CHAPTER 3 Atomic Structure: Explaining the Properties of · PDF file ·...

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CHAPTER 3 Atomic Structure: Explaining the Properties of Elements

We are going to learn about the electronic structure of the atom,

and will be able to explain many things, including atomic

orbitals, oxidation numbers, and periodic trends.

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Chapter Outline

3.1 Waves of Light 3.2 Atomic Spectra 3.3 Particles of Light: Quantum Theory 3.4 The Hydrogen Spectrum and the Bohr Model 3.5 Electrons as Waves 3.6 Quantum Numbers 3.7 The Sizes and Shapes of Atomic Orbitals 3.8 The Periodic Table and Filling Orbitals 3.9 Electron Configurations of Ions 3.10 The Sizes of Atoms and Ions 3.11 Ionization Energies 3.12 Electron Affinities

The Electromagnetic Spectrum Continuous range of radiant energy,

(also called electromagnetic radiation).

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Electromagnetic Radiation Mutually propagating electric and magnetic fields, at right

angles to each other, traveling at the speed of light c

Speed of light (c) in vacuum = 2.998 x 108 m/s

a) Electric b) Magnetic

Properties of Waves - in the examples below,

both waves are traveling at the same velocity

Long wavelength = low frequency

Short wavelength = high frequency

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Units: wavelength = meters (m)

frequency = cycles per second or Hertz (s-1)

wavelength (m) x frequency (s-1) = velocity (m/s)

· u = wavelength, = frequency, u = velocity

Example: A FM radio station in Portland has a carrier wave frequency of 105.1 MHz. What is the wavelength?

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Chapter Outline


a) Absorption: Fraunhofer lines (dark spectra)

b) Emission: e.g Na (bright line spectra)

Atomic Spectra

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a) Hydrogen b) Helium c) Neon

Atomic Absorption Spectra: Dark Lines Spectrometer - a device that separates out the different wavelengths of

light. A “white” light sources produces a “continuous” spectrum; atomic

sources produces a "discrete" spectrum.

Atomic Emission (Line) Spectra

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Chemistry in Action: Element from the Sun

In 1868, Pierre Janssen detected a new emission line in the solar

emission spectrum that did not match known emission lines

The mystery element was named --

Chapter Outline


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Blackbody Radiation

Photoelectric Effect • phenomenon of light striking a metal surface and

producing an electric current (flow of electrons).

• If radiation below threshold energy, no electrons released.

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Explained by a new theory: Quantum Theory

Blackbody Radiation and the Photoelectric Effect

• Radiant energy is “quantized” – Having values restricted to whole-number

multiples of a specific base value.

• Quantum = smallest discrete quantity of energy.

• Photon = a quantum of electromagnetic radiation

Quantized States

Quantized states: discrete energy levels.

Continuum states: smooth transition between levels.

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The energy of the photon is given by Planck’s Equation.

E = h h = 6.626 × 10−34 J∙s

(Planck’s constant)

Sample Exercise 7.2 What is the energy of a photon of red light

that has a wavelength of 656 nm? The value of Planck’s constant (h) is 6.626 × 10-34 J . s, and the speed of light is 3.00 × 108 m/s.

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Chapter Outline


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The Hydrogen Spectrum and the Rydberg Equation

22

12 11100971

1

fi nn . =

λnm

Exercise 7.4: using the Rydberg Equation

What is the wavelength of the line in the emission spectrum of Hydrogen corresponding from ni = 7 to nf = 2?

22

12 11100971

1

fi nn . =

λnm

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Using the Rydberg Equation for Absorption

What is the wavelength of the line in the absorption spectrum of Hydrogen corresponding from ni = 2 to nf = 4?

22

12 11100971

1

fi nn . =

λnm

Neils Bohr used Planck and Einstein’s ideas of photons and quantization

of energy to explain the atomic spectra of hydrogen

+

n = 1

n = 2

n = 3

photon of

light (h)

n = 1

n = 2

n = 3

absorption emission

h h

n = 4

The Bohr Model of Hydrogen

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Electronic States

• Energy Level:

• An allowed state that an electron can occupy in an atom.

• Ground State:

• Lowest energy level available to an electron in an atom.

• Excited State:

• Any energy state above the ground state.

“Solar system” model of the atom where each “orbit”

has a fixed, QUANTIZED energy given by -

where n = “principle quantum number” = 1, 2, 3….

This energy is exothermic because it is potential

energy lost by an unbound electron as it is attracted

towards the positive charge of the nucleus.

2

-18

orbitn

Joules10 x 2.178E

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E = h

E = h

Ephoton = DE = Ef - Ei

The Rydberg Equation can be derived from Bohr’s theory -

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Example DE Calculation

Calculate the energy of a photon absorbed when an electron is promoted from ni = 2 to nf = 5.

Sample Exercise 3.5

How much energy is required to ionize a ground-state hydrogen atom? Put another way, what is the ionization energy of hydrogen?

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Strengths and Weaknesses of the Bohr Model

• Strengths: • Accurately predicts energy needed to remove an

electron from an atom (ionization).

• Allowed scientists to begin using quantum theory to explain matter at atomic level.

• Limitations: • Applies only to one-electron atoms/ions; does not

account for spectra of multielectron atoms.

• Movement of electrons in atoms is less clearly defined than Bohr allowed.

Chapter Outline


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Light behaves both as a wave and a particle -

Classical physics - light as a wave:

c = = 2.998 x 108 m/s

Quantum Physics -

Planck and Einstein:

photons (particles) of light, E = h

Several blind men were asked to describe an elephant. Each tried to determine

what the elephant was like by touching it. The first blind man said the elephant

was like a tree trunk; he had felt the elephant's massive leg. The second blind

man disagreed, saying that the elephant was like a rope, having grasped the

elephant's tail. The third blind man had felt the elephant's ear, and likened the

elephant to a palm leaf, while the fourth, holding the beast's trunk, contended

that the elephant was more like a snake. Of course each blind man was giving a

good description of that one aspect of the elephant that he was observing, but

none was entirely correct. In much the same way, we use the wave and particle

analogies to describe different manifestations of the phenomenon that we call

radiant energy, because as yet we have no single qualitative analogy that will

explain all of our observations.

http://www.wordinfo.info/words/images/blindmen-elephant.gif

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Standing Waves

Not only does light behave like a particle

sometimes, but particles like the electron

behave like waves! WAVE-PARTICLE

DUALITY

Combined these two equations:

E = mc2 and E = h, therefore -

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The DeBroglie wavelength explains why only certain

orbits are "allowed" -

a) stable b) not stable

Sample Exercise 3.6 (Modified): calculating the wavelength of a particle in motion. (a)Calculate the deBroglie wavelength of a 142 g baseball thrown at

44 m/s (98 mi/hr)

(b)Compare to the wavelength of a hydrogen atom (9.11 x 10-31 kg)

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Using the wavelike properties of the electron.

Close-up of a milkweed bug Atomic arrangement of a Bi-Sr-

Ca-Cu-O superconductor

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Chapter Outline

3.1 Waves of Light 3.2 Atomic Spectra 3.3 Particles of Light: Quantum Theory 3.4 The Hydrogen Spectrum and the Bohr Model 3.5 Electrons as Waves 3.6 Quantum Numbers NOTE: will do Section 3.7 first 3.7 The Sizes and Shapes of Atomic Orbitals 3.8 The Periodic Table and Filling Orbitals 3.9 Electron Configurations of Ions 3.10 The Sizes of Atoms and Ions 3.11 Ionization Energies 3.12 Electron Affinities

The electron as a Standing Wave

E. Schrödinger (1927)

mathematical treatment results in a “wave function”,

= the complete description of electron position and energy

electrons are found within 3-D “shells”, not 2-D Bohr orbits

shells contain atomic “orbitals” (s, p, d, f)

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Each orbital can hold up to 2 electrons

The probability of finding the electron = 2

Probabilities are required because of “Heisenberg’s Uncertainty Principle”

The electron as a Standing Wave

E. Schrödinger (1927)

We can never SIMULTANEOUSLY know with absolute

precision both the exact position (x), and momentum

(p = mass·velocity or mv), of the electron.

Dx·D(mv) h/4 Uncertainty in

momentum

Uncertainty in

position

If one uncertainty gets very small, then the other becomes

corresponding larger. If we try to pinpoint the electron momentum,

it's position becomes "fuzzy". So we assign a probability to where the

electron is found = atomic orbital.

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If an electron is moving at 1.0 X 108 m/s with an uncertainty in

velocity of 0.10 %, then what is the uncertainty in position?

Dx•D(mv) h/4 and rearranging

Dx h/[4D(mv)] or since the mass is constant

Dx h/[4mDv]

Dx 6 x 10-10 m or 600 pm

Dx (6.63 x 10-34 Js)

4(9.11 x 10-31 kg)(.001 x 1 x 108 m/s)

Probability Electron

Density for 1s Orbital

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Electron “Cloud” Representation

Electron “Orbital” Representation

90%

probablity

surface

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nodes

One “s”

orbital in

each shell.

Comparison of “s” Orbitals

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The Three 2p Orbitals

The Five 3d Orbitals

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The Seven “f” Orbitals

+

n = 1

n = 2

n = 3

1s

2s

3s

Orbitals are found in 3-D shells

instead of 2-D Bohr orbits. The Bohr

radius for n=1, 2, 3 etc was correct,

however.

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+

n = 1

n = 2

n = 3

3px 3py 3pz

2px 2py 2pz

Do not appear until the 2nd shell and higher

+

n = 1

n = 2

n = 3

Do not appear until the 3rd shell and higher

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“The Shell Game”

(n = 1)

+

n = 1

n = 2

n = 3

In the first shell there is

only an s "subshell"


n = 2

+

n = 1

n = 2

n = 3

In the second shell

there is an s "subshell"

and a p "subshell"

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n = 3

+

n = 1

n = 2

n = 3

In the third shell

there are s, p, and d

"subshells"

“f” Orbitals don’t appear

until the 4th shell


n = 4

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Chapter Outline


Completely describe the position and energy of the electron

(part of the wave function )

1. Principle quantum number (n):

n = 1, 2, 3……

gives principle energy level or

"shell"

http://www.calstatela.edu/faculty/acolvil/mineral/atom_structure2.jpg

2nn

constantsE

(just like Bohr's theory)

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2. angular momentum quantum number (l) :

l = 0, 1, 2, 3……n-1

describes the type of orbital or shape

l = 0 s-orbital

l = 1 p-orbital

l = 2 d-orbital

l = 3 f-orbital

Equal to the number of

"angular nodes"

3. magnetic quantum number (ml):

ml = - l to + l in steps of 1 (including 0)

indicates spatial orientation

If l = 0, then ml = 0 (only one kind of s-orbital)

ifl= 1, then ml = -1, 0, +1 (three kinds of p-orbitals)

if l = 2, then ml = -2, -1, 0, +1, +2 (five kinds of d-orbitals)

if l = 3, then ml = -3, -2, -1, 0, +1, +2, +3 (seven kinds of f-orbitals)

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Electron Spin

• Not all spectra features explained by wave

equations:

– Appearance of “doublets” in atoms with a single

electron in outermost shell.

• Electron Spin

– Up / down.

4. spin quantum number (ms): ms = 1/2 or -1/2

Electrons “spin” on their axis, producing a magnetic field

ms = +1/2

spin “up”

ms = -1/2

spin “down”

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n = 1

2

3 4

5

6

l = 0 1 2 3

ml = 0

-1 0 +1

-2 -1 0 +1 +2

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

orbital = s p d f

max electrons/subshell = 2(2l + 1)

max electrons/shell = 2n2

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Sample Exercise 3.9: Identifying Valid Sets of Quantum Numbers Which of these five combinations of quantum numbers are valid?

n l ml ms

(a) 1 0 -1 +1/2

(b) 3 2 -2 +1/2

(c) 2 2 0 0

(d) 2 0 0 -1/2

(e) -3 -2 -1 -1/2

Chapter Outline


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Electron Configurations: In what order do electrons occupy available orbitals?

Orbital Energy Levels for Hydrogen Atoms

E

3s 3p 3d

2s 2p

1s

Energy of orbitals in multi-electron atoms

Energy depends on n + l

1 + 0 = 1

2 + 0 = 2

2 + 1 = 3

3 + 0 = 3

3 + 1 = 4

4 + 0 = 4

3 + 2 = 5

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http://www.pha.jhu.edu/~rt19/hydro/img73.gif

1s

2s

3s 4s

2p

3p

4p

3d 4f 4d

distance from nucleus →

"Penetration"

s > p > d > f

for the same shell (e.g.

n=4) the s-electron

penetrates closer to

the nucleus and feels a

stronger nuclear pull or

charge.

Pro

ba

bil

ity o

f fi

nd

ing

th

e e

lec

tro

n →

Filling order of orbitals in multi-electron atoms

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

Aufbau Principle - the lowest energy orbitals fill up first

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Shorthand description of orbital occupancy

1. No more than 2 electrons maximum per orbital

2. Electrons occupy orbitals in such a way to minimize the

total energy of the atom = “Aufbau Principle”

(use filling order diagram)

3. No 2 electrons can have the same 4 quantum numbers

= “Pauli Exclusion Principle” (pair electron spins)

ms = +1/2

spin “up”

ms = -1/2

spin

“down”

•No two electrons in an atom can have the same set of four

quantum numbers (n, l, ml, ms)

•electrons must "pair up" before entering the same orbital

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4. When filling a subshell, electrons occupy empty

orbitals first before pairing up = “Hund’s Rule”

Px Py Pz

NOT

Px Py Pz

“orbital box diagram”

Electron Shells and Orbitals

• Orbitals that have the exact same energy level are called degenerate.

• Core electrons are those in the filled, inner shells in an atom and are not involved in chemical reactions.

• Valence electrons are those in the outermost shell of an atom and have the most influence on the atom’s chemical behavior.

Px Py Pz

+

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H:

He:

Li:

Be:

B:

C:

N:

O:

F:

Ne:

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Transition metals are characterized by having incompletely

filled d-subshells (or form cations as such).

Electron Configurations from the Periodic Table

n - 1

n - 2

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Chapter Outline


Electron Configurations: Ions

• Formation of Ions:

– Gain/loss of valence electrons to achieve stable electron configuration (filled shell = “octet rule”).

– Cations:

– Anions:

– Isoelectronic:

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Cations of Transition Metals Outer shell “s” and “p” electrons removed 1st

Fe = [Ar]3d64s2

Cu = [Ar]3d104s1

Sn = [Kr]4d105s25p2

Cu+

Cu

Cu2+

Fe2+

Fe3+

Fe

Sn

Sn4+

Sn2+

Sample Exercise 3.11: Determining Isoelectronic Species in Main Group Ions

a) Determine the electron configuration of each of the following ions: Mg2+, Cl-, Ca2+, and O2-

b) Which ions are isoelectronic with Ne?

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Chapter Outline


Periodic Trends – trends in atomic and ionic radii, ionization energies, and electron affinities

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Effective nuclear charge (Zeff) – Inner shell electrons

“SHIELD” the outer shell electrons from the nucleus

Na

Mg

Al

Si

11

12

13

14

10

10

10

10

1

2

3

4

186

160

143

132

Zeff Core Z Radius (nm)

Zeff = Z - s (s = shielding constant)

Zeff Z – number of inner or core electrons

Across a period -

Down a family -

Effective nuclear charge (Zeff) – Inner shell electrons

“SHIELD” the outer shell electrons from the nucleus

Na

K

Rb

Cs

11

19

37

55

10

18

36

54

1

1

1

1

186

227

247

265

Zeff Core Z Radius (nm)

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Trends in Effective Nuclear Charge (Zeff)

and the Shielding Effect

increasing Zeff

incre

asin

g S

hie

ldin

g

Atomic, Metallic, Ionic Radii

For diatomic molecules, equal to covalent radius (one-half the distance between nuclei).

For metals, equal to metallic radius (one-half the distance between nuclei in metal lattice).

For ions, ionic radius equals one-half the distance between ions in ionic crystal lattice.

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Trends in Atomic Size for the “Representative (Main Group) Elements”

Decreasing Atomic Size

Incre

asin

g A

tom

ic S

ize

Cation is always smaller than atom from

which it is formed.

Anion is always larger than atom from

which it is formed.

Radius of Ions

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Radii of Atoms and Ions must compare cations to cations and anions to anions

Decreasing Ionic Radius

Incre

asin

g I

onic

Radiu

s

Sample Exercise 3.13: Ordering Atoms and Ions by Size

Arrange each by size from largest to smallest: (a) O, P, S

(b) Na+, Na, K

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Chapter Outline


Ionization energy is the minimum energy (kJ/mol)

required to remove an electron from a gaseous

atom in its ground state.

I1 + X (g) X+

(g) + e-

I2 + X (g) X2+

(g) + e-

I3 + X (g) X3+

g) + e-

I1 first ionization energy

I2 second ionization energy

I3 third ionization energy

I1 < I2 < I3 < …..

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General Trend in First Ionization Energies

Increasing First Ionization Energy

Decre

asin

g F

irst Io

niz

ation E

nerg

y

Ionization Energies

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http://2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0/s11-03-energetics-of-ion-formation.html

Successive Ionization Energies (kJ/mol)

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Trends in the 1st Ionization Energy for the 2nd Row

Li 520 kJ/mol 1s22s1 1s2

Be 899 1s22s2 1s22s1

B 801 1s22s22p1 1s22s2

C 1086 1s22s22p2 1s22s22p1

N 1402 1s22s22p3 1s22s22p2

O 1314 1s22s22p4 1s22s22p3

F 1681 1s22s22p5 1s22s22p4

Ne 2081 1s22s22p6 1s22s22p5

Sample Exercise 3.14: Recognizing Trends in Ionization Energies

Arrange Ar, Mg, and P in order of increasing IE

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Chapter Outline


Electron affinity is the energy release that occurs

when an electron is accepted by an atom in the gaseous

state to form an anion.

F (g) + e- → F-(g) EA = -328 kJ/mol

O (g) + e- → O-(g) EA = -141 kJ/mol

X (g) + e- → X-(g) Energy released = E.A. (kJ/mol)

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Periodic Trends in Electron Affinity

http://2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0/s11-03-energetics-of-ion-formation.html

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