CHAPTER 3 Atomic Structure: Explaining the Properties of Elements

Home , Atomic orbital, Aufbau principle, Shielding effect

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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 a) Electric b) Magnetic

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

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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·  u  = wavelength,  = frequency, u = velocity

Units: wavelength = meters (m)

frequency = cycles per second or Hertz (s-1) wavelength (m) x frequency (s-1) = velocity (m/s)

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

Atomic Emission (Line) Spectra

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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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Blackbody Radiation and the Photoelectric Effect Explained by a new theory: Quantum Theory

• 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: Continuum states: discrete energy smooth transition levels. 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

1  1 1   = 1.097102 nm1    2 2  λ  ni n f 

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?

1  1 1   = 1.097102 nm1    2 2  λ  ni n f 

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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?

1  1 1   = 1.097102 nm1    2 2  λ  ni n f 

The Bohr Model of Hydrogen

Neils Bohr used Planck and Einstein’s ideas of photons and quantization of energy to explain the atomic spectra of hydrogen

photon of light (h) n = 4 n = 3 n = 2

+ h h n = 1

n = 2 n = 1 n = 3 absorption emission

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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 -

2.178686 x 10−18 Joules En=− n2 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.

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E = h

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

Ephoton = DE = Ef - Ei

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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 an electron travelling at 2/3’s the speed of light. Mass electron = 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

E. Schrödinger (1927) The electron as a Standing Wave

. 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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E. Schrödinger (1927) The electron as a Standing Wave

.Each orbital can hold up to 2 electrons .The probability of finding the electron = 2 .Probabilities are required because of “Heisenberg’s Uncertainty Principle”

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 Uncertainty in position momentum

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

Dx  (6.63 x 10-34 Js) 4(9.11 x 10-31 kg)(.001 x 1 x 108 m/s)

Dx  6 x 10-10 m or 600 pm

Probability Electron Density for 1s Orbital

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Electron “Cloud” Representation

Electron “Orbital” Representation

90% probablity surface

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Comparison of “s” Orbitals

One “s” orbital in each shell. nodes

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The Three 2p Orbitals

The Five 3d Orbitals

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The Seven “f” Orbitals

+ 2s n = 1 n = 2 n = 3

Orbitals are found in 3-D shells 1s instead of 2-D Bohr orbits. The Bohr radius for n=1, 2, 3 etc was correct, however.

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Do not appear until the 2nd shell and higher

3px 3py 3pz

+ n = 1 n = 2 n = 3

2px 2py 2pz

Do not appear until the 3rd shell and higher

+ n = 1 n = 2 n = 3

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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"

“The Shell Game” n = 2

+ In the second shell n = 1 there is an s "subshell" and a p "subshell" n = 2 n = 3

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“The Shell Game” n = 3

+ n = 1 n = 2 n = 3 In the third shell there are s, p, and d "subshells"

“The Shell Game” “f” Orbitals don’t appear n = 4 until the 4th shell

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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" constants E   n n2

(just like Bohr's theory)

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

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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 Equal to the number of l = 2 d-orbital "angular nodes" l = 3 f-orbital

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

m = -1/2 ms = +1/2 s spin “up” spin “down”

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orbital = s p d f

l = 0 1 2 3

ml = 0 n = 1 -1 0 +1 2 -2 -1 0 +1 +2 3 -3 -2 -1 0 +1 +2 +3 4 5 6

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

(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

3s 3p 3d

E 2s 2p

Energy of orbitals in multi-electron atoms Energy depends on n + l

3 + 2 = 5 4 + 0 = 4 3 + 1 = 4 3 + 0 = 3 2 + 1 = 3 2 + 0 = 2

1 + 0 = 1

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1s "Penetration"

→ s > p > d > f 2s 3s for the same shell (e.g. 4s n=4) the s-electron penetrates closer to 2p the nucleus and feels a 3p stronger nuclear pull or 4p charge.

Probability electron of thefinding Probability 3d 4f 4d

distance from nucleus → http://www.pha.jhu.edu/~rt19/hydro/img73.gif

Aufbau Principle - the lowest energy orbitals fill up first Filling order of orbitals in multi-electron atoms

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

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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 ms = -1/2 spin “up” 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”

   NOT  

Px Py Pz Px Py Pz

“orbital box diagram”

Electron Shells and Orbitals

• Orbitals that have the exact    same energy level are called degenerate. Px Py Pz • 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.

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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 Fe Fe2+ Fe3+

Cu = [Ar]3d104s1 Cu Cu+

Cu2+

Sn = [Kr]4d105s25p2 Sn Sn2+

Sn4+

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

Zeff = Z - s (s = shielding constant)

Zeff  Z – number of inner or core electrons Across a period -

Z Core Zeff Radius (nm) Na 11 10 1 186

Mg 12 10 2 160

Al 13 10 3 143

Si 14 10 4 132

Effective nuclear charge (Zeff) – Inner shell electrons “SHIELD” the outer shell electrons from the nucleus

Down a family -

Z Core Zeff Radius (nm) Na 11 10 1 186

K 19 18 1 227

Rb 37 36 1 247

Cs 55 54 1 265

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Trends in Effective Nuclear Charge (Zeff) and the Shielding Effect

increasing Zeff increasingShielding

Atomic, Metallic, Ionic Radii

For diatomic For metals, equal to For ions, ionic radius molecules, equal to metallic radius (one- equals one-half the covalent radius half the distance distance between (one-half the between nuclei in ions in ionic crystal distance between metal lattice). lattice. nuclei).

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

Decreasing Atomic Size Increasing Atomic SizeAtomic Increasing

Radius of Ions

Cation is always smaller than atom from which it is formed. Anion is always larger than atom from which it is formed.

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

Decreasing Ionic Radius Increasing Increasing Ionic Radius

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 I1 first ionization energy

2+ - I2 + X (g) X (g) + e I2 second ionization energy

3+ - I3 + X (g) X g) + e I3 third ionization energy

I1 < I2 < I3 < …..

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General Trend in First Ionization Energies

Increasing First Ionization Energy Decreasing First Ionization Decreasing FirstIonization Energy

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.

- - X (g) + e → X (g) Energy released = E.A. (kJ/mol) - - F (g) + e → F (g) EA = -328 kJ/mol

- - O (g) + e → O (g) EA = -141 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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