Atomic Structure: Chapter 5. Chapter Outline. Chapter Outline

Atomic Structure: Chapter 5 Chem 101 Fall 2004 Chapter Outline The Electronic Structures of Atoms • Electromagnetic radiation • The Photoelectric Ef...
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Atomic Structure: Chapter 5

Chem 101 Fall 2004

Chapter Outline The Electronic Structures of Atoms • Electromagnetic radiation • The Photoelectric Effect • Atomic Spectra and the Bohr Atom • The Wave Nature of the Electron • The Quantum Mechanical Picture of the Atom • Quantum Numbers

Chem 101 Fall 2004

Chapter Outline The Electronic Structures of Atoms • Atomic Orbitals • Electron Configurations • Paramagnetism and Diamagnetism • The Periodic Table and Electron Configurations

Chem 101 Fall 2004

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Quantum Mechanical Picture of the Atom • Werner Heisenberg in 1927 developed the concept of the Uncertainty Principle. • It is impossible to determine simultaneously both the position and momentum of an electron (or any other small particle).

Chem 101 Fall 2004

Quantum Mechanical Picture of the Atom • Consequently, we must must speak of the electrons’ position about the atom in terms of probability functions. • These probability functions are represented as orbitals in quantum mechanics.

Chem 101 Fall 2004

Postulates of Quantum Mechanics • Atoms and molecules can exist only in certain energy states. In each energy state, the atom or molecule has a definite energy. When an atom or molecule changes its energy state, it must emit or absorb just enough energy to bring it to the new energy state (the quantum condition).

Chem 101 Fall 2004

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Postulates of Quantum Mechanics • Atoms or molecules emit or absorb radiation (light) as they change their energies. The frequency of the light emitted or absorbed is related to the energy change by a simple equation.

E = hν =

hc λ

Chem 101 Fall 2004

Postulates of Quantum Mechanics • The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers. • Quantum numbers are the solutions of the Schrodinger, Heisenberg & Dirac equations. • Four quantum numbers are necessary to describe energy states of electrons in atoms. ..

Schr o dinger equation −

b 2  ∂ 2Ψ ∂ 2Ψ ∂ 2Ψ   + V Ψ = EΨ  + + 8π 2 m  ∂ 2 x ∂ 2 y ∂ 2 z 

Chem 101 Fall 2004

Quantum Numbers • Quantum numbers are called n, l, and ml are also called the “principal,” “azimuthal,” and “magnetic” quantum numbers. • A set of these 3 defines an orbital. • An orbital is the wave representation of an electron in an atom.

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Quantum Numbers • The principal quantum number has the symbol – n. n = 1, 2, 3, 4, ...... “shells” n = K, L, M, N, ...... The electron’s energy depends principally on n .

Chem 101 Fall 2004

Quantum Numbers • The angular momentum quantum number has the symbol   = 0, 1, 2, 3, 4, 5, .......(n-1)  s, p, d, f, g, h, .......(n-1)  tells us the shape of the orbitals. • These orbitals are the volume around the atom that the electrons occupy 90-95% of the time.

Chem 101 Fall 2004

Quantum Numbers • The symbol for the magnetic quantum number is m m













• If  = 0 (or an s orbital), then m 0. • Notice that there is only 1 value of m

This implies that there is one s orbital per n value. n ≥ 1

• If  = 1 (or a p orbital), then m • There are 3 values of m

-1,0,+1.

Thus there are three p orbitals per n value. n ≥ 2

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Quantum Numbers • If  = 2 (or a d orbital), then m

-2,-1,0,+1,+2.

• There are 5 values of m Thus there are five d orbitals per n value. n ≥ 3

• If  = 3 (or an f orbital), then m +3.

-3,-2,-1,0,+1,+2,

• There are 7 values of m Thus there are seven f orbitals per n value, n

• Theoretically, this series continues on to g,h,i, etc. orbitals. • Practically speaking atoms that have been discovered or made up to this point in time only have electrons in s, p, d, or f orbitals in their ground state configurations. Chem 101 Fall 2004

Quantum Numbers • The last quantum number is the spin quantum number which has the symbol ms. • The spin quantum number only has two possible values. • ms = +1/2 or -1/2 • ms = ± 1/2

• This quantum number tells us the spin and orientation of the magnetic field of the electrons. • Wolfgang Pauli in 1925 discovered the Exclusion Principle. • No two electrons in an atom can have the same set of 4 quantum numbers. Chem 101 Fall 2004

Quantum Numbers • The last quantum number is the spin quantum number which has the symbol ms. • The spin quantum number only has two possible values. • ms = +1/2 or -1/2 • ms = ± 1/2

• This quantum number tells us the spin and orientation of the magnetic field of the electrons. • Wolfgang Pauli in 1925 discovered the Exclusion Principle. • No two electrons in an atom can have the same set of 4 quantum numbers. Chem 101 Fall 2004

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Quantum Numbers: Possible Combinations n

l

1 2

0 0 1 0 1 2

3

ml

# of orbitals 0 1 0 1 -1,0,+1 3 0 1 -1,0,+1 3 -2,-1, 0,+1,+2 5

type of orbitals 1s 2s 2p 3s 3p 3d

Chem 101 Fall 2004

Atomic Orbitals • Atomic orbitals are regions of space where the probability of finding an electron about an atom is highest. • s-orbital properties: • There is one s orbital per n level • =0 1 value of m

Chem 101 Fall 2004

Atomic Orbitals: s-Orbitals • s-orbitals are spherically symmetric. 2s Orbital Probability

Electron Probability

1s Orbital

Distance from nucleus,r

Distance from the nucleus,r

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Atomic Orbitals: s-Orbitals • s-orbitals are spherically symmetric.

Probability

2s Orbital

Orbital Density

Electron Contour

Distance from the nucleus,r Chem 101 Fall 2004

Atomic Orbitals: p-Orbitals • p-orbital properties: • The first p orbitals appear in the n = 2 shell.

• p-orbitals are peanut or dumbbell shaped volumes. • They are directed along the axes of a Cartesian coordinate system.

• There are 3 p-orbitals per n level. • The three orbitals are named px, py, pz. • They have an  = 1. • m -1,0,+1 3 values of m

Chem 101 Fall 2004

Atomic Orbitals: p-Orbitals • p-orbitals are peanut or dumbbell shaped.

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Atomic Orbitals: d-Orbitals • d-orbital properties: • The first d orbitals appear in the n = 3 shell.

• The five d-orbitals have two different shapes: • 4 are clover leaf shaped. • 1 is peanut shaped with a doughnut around it. • The orbitals lie directly on the Cartesian axes or are rotated 45o from the axes.

• There are 5 d-orbitals per n level. • The five orbitals are named d xy , d yz , d xz , d x 2 - y2 , d z 2 • They have an  = 2. m = -2,-1,0,+1,+2 • 5 values of m  Chem 101 Fall 2004

Atomic Orbitals: d-Orbitals • d-orbital shapes

Chem 101 Fall 2004

Atomic Orbitals • Spin quantum number effects: • Every orbital can hold up to two electrons. • Consequence of the Pauli Exclusion Principle.

• The two electrons are designated as having • one spin up ↑ and one spin down ↓

• Spin describes the direction of the electron’s magnetic fields.

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Paramagnetism and Diamagnetism • Unpaired electrons have their spins aligned ↑↑ or ↓↓ • This increases the magnetic field of the atom. • Atoms with unpaired electrons are called paramagnetic . • Paramagnetic atoms are attracted to a magnet.

Chem 101 Fall 2004

Paramagnetism and Diamagnetism • Paired electrons have their spins unaligned ↑↓. • Paired electrons have no net magnetic field.

• Atoms with unpaired electrons are called diamagnetic. • Diamagnetic atoms are repelled by a magnet.

Chem 101 Fall 2004

Paramagnetism and Diamagnetism • Because two electrons in the same orbital must be paired, it is possible to calculate the number of orbitals and the number of electrons in each n shell. • The number of orbitals per n level is given by n2. • The maximum number of electrons per n level is 2n2. • The value is 2n2 because of the two paired electrons.

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Paramagnetism and Diamagnetism Energy Level n 1 2

# of Orbitals n2 1 4

Max. # of e2n2 2 8

Chem 101 Fall 2004

The Periodic Table and Electron Configurations • The principle that describes how the periodic chart is a function of electronic configurations is the Aufbau Principle. • Each orbital can “hold” 2 electrons, provided they have opposite spins. • Build up atoms by filling orbitals with appropriate # of electrons. • Start at low energy, work toward high energy.

Chem 101 Fall 2004

The Periodic Table and Electron Configurations • Low energy orbitals fill first. • Orbital energy increases as • n increases & l increases • Pauli exclusion principle: Electrons can’t have identical quantum numbers. 2 e–’s per orbital, opposite spins • Hund’s rule: For lowest total energy, all unpaired e–’s will have the same spin. Chem 101 Fall 2004

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The Periodic Table and Electron Configurations

Energy

• “Electron configurations” 4s 3s 2s

4d 3d

4p 3p 2p

1s Chem 101 Fall 2004

The Periodic Table and Electron Configurations • Filling Order

1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 5g 6s 6p 6d 6f 6g 6h 7s 7p 7d 7f 7g 7h 7i

Chem 101 Fall 2004

The Periodic Table and Electron Configurations • “Electron configurations”

s-block

d-block

p-block

f-block

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The Periodic Table and Electron Configurations • 1st Row Elements

1s

Configuration



1s1

1

H

2

He ↑↓

1s2

Chem 101 Fall 2004

The Periodic Table and Electron Configurations • Now we can write a complete set of quantum numbers for all of the electrons in these three elements as examples. Na, Ca, Fe • First for 11Na. • When completed there must be one set of 4 quantum numbers for each of the 11 electrons in Na (remember Ne has 10 electrons)

3s 11

Na

[Ne]

3p

Configuration

[Ne] 3s1



Chem 101 Fall 2004

The Periodic Table and Electron Configurations • 2nd Row Elements 1s

2s

2p

↑↓ ↑

Configurat ion 1s 2 2s1

3

Li

4

Be ↑↓ ↑ ↓

5

B

↑↓ ↑ ↓ ↑

1s 2 2s 2 2p1

6

C

↑↓ ↑ ↓ ↑ ↑

1s 2 2s 2 2p 2

7

N

↑↓ ↑ ↓ ↑ ↑ ↑

1s 2 2s 2 2p 3

1s 2 2s 2

Chem 101 Fall 2004

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The Periodic Table and Electron Configurations • 2nd Row Elements 1s 3 Li

Chem 101 Fall 2004

2s

2p

Configuration

↑↓ ↑

1s 2 2s1

4

Be ↑↓ ↑ ↓

5

B

↑↓ ↑ ↓ ↑

1s 2 2s 2 2p1

6

C

↑↓ ↑ ↓ ↑ ↑

1s 2 2s 2 2p 2

7

N

↑↓ ↑ ↓ ↑ ↑ ↑

1s 2 2s 2 2p3

8

O

↑↓ ↑ ↓ ↑↓ ↑ ↑

1s 2 2s 2 2p 4

9

F

↑↓ ↑ ↓ ↑↓ ↑↓ ↑

1s 2 2s 2 2p5

10

1s 2 2s 2

Ne ↑↓ ↑ ↓ ↑↓ ↑↓ ↑↓ 1s 2 2s 2 2p6

The Periodic Table and Electron Configurations • 3rd Row Elements 3s 11

Na

13

Al

[Ne]

3p

Configuration



12 Mg [Ne ] ↑↓

14 Si 15 P 16 S 17

Cl

18

Ar

[Ne] ↑↓ [Ne] ↑↓ [Ne] ↑↓ [Ne] ↑↓ [Ne] ↑↓ [Ne ] ↑↓

↑ ↑ ↑ ↑ ↑ ↑ ↑↓ ↑ ↑ ↑↓ ↑↓ ↑ ↑↓ ↑↓ ↑↓

[Ne] 3s1 [Ne] 3s2 [Ne] 3s2 3p1 [Ne] 3s2 3p2 [Ne] 3s2 3p3 [Ne] 3s2 3p4 [Ne ] 3s2 3p5 [Ne] 3s2 3p6

Chem 101 Fall 2004

Next Class: Chemical Periodicity: Chapter 6 • Start work on OWL homework Chapter 6 • Start Reading Chapter 6

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