrons: 5s2

●

Gallium: [Ar]4s23d104p1

valence electrons: 4s24p1

●

Vanadium: [Ar]4s2_3d3

valence electrons: 4s2 or 3d34s2

Identify all electrons at the highest

principal quantum number (

n

)

Use on exams, but recognize

limitations

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Pseudo noble gas core

includes:



noble gas electron core



d

electrons (

not very reactive

)

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Pseudo noble gas core

includes:



noble gas core



d

electrons

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Paramagnetic

: atoms with unpaired electrons that

are weakly attracted to a magnet.

Diamagnetic

: atoms with paired electrons that are

not attracted to a magnet

.

Paramagnetic

: atoms with unpaired electrons that

are weakly attracted to a magnet.

Diamagnetic

: atoms with paired electrons that are

not attracted to a magnet

.

For the ground state oxygen atom:

spdf configuration:

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