Electronic Structure of Atoms

Chapter 6

Light

• Made up of electromagnetic radiation.

• Waves of electric and magnetic fields at right angles to each other.

Parts of a wave

lWavelength

Frequency (n = number of cycles in 1 secondMeasured in hertz 1 hertz = 1cycle/second

Frequency = n

Kinds of EM waves

• There are many different EM waves • different l and n• Visible Light is only the part our eyes can

detect. (colors of the rainbow)• Greater wavelength means, smaller frequency

X-RaysGamma

Rays UV InfraredMicro-

waveRadio

Visible Spectrum

The speed of light, c

• in a vacuum is 2.998 x 108 m/s• c = 3.0 x 108 m/s• c = ln

Examples

c 3.0 x 108 m/sv = = = 6.20 x 1014 Hz 484 x 109 m

c 3.0 x 108 m/sl = = = 5.09 x 10-7 m = 509 nm v 5.89 x 1014 Hz (green light)

What is the wavelength of light with a frequency 5.89 x 1014 Hz?

What is the frequency of blue light with a wavelength of 484 nm?

Planck and the Quantum Theory

• Energy is gained or lost in whole number multiples (n) of the quantity hv.

• Similar to energy required to go up stairs (opposed to going up a ramp)

• Planck found that Energy is transferred to matter in “energy packets” called a quantum (hv)

• Frequency = v• Planck’s constant = h = 6.63 x 10-34 J-s

DE = nhn

Einstein, the Photoelectric Effect, and Photons

• EM radiation is quantized a stream of particles -- “photons”

• Ephoton = hn = hc/l • Combine this with E = mc2 • You get the apparent mass of a photon.

m = h / (lc)

Is light a Wave or does it consist of particles?

• Both…• Macroscopically like a wave,• But consists of a collection of photons that

we only see at the atomic level.• called The Wave-Particle Duality(Like describing an entire beach and then

beginning to examine the grains of sand.)

Examples

• Calculate the energy of one photon of yellow light whose wavelength is 589nm

1. Find the frequency• 5.09 x 1014 s-1

2. Then use Plank’s equation to find E• 3.37 x 10-19 J

Matter as a wave

• Using the velocity (v) instead of the frequency ( )n we get:

• De Broglie’s equation l = h/mv• Can calculate the wavelength of an object.

Line Spectra

• Spectrum = the range of frequencies present in light

• Continuous Spectrum = contains all wavelengths of light. (white light… can be broken down into “rainbow”)

• Line Spectrum = contains only specific wavelengths of light.

Hydrogen spectrum

• Emission spectrum because these are the colors it gives off or emits.

• Called a bright line emission spectrum.• There are just a few discrete lines showing

410 nm

434 nm

486 nm

656 nm

Visible Spectrum

Bright Line Spectra

• Excited electrons return to lower NRG states• NRG is emitted in the form of a photon of definite

wavelength.• Definite change in energy corresponds to:

– Definite frequency – Definite wavelength

• Use DE = h n = hc / l• Only certain energies are possible within any atom.

Niels Bohr

• Developed the Quantum Model• Described the atom like a solar system• Electrons attracted to (+) nucleus because of

their (-) charge• Electrons didn’t fall into nucleus because

they were moving around

Bohr’s atom

• Found only certain NRGs were allowed; called them NRG levels.

• Putting NRG into atom moves electron away from the nucleus (ground state excited state)

• When e- returns to ground state, it gives off light of a certain NRG

The Bohr Atom

n = 3n = 4

n = 2n = 1

Available NRG levels

E = -2.178 x 10-18 J (Z2 / n2 )• n = quantum number (NRG level)• Z = nuclear charge (+1 for Hydrogen)• J = energy in joules

• The more negative the NRG is, the more stable the atom will be.

change in Energy• When the electron moves from one

energy level to another:• DE = Efinal - Einitial

DE = -2.178 x 10-18J [(1/ nf2)–(1/ ni

2)]

l = hc / DE

Shortcomings of Bohr Model

• Only works for Hydrogen atoms• Electrons don’t move in circular orbits• The quantization of energy is right, but not

because they are circling like planets• Questions Bohr couldn’t answer: Why are e- confined to only certain energy levels? Why don’t e- eventually spiral and crash into the nucleus?

The Quantum Mechanical Model

• New approach that viewed electron as a standing wave of NRG

• Standing waves don’t propagate through space

• Standing waves are fixed at both ends(similar to vibrations of a stringed instrument)

What’s possible?

• You can only have a standing wave if you have complete waves.

• There are only certain allowed waves.• In the atom there are certain allowed waves

called electrons.• 1925 Erwin Schroedinger described the wave

function of the electron. “The Schroedinger Equation”

• Much math but what is important are the solutions.

Schroedinger’s Equation

• The wave function, is a F(x, y, z)• Solutions to the equation are called orbitals.• These are not Bohr orbits.• Each solution is tied to a certain energy.• These are the energy levels.• Many strange and seemingly impossible behaviors

occur when the electron is treated as a wave!

22 22 22 82m

2x2 2y2 2z2 h2 (E V) = 0

Orbitals

• Orbitals are not circular orbits for electrons

• Orbitals are areas of probability for locating electrons

There is a limit to what we can know…

• about how the electron is moving or how it gets from one energy level to another.

• about both the position and the momentum of an object.

• The Heisenberg Uncertainty Principle - “we cannot know the exact location and exact momentum of an electron at the same time.”

Quantum Mechanical Model and Quantum Numbers

• Note: A quantum mechanical orbital is not the same as a Bohr orbit because the motion of the electron in an atom cannot be precisely measured or tracked. (Heisenberg uncertainty Principle)

• There are 4 quantum numbers to describe the “location” of an electron. (sort of like how a zip code works)

Principal Quantum Number (n)

• Indicates probable distance from the nucleus (old Bohr orbitals)

• Gives the size and energy of the orbital• Has integer values >0• According to the periodic table, what would

the highest principal quantum number be?

Angular Momentum Quantum (l )• Gives the shape of the orbital (more detail to

come)• Integral values from 0 to (n-1) for each principal

quantum number (n)Value of l 0 1 2 3 4

Letter used for shape*

s p d f g

*letters s, p, d, f come from the words sharp, principal, diffuse, and fundamental, which were used to describe certain features of spectra before quantum mechanics was developed.

Magnetic Quantum Number (ml )

• Relates to the orientation of the orbital in space relative to the other orbitals. (It tells you if the orbital will be on the x, y or z axis.)

• Integral values from l to –l including 0.

n l Orbital designation

ml # of orbitals

1 0 1s 0 1

2 0 2s 0 1

1 2p -1, 0, 1 3

3 0 3s 0 1

1 3p -1, 0, 1 3

2 3d -2, -1, 0, 1, 2 5

4 0 4s 0 1

1 4p -1, 0, 1 3

2 4d -2, -1, 0, 1, 2 5

3 4f -3, -2, -1, 0, 1, 2, 3 7

Important Observations

1. The shell w/ quantum #n will have exactly n subshells.

2. Each subshell has a specific number of orbitals. Each orbital corresponds to a different allowed value of ml. For a given value of l, there are 2l + 1 allowed values of ml.

3. The total number of orbitals in a shell is n2. The resulting number of orbitals for the shells – 1, 4, 9, 16 – is related to a pattern seen in the periodic table… We see the number of elements in the table – 2, 8, 18, 32 – equal twice these numbers…

S orbitals

n = 1 n = 2 n = 3

P orbitals

At another energy level the solutions are “dumbell” shaped.

There are 3 possible solutions for this energy level.

P OrbitalsAll 3 p orbitals may exist at the same time.

d orbitalsAt another energy we get “flower” shaped orbitals for a solution.

All 5 may exist

at the same

time

F orbitalsAnd finally, at another energy, 7 f orbitals are the solution.

Orbital Energies

• All orbitals with the same value of n have the same energy

• The lowest energy state is called the “ground state”

• When the atom absorbs energy, electrons may move to higher energy orbitals – “excited state”

Electron Spin Quantum Number (ms )

• An individual orbital can hold only 2 electrons

• Electrons must have opposite spins (why important?)

• Spin can have two values +½ or –½

Pauli Exclusion Principle

“in a given atom, no two electrons can have the same set of four quantum numbers”

What this means for the atom?• Each atomic sub-orbital may contain a

maximum of 2 electrons• Those electrons must have opposite spins

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s7s

2p

3p

4p

5p

6p

3d

4d

5d

7p

6d

4f

5f

Helium with 2 electrons

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s7s

2p

3p

4p

5p

6p

3d

4d

5d

7p

6d

4f

5f

Li with 3 electrons

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s7s

2p

3p

4p

5p

6p

3d

4d

5d

7p

6d

4f

5f

Boron with 5 electrons

2 more important rules:

• Aufbau Principle – electrons enter orbitals of lowest energy first.

• Hund’s Rule -- When electrons occupy orbitals of equal energy, one electron enters each orbital before they pair.

For Example:

2s 2p

After the s sublevel gets two electrons, three electrons enter the p orbitals before they pair.

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s7s

2p

3p

4p

5p

6p

3d

4d

5d

7p

6d

4f

5f

s p

d

f

Electron Configuratoin

3 QUESTIONS TO ASK

• What Row? –(principle energy level)

• What section? –(type of sub-orbital)

• What seat? –(how many electrons in that sub-

orbital)

Example 1:Write the electron configuration for nitrogen.7N 1s22s22p3

Example 2:Write the electron configuration for Fe.

26Fe 1s22s22p63s23p64s23d6

Condensed Electron Configurations

• Put the symbol for the Noble gas from the previous principal energy level, then add the electron configuration after that point.

• Example 1 for Nitrogen:[He] 2s22p3

• Example 2 for Iron:• [Ar] 4s23d6

The History of the Modern

Periodic TableSee separate slide show for Periodic Table History

Periodic Law• When elements are arranged in order of

increasing atomic #, elements with similar properties appear at regular intervals.

0

50

100

150

200

250

0 5 10 15 20

Ato

mic

Ra

diu

s (

pm

)

Atomic Number

Chemical ReactivityFamilies Similar valence e- within a group

result in similar chemical properties

1

2

3

4 5

6

7

•Alkali Metals•Alkaline Earth Metals•Transition Metals•Halogens•Noble Gases

Periodic Table Reveals Periodic Trends

• Effective Nuclear charge

• atomic size or radius

• ionization energy

• electron affinity

• electronegativity

• metallic character

• Reactivity

• bonding characteristics

• crystal configurations

• acidic properties

• densities

• Melting/Boiling points

Electron screening or shielding

• Electrons are attracted to the nucleus• Electrons are repulsed by other electrons• Electrons would be bound more tightly if

other electrons weren’t present.• The net nuclear charge felt by an electron is

called the effective nuclear charge ( Zeff ).

Quantum Mechanical Model

Zeff is lower than actual nuclear charge.

Zeff increases toward nucleus ns > np > nd > nf

This explains certain periodic changes observed.

Effective Nuclear Charge ( Zeff)

• The effective nuclear charge acting on an electron equals the number of protons in the nucleus, Z, minus the average number of electrons, S that are between the nucleus and the electron in question.

Zeff = # protons # shielding electrons

Zeff = attractive forces repulsive forces Zeff = Z S

For Example, Lithium vs. Carbon

Li Zeff = 3 2 = 1

C Zeff = 6 2 = 4

So, carbon has a much smaller atomic radius compared to lithium: Rcarbon =77

pm Rlithium = 152 pm

When moving across a row:The greater the Zeff value, the smaller the atom’s radius.

Trend #1 Atomic Radii

1

2

3

4 5

6

7

Increases to Left and Down

•Why larger going down?

•Why smaller to the right?

• Higher energy levels have larger orbitals

• Shielding - core e- block the attraction between the nucleus and the valence e-

• Increased nuclear charge without additional shielding pulls e- in tighter

Practice…

• Referring to a periodic table, arrange the following atoms in order of increasing size:– Phosphorus– Sulfur– Arsenic– Selenium

• S < P < Se < As

Atomic radii

The Periodic Table & Radii

Periodic Trend is Due to Effective Nuclear Charge

Atomic Radii vs. Zeff:

Trends in Ionic Radii

• Using your knowledge of Zeff, how would the size of a cation compare to neutral atom? Anion?

Trends in Ionic Radii

• The cation of an atom decreases in size.

• The more positive an ion is, the smaller it is because Zeff increases

• The anion of an atom increases in size.

• The more negative an ion, the larger it is because Zeff decreases.

Cations lose electrons, become smaller

Anions gain electrons, become bigger

Ion Radii

1

2

3

4 5

6

7

+3 +4 -3 -2 -1

Increases downIncreases moving across, but depends if cation OR anion

Ions and Ionic Radii

Practice…• Arrange the following atoms and ions in order

of decreasing size: – Mg2+

– Ca2+

– Ca• Which of the following ions is the largest:

– S2-

– S– O2-

Practice…• Arrange the following ions in order of decreasing

size:– S2-

– Cl-

– K+

– Ca2+

• Which of the following ions is the largest?– Rb+

– Sr2+

– Y3+

Trend in Ionization Energy

• Ionization NRG is the NRG required to remove an electron from an atom

Successive Ionization NRG

• Ionization energy increases for successive electrons from the same atom.

*Notice the large jump in ionization energy when a core e is removed.

Why do you think there is such a big jump for Mg3+?

• The smaller the atom, the higher the ionization energy due to Zeff

• Bigger atoms have lower ionization NRG due to the fact that the electrons are further away from the nucleus and therefore easier to remove.

Increases

Dec

reas

es

Practice…• Which of the following elements would

have the highest second ionization energy? Justify your answer.–Sodium, Sulfur, or Calcium

• Which will have the greater third ionization energy, Ca or S? Justify your answer.

Practice…

• Referring to a periodic table, arrange the following atoms in order of increasing first ionization energy (Ne, Na, P, Ar, K) Justify your answer.

• Based on the trends discussed in this section, predict which of the following atoms (B, Al, C or Si) has the lowest first ionization energy and which has the highest first ionization energy.

Electron Affinity

• The energy change associated with the addition of an electron

• Tends to increase across a period• Tends to decrease as you go down a group• Abbreviation is Eea, it has units of kJ/mol. Values are

generally negative because energy is released.• Value of Eea results from interplay of nucleus

electron attraction, and electron–electron repulsion.

Ionization NRG vs. Electron Affinity• Ionization energy measures the ease with

which an atom loses an electron • Electron affinity measures the ease with

which an atom gains an electron

Electron Affinity

Trends in Electronegativity

• tendency for an atom to attract electrons when it is chemically combined with another atom.

• decreases as you move down a group• increases as you go across a period from

left to right.

Trend #5 Metallic Character• The metallic character of atoms can be related

to the desire to lose electrons.

• The lower an atom’s ionizatoin energy, the

greater its metallic character will be.

• On the periodic table, the metallic character of

the atoms increase down a family and decreases

from left to right across a period.

Metals Nonmetals

• Shiny Luster• Various colors (most

silvery)• Solids are malleable and

ductile• Good conductors of heat

and electricity• Most metal oxides are

ionic solids that are basic• Tend to form cations in

aqueous solution

• No luster• Various colors• Brittle solids• Poor conductors of heat

and electricity• Most nonmetal oxides

are molecular substances that form acidic solutions

• Tend to form anions or oxyanions in aqueous solution

Metallic Character

1

2

3

4

5

6

7

Increases moving down and across to the left

Fr

Cs Ba

Ra

Lower left corner -- elements mostlikely to lose their valence electrons

Rb

Metals and Nonmetals

• Low ionization energies of metals means they tend to form cations (positive ions) relatively easily

• Due to their electron affinities, nonmetals tend to gain electrons when they react with metals.

# 6 Melting/Boiling Points

• Highest in the middle of a period (generally).

1

2

3

4 5

6

7

Some Important Properties of Alkali Metals

• Soft metallic solids• Easily lose valence electrons (Reducing

Agents)– React with halogens to form salts– React violently with water

• Large Hydration NRG– Positive ionic charge makes ions attractive to

polar water molecules

Alkaline Earth Metals…• Harder and more dense than Alkali Metals• Less reactive than alkali metals (lower first

ionization energies)• Reactivity increases as you move down the

periodic table.

The Halogens…

• “Salt Formers”• Melting and Boiling Points increase with

atomic number.• Highly negative electron affinities• Tendency to gain electrons and form halide

ions

Noble Gases …

• Monoatomic ions• Gases at room temperature• Large 1st ionization energies• “Exceptionally” unreactive

Practice…

• Look at Sample Integrative Exercise 7 on page 264