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PACS 2008 PACS 2008 Unit: Atomic Structures Unit: Atomic Structures Mr. Nylen Mr. Nylen Pulaski Academy Pulaski Academy High School High School 2008 2008

PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

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Page 1: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

PACS 2008PACS 2008

Unit: Atomic StructuresUnit: Atomic Structures

Mr. NylenMr. NylenPulaski Academy Pulaski Academy

High SchoolHigh School

20082008

Page 2: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

The Modern AtomThe Modern Atom Atom – smallest indivisible particle of Atom – smallest indivisible particle of

mattermatter Each specific element is made up of the Each specific element is made up of the

same type of atomssame type of atoms Every Hydrogen atom has the same number Every Hydrogen atom has the same number

of subatomic particlesof subatomic particles Every Helium atom has the same number of Every Helium atom has the same number of

subatomic particlessubatomic particles

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Page 3: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

AtomsAtoms

Hydrogen AtomHydrogen Atom Oxygen AtomOxygen Atom

Element (H)Element (H) Element Element (Oxygen)(Oxygen)

Compounds Compounds

(H(H22O)O)

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Page 4: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Sub-Atomic ParticlesSub-Atomic Particles

Atoms are made up of subatomic Atoms are made up of subatomic particlesparticles ProtonsProtons ElectronsElectrons NeutronsNeutrons

All atoms contain subatomic particlesAll atoms contain subatomic particles A group of atoms making up an A group of atoms making up an

element are all IDENTICALelement are all IDENTICALPACS 2008PACS 2008

Page 5: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

The main sub-atomic The main sub-atomic particlesparticles

Particle Charge Mass Symbol Location

Proton 1 1 amu H+ , or + Nucleus

Neutron 0 1 amu Nucleus

Electron -1 0 amu e- , or - Outer shell

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Page 6: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Atomic MassAtomic Mass

Mass of the atom – made up mostly Mass of the atom – made up mostly of mass of protons and neutronsof mass of protons and neutrons

Measured in Atomic Mass UnitsMeasured in Atomic Mass Units 1 amu = 1/12 the mass of 1 amu = 1/12 the mass of

a Carbon-12 atom (the a Carbon-12 atom (the

standard for all relative standard for all relative

atomic masses)atomic masses)

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Page 7: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Atomic Mass (A)Atomic Mass (A)

Since a proton = 1 amu, and a Since a proton = 1 amu, and a neutron = 1 amu (or u), atomic mass neutron = 1 amu (or u), atomic mass also represents the number of also represents the number of protons and neutrons in the nucleusprotons and neutrons in the nucleus

Electrons have negligible weight and Electrons have negligible weight and aren’t factored in to atomic massaren’t factored in to atomic mass

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Page 8: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Atomic Number (Z)Atomic Number (Z)

Represents the charge in the nucleusRepresents the charge in the nucleus For atoms this means Z = the For atoms this means Z = the

number of protons in the nucleusnumber of protons in the nucleus This is what makes an atom of an This is what makes an atom of an

element different compared to other element different compared to other elementselements

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Page 9: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Charting Atoms/ElementsCharting Atoms/Elements Symbol – Accepted letter or letters Symbol – Accepted letter or letters

representing that atom (or element)representing that atom (or element) Atomic Number – Directly proportional Atomic Number – Directly proportional

to number of protons in the nucleusto number of protons in the nucleus Also represents charge in the nucleusAlso represents charge in the nucleus

Atomic Mass – Mass of the nucleusAtomic Mass – Mass of the nucleus Remember, electrons are negligibleRemember, electrons are negligible Protons + NeutronsProtons + Neutrons

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Page 10: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Charting Atoms/ElementsCharting Atoms/Elements Number of Protons – Same as atomic number, Number of Protons – Same as atomic number,

or usually half of atomic massor usually half of atomic mass Number of electronsNumber of electrons

Assuming atom or element has zero chargeAssuming atom or element has zero charge # Electrons equal the number of protons# Electrons equal the number of protons

Number of neutronsNumber of neutrons All the mass of an atom is made up of protons + All the mass of an atom is made up of protons +

neutronsneutrons We know the number of protons so we can We know the number of protons so we can

calculate the number of neutronscalculate the number of neutrons

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Page 11: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Page 4-5Page 4-5

Work in small groupsWork in small groups

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Page 12: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

TogetherTogether

Notes p. 6 and 7Notes p. 6 and 7

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Page 13: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

IsotopesIsotopes

Atoms of the same element (w/same Atoms of the same element (w/same # of protons and same charge) BUT # of protons and same charge) BUT different number of neutrons different number of neutrons (therefore different atomic mass)(therefore different atomic mass)

Ex. The 3 naturally occurring Ex. The 3 naturally occurring isotopes of CARBONisotopes of CARBON Carbon 12, Carbon 13, Carbon 14Carbon 12, Carbon 13, Carbon 14

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Page 14: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Carbon 12, 13, and 14Carbon 12, 13, and 14

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14

Page 15: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Isotopes of HydrogenIsotopes of Hydrogen Hydrogen usually Hydrogen usually

has 1 proton, and has 1 proton, and atomic mass of 1atomic mass of 1

Isotopes of Hydrogen Isotopes of Hydrogen can have an atomic can have an atomic mass of 2 or 3mass of 2 or 3 How many protons in How many protons in

these isotopes?these isotopes? How many neutrons?How many neutrons?

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Page 16: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Page 8, Weighted Atomic Page 8, Weighted Atomic MassMass

Atomic mass shown in periodic table Atomic mass shown in periodic table is a weighted average of the masses is a weighted average of the masses of the naturally occurring isotopes of of the naturally occurring isotopes of the element.the element.

This is why hydrogen has a mass of This is why hydrogen has a mass of 1.000741.00074

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Page 17: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Weighted Atomic MassWeighted Atomic Mass You take an exam having three You take an exam having three

parts. The first multiple choice part parts. The first multiple choice part is weighted 20%, the second part is is weighted 20%, the second part is weighted 40%, and the third part is weighted 40%, and the third part is weighted 40%weighted 40%

A student scores the followingA student scores the following

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Exam Score

Weighted Percent

Fraction of points earned

Overall Score

Part A - 80 20%

Part B - 72 40%

Part C - 94 40%

Page 18: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Weighted Atomic MassWeighted Atomic Mass

An element has three isotopes An element has three isotopes (different number of neutrons). What (different number of neutrons). What is the weighted atomic mass of the is the weighted atomic mass of the element?element?

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Isotope % abundance in nature

Fractional Abundance

Product

Carbon 12 98.9% 12 * (.989) =

Carbon 13 1.05% 13 * (.0105) =

Carbon 14 .05% 14 * (.0005) =

Weighted Atomic Mass:

Page 19: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Weighted Atomic Mass (K)Weighted Atomic Mass (K)

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Isotope % abundance in nature

Fractional Abundance

Product

K- 39 93.12%

K- 40 6.88%

Weighted Atomic Mass:

Page 20: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Lab – Isotopes of PenniumLab – Isotopes of Pennium

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Page 21: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Problem Set – Pg. 9Problem Set – Pg. 9

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Page 22: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Isotopes = neutronsIsotopes = neutronsIons = electronsIons = electrons

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Page 23: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Page 10 - IonsPage 10 - Ions

Atoms with a net charge. Formed Atoms with a net charge. Formed when atoms gain or lose electrons (If when atoms gain or lose electrons (If an element loses a proton it isn’t the an element loses a proton it isn’t the same element anymore!)same element anymore!)

Therefore the number of protons Therefore the number of protons doesn’t equal the number of doesn’t equal the number of electronselectrons

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Page 24: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Ions - continuedIons - continued

If we lose electrons, we become more If we lose electrons, we become more positive (take away negative charge)positive (take away negative charge)

If we gain electrons, we become more If we gain electrons, we become more negative (adding negative charge)negative (adding negative charge)

If we lose or gain protons, we If we lose or gain protons, we completely change the atom or completely change the atom or element!element!

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Page 25: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Ions - SUMMARYIons - SUMMARY

Never change # of protonsNever change # of protons Charge comes from # electronsCharge comes from # electrons

If electrons = protons, charge is 0If electrons = protons, charge is 0 If electrons > protons, charge is negativeIf electrons > protons, charge is negative If electrons < protons, charge is positiveIf electrons < protons, charge is positive Neutrons are used to make up difference Neutrons are used to make up difference

in atomic mass ONLY (they have no in atomic mass ONLY (they have no charge)charge)

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Page 26: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

ClassworkClasswork

Finish table at bottom of page 10Finish table at bottom of page 10

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Page 27: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Lab - Page 11 - 14Lab - Page 11 - 14

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Page 28: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

HomeworkHomework

Read section 3-2 in textRead section 3-2 in text Do p. 6-7 At. Structure notesDo p. 6-7 At. Structure notes

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Page 29: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Ions – Counting neutrons…Ions – Counting neutrons…

Bottom of page 10Bottom of page 10

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Page 30: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Isotope LabIsotope Lab

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Page 31: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Pages 16 – 21 in NotesPages 16 – 21 in Notes

Answer questions in notesAnswer questions in notes Work in computer labWork in computer lab Work quietly as there is a class next Work quietly as there is a class next

doordoor

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Page 32: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Models of the atomModels of the atom

Dalton’s Indivisible AtomDalton’s Indivisible Atom

J.J. Thomson’s Plum Pudding ModelJ.J. Thomson’s Plum Pudding Model

Rutherford’s Solar System ModelRutherford’s Solar System Model

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Page 33: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Dalton’s Indivisible AtomDalton’s Indivisible Atom

Elements consist of tiny particles Elements consist of tiny particles called “atoms”called “atoms”

Atoms of different elements are Atoms of different elements are differentdifferent

Compounds have constant composition Compounds have constant composition because they contain a fixed ratio of because they contain a fixed ratio of atomsatoms

tiny, indivisible, indestructible particles tiny, indivisible, indestructible particles

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Page 34: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

J.J. Thomson’s “Plum J.J. Thomson’s “Plum Pudding” ModelPudding” Model

Discovered eDiscovered e-- in 1897 in 1897 Also called chocolate Also called chocolate

chip cookie modelchip cookie model How does this differ How does this differ

from what we know from what we know about the modern about the modern theory of the atom?theory of the atom?

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Page 35: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Rutherford’s AtomRutherford’s Atom

““Gold foil” Gold foil” experimentexperiment

Region of dense Region of dense charge in center charge in center of atomof atom

Electrons orbit Electrons orbit around this around this “center”“center”

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Page 36: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Bohr’s Modern TheoryBohr’s Modern Theory

Most accepted Most accepted during mid/late during mid/late 1900’s1900’s

ee-- actually fill actually fill imaginary imaginary “shells”“shells”

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Page 37: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Wave Mechanical ModelWave Mechanical Model

Electrons aren’t in “shells”, but rather Electrons aren’t in “shells”, but rather are in “regions of probability”are in “regions of probability”

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Page 38: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

PostersPosters Create a poster outlining one of the models of the Create a poster outlining one of the models of the

atom we talked aboutatom we talked about DaltonDalton J.J. ThomsonJ.J. Thomson Rutherford (gold foil experiment or atom)Rutherford (gold foil experiment or atom) BohrBohr Wave MechanicalWave Mechanical Sequential Development of the atomSequential Development of the atom

Poster should contain visuals as well as any other Poster should contain visuals as well as any other necessary informationnecessary information

You will be graded as a group and you will present You will be graded as a group and you will present these to the classthese to the class

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Page 39: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Vocab activityVocab activity UnderstandingUnderstanding

IsotopesIsotopes IonsIons AllotropesAllotropes AtomsAtoms Plum pudding modelPlum pudding model Bohr modelBohr model Wave mechanical modelWave mechanical model Gold Foil experimentGold Foil experiment

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Page 40: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Create a “puzzle” using Create a “puzzle” using

Using your topic, create a 9 piece puzzle Using your topic, create a 9 piece puzzle using definitions about that topicusing definitions about that topic ExampleExample

Once you have all of your definitions, Once you have all of your definitions, cut out pieces so they fit together like a cut out pieces so they fit together like a puzzle.puzzle.

Hide your pieces around the room for Hide your pieces around the room for another group, bring me the main pieceanother group, bring me the main piece

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Page 41: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Notes pg 22Notes pg 22

Use the timeline on the back of the Use the timeline on the back of the page to answer questionspage to answer questions

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Page 42: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Notes pg. 24-25Notes pg. 24-25

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Page 43: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Notes pg. 26-27Notes pg. 26-27

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Page 44: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Problem SetProblem Set

Describe Rutherfords gold foil Describe Rutherfords gold foil experiment and write his two experiment and write his two conclusions about the atomconclusions about the atom

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Page 45: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Light as a Wave – Light as a Wave – Electromagnetic RadiationElectromagnetic Radiation

Visible light is energy that travels in Visible light is energy that travels in the form of an electromagnetic wavethe form of an electromagnetic wave

We can use a sine wave drawing as a We can use a sine wave drawing as a model of an electromagnetic wave.model of an electromagnetic wave.

Wavelength = Wavelength = λλ

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crest crest

wavelength

crest crest

wavelength

Page 46: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Light as a WaveLight as a Wave

Wave frequency – The number of crests Wave frequency – The number of crests passing a point each second. Units = passing a point each second. Units = 1/seconds (Hertz, Hz)1/seconds (Hertz, Hz)

Wave speed = The speed of all Wave speed = The speed of all electromagnetic waves in a vacuum is electromagnetic waves in a vacuum is 3x103x1088 m/s (This is the speed of light) m/s (This is the speed of light)

c = f c = f λλ c = speed of light, f = frequency, c = speed of light, f = frequency, λλ = wavelength = wavelength

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Page 47: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Electromagnetic SpectrumElectromagnetic Spectrum

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Page 48: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

SpectraSpectra Looks like a rainbowLooks like a rainbow All frequencies of visible light in one All frequencies of visible light in one

continuous bandcontinuous band Produced by passing white light Produced by passing white light

through a prism through a prism

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Page 49: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Bright Line (Emission) Bright Line (Emission) SpectraSpectra

Looks like bright colored lines on a black Looks like bright colored lines on a black backgroundbackground

Only specific frequencies of visible light Only specific frequencies of visible light observed, called Spectral Linesobserved, called Spectral Lines

Produced by adding energy (by putting in Produced by adding energy (by putting in a flame or adding electricity) and viewing a flame or adding electricity) and viewing light through a prismlight through a prism

Emission spectra is like a fingerprint for an Emission spectra is like a fingerprint for an elementelement

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Page 50: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Emission Emission SpectraSpectra

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Page 51: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Bohr Model of the Atom

Applied Quantum Theory to the Atom Energy is absorbed and emitted by

atoms in discrete amounts Electrons may only be located in specific

orbits Electrons possess definite amounts of

energy

Page 52: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Bohr Model Electrons arrange themselves in

specified energy orbits around nucleus

Electrons fill lower energy levels first

Arrangement of electrons equals electron configuration

Page 53: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Principal Energy Levels

K shell (holds 2 electrons) L shell (holds 8 electrons) M shell (holds 18 electrons) N shell (holds 36 electrons)

If electrons absorb exactly the difference between 2 orbits, they will “jump up”

This is an all or nothing proposition This jumping orbital change causes

emission spectra

Page 54: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Lab – Spectral LinesLab – Spectral Lines

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Page 55: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

QuizQuiz

Models of the AtomModels of the Atom

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Page 56: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Ground State vs. Excited State

Ground State The normal energy configuration of electrons Electrons occupy Lowest orbits first Very energetically stable

Excited State Electrons absorb energy from external

source Electrons jump to higher orbits Higher than normal orbits = excited state

Page 57: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Excited StateExcited State Very unstableVery unstable Electrons want to fall back Electrons want to fall back

to ground stateto ground state Energy is released when Energy is released when

electrons fall backelectrons fall back In the form of electromagnetic In the form of electromagnetic

radiationradiation These can be in visible These can be in visible range (photons)range (photons) Each jump represents EMR Each jump represents EMR

frequence of energyfrequence of energy

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Page 58: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Electron ConfigurationsElectron Configurations Add up # electronsAdd up # electrons Match to element on periodic tableMatch to element on periodic table See if electron configuration matches See if electron configuration matches

that on periodic table (if so, it is in that on periodic table (if so, it is in ground state)ground state)

If no, then it is in excited stateIf no, then it is in excited state

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Example: Example: 1212MgMg

Ground = 2-8-2Ground = 2-8-2

Excited = 2-7-3, or 1-8-3, or 1-7-4Excited = 2-7-3, or 1-8-3, or 1-7-4

Page 59: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

PracticePractice

Zinc = atomic number 30Zinc = atomic number 30 30 electrons30 electrons Ground state = 2-8-18-2Ground state = 2-8-18-2

Electron configuration = 2-5-8Electron configuration = 2-5-8 15 electrons, atomic number 15 = 15 electrons, atomic number 15 =

Element Element PhosphorousPhosphorous Ground state = 2-8-5, so it must be excitedGround state = 2-8-5, so it must be excited

Notice: Total number of electrons do not Notice: Total number of electrons do not change from ground to excited statechange from ground to excited state

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Page 60: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

More PracticeMore Practice

Electron configuration 2-7Electron configuration 2-7 Number of electrons =Number of electrons = Atomic Number must equal…Atomic Number must equal… Element must be…Element must be… Ground state for element is…Ground state for element is… Does Ground state match 2-7…Does Ground state match 2-7…

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Page 61: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Try the last 2 on your ownTry the last 2 on your own

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Page 62: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Quantum Mechanical Quantum Mechanical Model of the AtomModel of the Atom

Incorporated findings that electrons Incorporated findings that electrons behave like waves and particlesbehave like waves and particles

Electrons do not move in definite, Electrons do not move in definite, fixed orbits, they move in areas fixed orbits, they move in areas around the nucleus called orbitalsaround the nucleus called orbitals

Orbital = region of space around Orbital = region of space around nucleus where an electron of a certain nucleus where an electron of a certain energy is MOST LIKELY to be foundenergy is MOST LIKELY to be found

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Page 63: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Notes pg. 26Notes pg. 26

Use Text 3-3 as a guideUse Text 3-3 as a guide

Part 2: Type of radiation means Tv, Part 2: Type of radiation means Tv, microwaves, infrared, etc.microwaves, infrared, etc.

For visible spectrum, list the 7 colors For visible spectrum, list the 7 colors of the rainbow (which has the highest of the rainbow (which has the highest wavelength?)wavelength?)

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Page 64: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Problem SetProblem Set Explain the difference between the Explain the difference between the

following following in terms of subatomic in terms of subatomic particlesparticles:: IonsIons IsotopesIsotopes AtomsAtoms

Write a ground state and excited state Write a ground state and excited state electron configuration for electron configuration for BrBromineomine

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Page 65: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

Review ActivityReview Activity

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Page 66: PACS 2008 Unit: Atomic Structures Mr. Nylen Pulaski Academy High School 2008

HomeworkHomework

Pg. 28 in notesPg. 28 in notes

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