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Atomic Theory:The Quantum Model

of the Atom Chapter 11

Review: the planetary model of the atom(1911)

• Every atom contains an extremely small, extremely densenucleus.

• All of the positive charge and nearly all of the mass of anatom are concentrated in the nucleus.

• The nucleus is surrounded by a much larger volume ofnearly empty space that makes up the rest of the atom.

• In the vast open space that comprises most of the volumeof an atom, electrons travel in circular orbits around thenucleus

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Limitations of the planetary model

• First ionization Energy:Energy required toremove one electron froma gaseous atom of anelement

• The properties of theelements do not changesmoothly as the atomicnumber increases!

Limitations of the planetary model• Does not explain the different properties of

atoms in different groups (or chemical families)• Why are the noble gases so unreactive?

– Why are they gases?• Why do metals conduct electricity?

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Limitations of the planetary model• Does not allow us to understand or predict the way that

atoms will bond to create molecules

• Why do the atoms of some elements tend to form anions,while others form cations?

• Why do the atoms of the element oxygen tend to bond totwo others atoms (H2O), while carbon atoms make 4bonds (CH4)?

• And why don’t the electrons spiral down into the nucleus?

Na+

Ca2+

Cl-

Fe3+

Fe2+

Br-

“Quantization” of light

• White light shone through a prism produces a continuousspectrum

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The “Quantization” of light

• When an element is heated until it emits light and thatlight passes through a prism, a line spectrum forms

• The light only contains a few wavelengths - only waveswith specific energies

Each element has a unique linespectrum

• The line spectra of hydrogen, mercury, and neon• Each type of atom emits specific, but different, wavelengths

of light

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Absorption and emission of light

• Energy is absorbed as an electron is promoted from oneorbit to another

• Energy (light) is emitted as the electron returns to it’s groundstate - an exact amount of energy corresponding to aspecific wavelength of light

• The emission lines happen when heat excites the electrons,which emit photons when they return to the ground state

What have we learned?

• Only specific colors (wavelengths) of light are observed inemission spectra

• Energy is being emitted in specific amounts (quanta)• The electron orbitals have very specific energies• But so far we haven’t explained anything!

– what about the pattern of ionization energies?– why do the elements have different chemical properties?– why don’t electrons fall into the nucleus?

• Max Planck made the math work by only allowing certainspecific energies to exist– the energies needed for electrons to traverse “the last spiral” into

the nucleus are not available to those electrons!

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The Quantum concept

The Bohr model of the hydrogen atom

• Proposed by Niels Bohr, a Danish scientist, in 1913.• Bohr took Planck’s “mathematical cheat” and assumed it

was real• Electrons can only be in certain orbits

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The Bohr model• Ground State: Lowest-energy orbit available• Excited States: Orbits with higher energy than the ground

state• Orbits in the Bohr model are called Principal Energy Levels or Principal Quantum Numbers (n)

Explains the line spectra and keeps the electrons awayfrom the nucleus, but leaves us with some questions

• Why do the electrons only occupy certain orbits?• Why do elements have the properties we observe?

• de Broglie (1924): Matter in motion, such as electrons, hasproperties that are normally associated with waves

• mv = h/λ– m = mass– v = velocity– h = Planck constant– λ = wavelength

• An electron traveling at one twentieth light speed has awavelength of 5 x 10-11 m - the radius of a hydrogen atom

• A 50 kg person running at 10 m/sec has a wavelength of1.3 x 10-36 m - which is not meaningful

• Schrödinger (1925-28): Applied the principles of wavemechanics to atoms

The quantum mechanical model ofthe atom

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Wave mechanics• The vibration of a constrained string (a guitar string is attached

at the bridge and the nut) has certain natural frequencies(harmonics) that are integer multiples of the fundamental

• The same is true for an electron behaving as a wave,constrained by the potential well of the nucleus

Suggests that electrons are particles,in specific locations.Heisenberg (1925-1927) showed thatthis was not a meaningful model dueto uncertainty in the speeds andpositions of the electrons.

Suggests that electrons are waves.Orbitals are interpreted asprobability densities.Electrons are fuzzy clouds ofcharge.

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Solutions to the Schrodinger equationfor the hydrogen atom

• Orbitals

• Region in spacearound a nucleus inwhich there is ahigh probability offinding an electron

• Each orbital can beoccupied by 0, 1 or2 electrons

s

p

d

The quantum mechanical description of each electron inin a multi-electron atom can be described using fourquantum numbers

For each electron there is a unique set of quantumnumbers

The quantum numbers describe the energy level andprobable location of the electron

Quantum numbers

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(Remember the Bohr “orbits”)

Principal Energy Levels, n

• n = 1,2,3,4,5,6,7• Generally, energy increases with increasing n• Distance of the electron from the nucleus increases

with increasing n

Sublevels and Orbitals

• For each principal energy level there are one or moresublevels (s, p, d, f) associated with different types of orbital

• The total number of sublevels is equal to n, the principalquantum number

Principal quantum number = 1The lowest energy level

• Just one solution to theSchrodinger equation,

• One sublevel, s• One orbital, which can

contain a maximum of twoelectrons

• If your atom only containstwo electrons they are likelyto be in this region of space

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Sublevels and Orbitals

• For each principal energy level there are one or moresublevels (s, p, d, f) associated with different types of orbital

• The total number of sublevels is equal to n, the principalquantum number

Principal quantum number(principal energy level) = 2

• Two sublevels, s and p• One orbital in the s sublevel

and three in the p sublevel• Each orbital can contain a

maximum of two electrons• Maximum electrons at this

principle energy level = 8

s

p

Sublevels and Orbitals

• For each principal energy level there are one or moresublevels (s, p, d, f) associated with different types of orbital• The total number of sublevels is equal to n, the principalquantum number

Principal quantum number = 3

• Three sublevels: s, p and d• One orbital in the s sublevel,

three in the p sublevel, 5 inthe d sublevel

• Each orbital can contain amaximum of two electronsfor a total of 18 electrons

• HOWEVER! The energy ofthe 4s sublevel is less thanthe 3d

s

p

d

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Sublevel energy level order:

1s < 2s < 2p < 3s < 3p <

4s < 3d < 4p < 5s < 4d <

5p < 6s < 4f < 5d < 6p <

7s < 5f < 6d

You can memorize this sequence or.…

This chart, or…..

Each box can hold0, 1 or 2 electrons

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Remember the pattern from the periodic table

The electron configurations

• Hydrogen has only one electron. It is in the 1s orbital (the lowestenergy orbital)

• Helium has two electrons, they can both go into the 1s orbital• Lithium has three electrons, so two go in the 1s orbital and one

goes into the 2s orbital• Carbon has 6 electrons, 2 in the 1s orbital, 2 in the 2s orbital and

2 in the 2p orbital

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Principal energy level• n = 1, 2, 3, 4, 5, 6, 7

Sublevel• s, p, d, f

Number of orbitals• s: 1, p: 3, d: 5, f: 7

Orbital occupancy, number of electrons in orbital• limited to 2

Summary

1. Electrons occupy the lowestenergy sublevel available

2. No more than two electronscan occupy any one orbital

Rules for writing electronconfigurations

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Example: Electron configuration for Al

• Write the electronconfiguration ofaluminum

• Step 1: Locate Al in theperiodic table

• The atomic number is13 (13 protons) so wemust have 13 electronsin the neutral atom

1s 2s 2p 3s 3p

Example: Electron configuration for Al

• Step 2: follow the periodic table to list all sublevels in order ofincreasing energy until you get to the block in which the elementis located

• This gives the energy levels and orbitals which will be occupied

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1s 2s 2p 3s 3p

Step 3: Add the appropriate number ofelectrons to each sublevel until all 13 are used

1s2 2s2 2p6 3s2 3p1

Step 4: Check for the correctnumber of electrons

2 + 2 + 6 + 2 + 1 = 13 = Z for Al

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Example: Electron configuration for C

• The atomic number is 6(6 protons) so we musthave 6 electrons in theneutral atom

• 1s 2s 2p

• 1s2 2s2 2p2

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Noble gas “cores”

• The noble gases (last column of the periodictable) are very stable

• All the orbitals within one principle energy levelare filled

• Electrons are not likely to leave these energylevels (for example, to form a bond withanother atom - the noble gases are veryunreactive!)

• For elements beyond Neon (Ne) the innermostelectrons form an unreactive “noble gas core”

1s22s22p63s23p1Al:

Ne

A noble-gas core is commonly usedwhen writing electron configurations

Al: [Ne]3s23p1

Since the n = 1 and 2 electrons are in the inner part of theatom and therefore not involved in bonding, we don’t

need much detail about their configurations

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2. Write the elemental symbol of the noble gas in squarebrackets, followed by the remaining configuration (the“valence electrons”)

1. Find the highest atomic-numbered noble gas (Group8A element) less than the atomic number of theelement for which the configuration is being written

Writing electron configurationsusing noble gas “cores”

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Example: Electron configuration for Ni

• The atomic number is28

• We have 28 electronsin the neutral atom

• Sublevels:

1s 2s 2p 3s 3p 4s 3d

• Orbital occupancy:

1s2 2s2 2p6 3s2 3p6 4s2

3d8

[Ar] 4s2 3d8

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The quantum model of an atom:Does it work?

• Does it explain (and predict!)experimentally observedbehavior?

• Example: trends in ionizationenergies (energy required toremove an electron from an atomleaving behind a charged ion)

Note two periodic trends in ionization energy:

1. Energy decreases down a group2. Energy increases across a period

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Explaining the trends in ionizationenergies

1. Energy decreases down a group

• Atoms are larger further down the table (more electrons,larger principle quantum numbers)

• The negative electrons in the outermost orbitals arefurther from the positive nucleus

• The electrostatic force holding them into the atom is less

Explaining the trends in ionizationenergies

2. Energy increases across a period (andzig-zags)

• Removing one electron from Li, Na, K leaves a noble gasstructure (very stable) and so is relatively easy

• Removing one electron from Be or Mg is a little harder,but from B or Al leaves a filled s orbital (relatively stable)

• Ionization energy increases as the energy level fills andthe atom becomes more stable

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Average size of atoms

Note two periodictrends in atomic size:

1.Size increases downa group

2.Size decreasesacross a period

1. Down a group:

The average distance of the outermost electronincreases with increasing n, so atoms become bigger

2. Across a period:

Nuclear charge increases, holding the electron more tightly,and the principal energy level of the outermost electron

remains the same, so atoms become smaller

Why?

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The quantum model of an atom:does it work?

• The orbital model of an atom failed to explain theperiodic behavior observed by Mendeleev

• Does this new model do better?• Yes, because all the elements with the same

valence electron configuration are groupedtogether

• These elements have similar properties(chemical families)