CHAPTER 3 Atomic Structure: Explaining the …postonp/ch221/pdf/Ch03-w20.pdf2/11/2020 2 We are going...

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CHAPTER 3Atomic Structure:Explaining the Properties of Elements

COLORS OF THE AURORA Some of the red and green

colors of an aurora display are produced when atoms of

oxygen in the upper atmosphere collide with high-speed

charged particles emitted by the sun.

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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 light

absorption and emission, atomic orbitals, and Periodic Trends.

Chapter Outline3.1 Nature’s Fireworks and the Electromagnetic Structure

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 Configuration of Ions

3.10 The Sizes of Atoms and Ions

3.11 Ionization Energies

3.12 Electron Affinities

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The Electromagnetic SpectrumContinuous range of wavelengths from high energy gamma and xrays on the left, through the UV and Vis, and Infrared through

low energy radio waves on the right.

Electromagnetic RadiationMutually 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) Electricb) Magnetic

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Properties of Waves

Long wavelength = low frequency

Short wavelength = high frequency

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

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Sample Exercise 3.1What is the frequency of the green light in auroras that is emitted by oxygen atoms? Its wavelength is 557.7 nm.


3.2 Atomic Spectra




3.6 Quantum Numbers







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Atomic Emission (Line) Spectra

Emission Spectrum of Hydrogen

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3.2 Atomic Spectra




3.6 Quantum Numbers







Blackbody Radiation

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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.

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

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Quantized States

Quantized states: discrete energy levels.

Continuum states: smooth transition between levels.

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

E = h where h = 6.626 × 10−34 J∙s (Planck’s constant)

The equation can be rewritten to include wavelength, and the velocity is equal to the speed of light, c

λν = c

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Sample Exercise 3.2 – Calculating the Energy of Photons

Ultra-high-definition televisions use tiny particles called quantum dots to more accurately reproduce the colors of transmitted images. The wavelengths of the light produced by quantum dots depend on their size. Figure 3.14 contains a plot of emission intensity as a function of wavelength for three quantum dots whose relative sizes are represented by the sizes of the spheres. What is the energy of a photon of light from the largest quantum dot that has a wavelength of 640 nm?


3.2 Atomic Spectra




3.6 Quantum Numbers







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The Hydrogen Spectrum and the Rydberg Equation

− −−

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12 11100971

1

fi nn . =

λnm

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Sample Exercise 3.4 - using the Rydberg Equation

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

− −−

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12 11100971

1

fi nn . =

λnm

Using the Rydberg Equation for Absorption

What is the final energy level nf if the initial level of the electron is ni = 2 and a photon with a wavelength of 656.3 nm is absorbed?

− −−

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12 11100971

1

fi nn . =

λnm

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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

hh

n = 4

The Bohr Model of Hydrogen

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.

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“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.

En=−2.178686 x 10−18 Joules

n2

E = h

E = h

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Ephoton = DE = Ef - Ei

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

Example DE Calculation

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

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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?

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.

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3.2 Atomic Spectra




3.6 Quantum Numbers







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

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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

Standing Waves and Nodes

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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 -

The DeBroglie wavelength explains why only certain

orbits are "allowed" -

a) stable b) not stable

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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 the speed of light. Mass electron = 9.11 x 10-31 kg.

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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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/4Uncertainty 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 6 x 10-10 m or 600 pm

∆x∙∆ mv ≥h

4π

∆x ≥h

4π ∆ mv

∆x ≥h

4π m∆v

∆x ≥6.63 x 10−34Js

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


3.2 Atomic Spectra




3.6 Quantum Numbers NOTE: will do Section 3.7 first







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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)

▪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)

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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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3.2 Atomic Spectra




3.6 Quantum Numbers







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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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


3.2 Atomic Spectra




3.6 Quantum Numbers







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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

3s4s

2p

3p

4p

3d 4f4d

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

“effective nuclear

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:

Illustrative Electron Configurations

Transition metals are characterized by having incompletely

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

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Electron Configurations from the Periodic Table

n - 1

n - 2


3.2 Atomic Spectra




3.6 Quantum Numbers







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Electron Configurations: Ions

• Formation of Ions:

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

– Cations:

– Anions:

– Isoelectronic:

Cations of Transition MetalsOuter 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+

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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?


3.2 Atomic Spectra




3.6 Quantum Numbers







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

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

ZeffCoreZ Radius (nm)

Zeff = Z - s (s = shielding constant)

Zeff Z – number of inner or core electrons

Across a period -

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Down a family -

Effective nuclear charge (Zeff) – Inner shell electrons

“SHIELD” the outer shell electrons from the nucleus

Na

K

Rb

Cs

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19

37

55

10

18

36

54

1

1

1

1

186

227

247

265

ZeffCoreZ Radius (nm)

Trends in Effective Nuclear Charge (Zeff)

and the Shielding Effect

increasing Zeff

incre

asin

g S

hie

ldin

g

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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.

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

Decreasing Atomic Size

Incre

asin

g A

tom

ic S

ize

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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

Radii of Atoms and Ionsmust compare cations to cations and anions to anions

Decreasing Ionic Radius

Incre

asin

g I

onic

Radiu

s

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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


3.2 Atomic Spectra




3.6 Quantum Numbers







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https://tinyurl.com/y8bqsr7g

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 + X2+(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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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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3.2 Atomic Spectra




3.6 Quantum Numbers







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


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