de broglie berg schrodinger quantum model

8/14/2019 De Broglie berg Schrodinger Quantum Model

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QuantumQuantumMechanical ModelMechanical Model

of the Atomof the AtomDeBroglies hypothesis, Heisenbergs

Uncertainty Principle, SchrdingersWave Equations, Quantum Numbers


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Warm Up!

Two naturally occurring isotopes of gallium are:

69

Ga &71

GaWhat is the percent abundance of eachisotope?


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1987)1987)

Light was found to have properties of matter, but is theopposite true? Does matter have wave properties?

In 1923 Louis de Broglie sought an answer to thisquestion.

For a particle with velocity v (not nu! Its really a lower case v), its mass is equal to h/ v.

Rearranging, we have =h/mv where mv is mass timesvelocity which is equal to momentum. This allows usto calculate the wavelength of a particle in motion.


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de Brogliede BroglieWavesWaves


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OK

OK

NOT

OK


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ou s e rog e ou s e rog e 1987)1987)

Compare the wavelength for anelectron (mass = 9.11 x 10 -31 kg)

traveling at a speed of 1.0 x 107

m/swith that for a ball (mass = 0.10 kg)traveling at 35 m/s.


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He sen erg Uncerta ntye sen erg ncer a n yPrinciplePrinciple

It is impossible to know exactly the position and momentum (mass times

velocity) of a particle. The better we know one, the less certain

we can know the other. The act of measuring changes the properties.


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smallsmall

To measure where a electron is,we use light.

But the light moves the electron And hitting the electron changes

the frequency of the light.


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MovingElectron

Photon

Before

ElectronChanges velocity

Photonchangeswavelength

After


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Schrdinger's WaveFunction

In 1926, Erwin Schrdinger used the hypothesis thatelectrons have a dual wave-particle nature to create awave function just gives you a formula for finding anelectron in space

The function is given the symbol, ( psi ).

More interesting to us is 2 a probability function for where the electron is most likely to be.

These probabilities give us orbitals, which are probabilityfields of where an electron might be located.


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Quantum MechanicalOrbitals

According to Schrodinger, electrons are notconstrained to specific pathways around anucleus.

There are mathematical equations to predictwhere an electron is likely to be

The three dimensional representations of this probability are called orbitals


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Orbital Shapes

The s orbital is

s pherical


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The p orbitals

are shapedlike

p eanuts.


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Four d orbitals areshaped like d oubled umbbells

One d orbital is ad umbbell with ahoola hoop


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Quantum Numberssymbol name formula values

n principle QN integers > 0 1, 2, 3, 4

l angular momentumQN

0 (n-1) 0, 1, 2n-1

m (m ) magnetic QN - + - ,-1, 0, 1,

s (m s) spin QN +, -


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n

m

s

1

0

0

-

2

-1 0 1

0 1

0

- - - -

orbital 1s 2s 2p x 2p y 2p z

1s has 2e 2s has 2e 2p has 6e


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Relative

Energies

1s

2s

2p

3s3p

4s

3d

IncreasingEnerg

y


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Electron Configurations

Aufbau Principle : Electrons go to thelowest energy orbital first.

Pauli Exclusion Principle : Every orbitalcan hold two electrons if they haveopposite spin.

Hunds Rule : Electrons would rather bealone if another equal energy orbital is

available.


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Orbital Diagram for Nitrogen

1s 2s 2p N

Nitrogen has 7 electrons.Following the aufbau principle we start with

the lowest energy.

Pauli says to fit two electrons, they must haveopposite spins.Hund says put one e- in each orbital, they

wont double up unless they have to.


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PracticeWhat are the orbital diagrams and electronconfigurations of the following atoms?

1s 2s 2p 3s 3p 4s 3dClCaCr

SnCl 1s 2 2s 2 2p 6 3s2 3p 5 Ca 1s 2 2s2 2p 6 3s2 3p 6 4s2 Cr 1s 2 2s2 2p 6 3s2 3p 6 4s2 3d 4 Sn 1s 2 2s2 2p 6 3s2 3p 6 4s2 3d 10 4p 6 5s 2 4d 10 5p 2


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Practice

Orbital diagrams and electron configurations for ionsare just the same, but the appropriate number of electrons have been added or removed.

1s 2s 2p 3s 3p 4s 3dSS2-

CoCo 2+


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Orbital Blocks

d p

Mg [Ne] 3s 2

1

2

3

4

5

6

row block

electron

s

(n= row -1)


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Electron configuration short hand

Write the electron configuration for each of these elements

Electron configuration Leave this column blank

Cl 1s 2 2s2 2p 6 3s2 3p 5

Cl - 1s2 2s2 2p 6 3s2 3p 6

Cr 1s 2 2s2 2p 6 3s2 3p 64s1 3d 5

Ru 2+ 1s2 2s2 2p 6 3s2 3p 64s2 3d 10 4p 6 5s0 4d6

Sn 1s2 2s 2 2p 6 3s 2 3p 64s2 3d 10 4p 6 5s2 4d 10 5p 2


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How do you remember the order?

Follow the order of elements on the PT

Electron configuration

P 1s 2 2s 2 2p 6 3s2 3p 4

O2- 1s2 2s 2 2p 6 3s2 3p 6

Ni 1s2

2s2

2p6

3s2

3p6

4s2

3d4

Ru 1s2 2s2 2p 6 3s2 3p 64s2 3d 10 4p 6 5s2 4d 6

Tl 1s 2 2s2 2p 6 3s 2 3p 64s 2 3d 10 4p 6 5s 2 4d 10 5p 2


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Vocabulary

Core electron: an electron in an inner shell (orbital), notused in the chemistry of the atom

Valence electron: an electron in the outermost shell

(orbital), added since the last noble gas, important inchemistry.

V 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 3

V [Ar] 4s 2 3d 3

Core electrons [Ar] Valence electrons


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de broglie berg schrodinger quantum model

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