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Models of the AtomModels of the Atom
a Historical Perspectivea Historical Perspective
Dr. Vijender Singh
GDC Memorial Degree College
Bahal
Atomos: Not to Be CutAtomos: Not to Be Cut
The History of Atomic TheoryThe History of Atomic Theory
Atomic ModelsAtomic Models
 This model of theThis model of the
atom may lookatom may look
familiar to you. This isfamiliar to you. This is
the Bohr model. Inthe Bohr model. In
this model, thethis model, the
nucleus is orbited bynucleus is orbited by
electrons, which areelectrons, which are
in different energyin different energy
levels.levels.
 A model uses familiar ideas toA model uses familiar ideas to
explain unfamiliar factsexplain unfamiliar facts
observed in nature.observed in nature.
 A model can be changed asA model can be changed as
new information is collected.new information is collected.
The atomicThe atomic
model hasmodel has
changedchanged
throughout thethroughout the
centuries,centuries,
starting in 400starting in 400
BC, when itBC, when it
looked likelooked like aa
billiard ballbilliard ball →→
Who are these men?Who are these men?
In this lesson, we’ll learn
about the men whose quests
for knowledge about the
fundamental nature of the
universe helped define our
views.
DemocritusDemocritus
 This is the GreekThis is the Greek
philosopher Democritusphilosopher Democritus
who began the search forwho began the search for
a description of mattera description of matter
more thanmore than 24002400 yearsyears
ago.ago.
 He asked: CouldHe asked: Could
matter be divided intomatter be divided into
smaller and smallersmaller and smaller
pieces forever, or waspieces forever, or was
there athere a limitlimit to theto the
number of times anumber of times a
piece of matter couldpiece of matter could
bebe divideddivided??
400 BC
AtomosAtomos
 His theory: Matter could notHis theory: Matter could not
be divided into smaller andbe divided into smaller and
smaller pieces forever,smaller pieces forever,
eventually the smallesteventually the smallest
possible piece would bepossible piece would be
obtained.obtained.
 This piece would beThis piece would be
indivisible.indivisible.
 He named the smallestHe named the smallest
piece of matter “atomos,”piece of matter “atomos,”
meaning “not to be cut.”meaning “not to be cut.”
AtomosAtomos
 To Democritus, atomsTo Democritus, atoms
werewere smallsmall, hard, hard
particles that were allparticles that were all
made of the samemade of the same
material but werematerial but were
differentdifferent shapes andshapes and
sizes.sizes.
 Atoms wereAtoms were infiniteinfinite inin
number, alwaysnumber, always
moving and capablemoving and capable
of joining together.of joining together.
This theory was ignored andThis theory was ignored and
forgotten for more thanforgotten for more than 20002000
years!years!
Why?Why?
 The eminentThe eminent
philosophersphilosophers
of the time,of the time,
AristotleAristotle andand
Plato, had aPlato, had a
moremore
respected,respected,
(and ultimately(and ultimately
wrongwrong) theory.) theory.
Aristotle and Plato favored the earth, fire, air
and water approach to the nature of matter.
Their ideas held sway because of their
eminence as philosophers. The atomos idea
was buried for approximately 2000 years.
Dalton’s ModelDalton’s Model
 In the early 1800s,In the early 1800s,
the Englishthe English
Chemist JohnChemist John
DaltonDalton performed aperformed a
number ofnumber of
experiments thatexperiments that
eventually led toeventually led to
the acceptance ofthe acceptance of
the idea of atoms.the idea of atoms.
Dalton’s TheoryDalton’s Theory
 He deduced that allHe deduced that all
elementselements are composed ofare composed of
atoms. Atoms areatoms. Atoms are
indivisible andindivisible and
indestructible particles.indestructible particles.
 Atoms of theAtoms of the samesame elementelement
are exactly alike.are exactly alike.
 Atoms ofAtoms of differentdifferent elementselements
areare differentdifferent..
 CompoundsCompounds are formed byare formed by
the joining of atoms of twothe joining of atoms of two
or more elements.or more elements.
..
This theoryThis theory
became onebecame one
of theof the
foundationsfoundations
of modernof modern
chemistry.chemistry.
Thomson’s Plum PuddingThomson’s Plum Pudding
ModelModel
InIn 18971897, the, the
English scientistEnglish scientist
J.J. ThomsonJ.J. Thomson
provided the firstprovided the first
hint that an atomhint that an atom
is made of evenis made of even
smallersmaller particles.particles.
Thomson’s “Plum Pudding” ModelThomson’s “Plum Pudding” Model
Thomson suggested that the
electrons in an atom were
embedded in a positively
charged, diffuse sphere.
(Early 20th century)
Claim:
Atoms contain an equal amount of positive
charge as negative charge
Thomson ModelThomson Model
 He proposed aHe proposed a
model of the atommodel of the atom
that is sometimesthat is sometimes
called the “called the “PlumPlum
PuddingPudding” model.” model.
 Atoms were madeAtoms were made
from a positivelyfrom a positively
chargedcharged substancesubstance
with negativelywith negatively
charged electronscharged electrons
scatteredscattered about,about,
like raisins in alike raisins in a
pudding.pudding.
Thomson’s “Plum Pudding” ModelThomson’s “Plum Pudding” Model
Reasoning:Reasoning:
 Since atoms were electrically neutral butSince atoms were electrically neutral but
contained negatively charged electrons, theycontained negatively charged electrons, they
must also contain an equal amount of positivemust also contain an equal amount of positive
charge.charge.
 Thomson had no experimental evidence for hisThomson had no experimental evidence for his
model but built on Lord Kelvin’s idea thatmodel but built on Lord Kelvin’s idea that
positive charge in an atom was spread evenlypositive charge in an atom was spread evenly
and diffusely throughout a spherical shape.and diffusely throughout a spherical shape.
(Early 20th century)
Thomson ModelThomson Model
Thomson studiedThomson studied
thethe passagepassage of anof an
electric currentelectric current
through a gas.through a gas.
As the currentAs the current
passed throughpassed through
the gas, it gave offthe gas, it gave off
rays ofrays of negativelynegatively
charged particles.charged particles.
Thomson ModelThomson Model
This surprisedThis surprised
Thomson,Thomson,
because thebecause the
atoms of the gasatoms of the gas
were uncharged.were uncharged.
Where had theWhere had the
negative chargesnegative charges
come from?come from?
Where did
they come
from?
Thomson concluded that the
negative charges came from within
the atom.
A particle smaller than an atom had
to exist.
The atom was divisible!
Thomson called the negatively
charged “corpuscles,” today known
as electrons.
Since the gas was known to be
neutral, having no charge, he
reasoned that there must be
positively charged particles in the
atom.
But he could never find them.
Rutherford’s Gold FoilRutherford’s Gold Foil
ExperimentExperiment
 In 1908, theIn 1908, the
English physicistEnglish physicist
Ernest RutherfordErnest Rutherford
was hard at workwas hard at work
on an experimenton an experiment
that seemed tothat seemed to
have little to dohave little to do
with unraveling thewith unraveling the
mysteries of themysteries of the
atomic structure.atomic structure.
Rutherford’s experiment InvolvedRutherford’s experiment Involved
firing a stream of tinyfiring a stream of tiny positivelypositively
chargedcharged particles at a thin sheet ofparticles at a thin sheet of
gold foilgold foil (2000 atoms thick)(2000 atoms thick)
Rutherford’s Gold FoilRutherford’s Gold Foil
ExperimentExperiment
 MostMost of the positivelyof the positively
charged “bullets” passedcharged “bullets” passed
right through the goldright through the gold
atoms in the sheet ofatoms in the sheet of
gold foilgold foil without changingwithout changing
course at all.course at all.
 SomeSome of the positivelyof the positively
charged “bullets,”charged “bullets,”
however, did bouncehowever, did bounce
away from the gold sheetaway from the gold sheet
as if they had hitas if they had hit
somethingsomething solidsolid. He. He
knew that positiveknew that positive
chargescharges repelrepel positivepositive
charges.charges.
Rutherford’s Gold FoilRutherford’s Gold Foil
ExperimentExperiment
 This could only mean that the gold atoms in theThis could only mean that the gold atoms in the
sheet were mostlysheet were mostly open spaceopen space. Atoms were. Atoms were notnot
a pudding filled with a positively chargeda pudding filled with a positively charged
material.material.
 Rutherford concluded that an atom had aRutherford concluded that an atom had a small,small,
dense, positively charged centerdense, positively charged center thatthat repelledrepelled
his positively charged “bullets.”his positively charged “bullets.”
 He called the center of the atom the “He called the center of the atom the “nucleusnucleus””
 The nucleus isThe nucleus is tinytiny compared to the atom as acompared to the atom as a
whole.whole.
RutherfordRutherford
 Rutherford reasonedRutherford reasoned
that all of an atom’sthat all of an atom’s
positively chargedpositively charged
particles wereparticles were
containedcontained in thein the
nucleus. Thenucleus. The
negatively chargednegatively charged
particles wereparticles were
scatteredscattered outside theoutside the
nucleus around thenucleus around the
atom’satom’s edgeedge..
Bohr ModelBohr Model
In 1913, theIn 1913, the
Danish scientistDanish scientist
Niels BohrNiels Bohr
proposed anproposed an
improvement. Inimprovement. In
his model, hehis model, he
placed eachplaced each
electron in aelectron in a
specificspecific energyenergy
level.level.
Bohr ModelBohr Model
 According toAccording to
Bohr’s atomicBohr’s atomic
model, electronsmodel, electrons
move in definitemove in definite
orbitsorbits around thearound the
nucleus, much likenucleus, much like
planets circle theplanets circle the
sun. These orbits,sun. These orbits,
or energyor energy levelslevels,,
are located atare located at
certaincertain distancesdistances
from the nucleus.from the nucleus.
This model of the atom isThis model of the atom is
still the most famous ofstill the most famous of
all models, and though itall models, and though it
is not the most accurate,is not the most accurate,
it predicts chemicalit predicts chemical
reactions very well. (It isreactions very well. (It is
important to remember,important to remember,
though, that atomsthough, that atoms
probably do not reallyprobably do not really
look like this.)look like this.)
Wave Model
The Wave ModelThe Wave Model
 Today’s atomicToday’s atomic
model is based onmodel is based on
the principles ofthe principles of
wavewave mechanicsmechanics..
 According to theAccording to the
theory of wavetheory of wave
mechanics,mechanics,
electronselectrons do notdo not
movemove about anabout an
atom in aatom in a definitedefinite
path,path, like thelike the
planets around theplanets around the
sun.sun.
Wave Model of Atoms:Wave Model of Atoms:
The Wave ModelThe Wave Model
 In fact, it isIn fact, it is impossibleimpossible to determine the exactto determine the exact
location of an electron. Thelocation of an electron. The probableprobable location oflocation of
an electron is based on how muchan electron is based on how much energyenergy thethe
electron has.electron has.
 According to the modern atomic model, at atomAccording to the modern atomic model, at atom
has ahas a small positively charged nucleussmall positively charged nucleus
surrounded by a large region in which there aresurrounded by a large region in which there are
enough electrons to make an atom neutral.enough electrons to make an atom neutral.
Electron Cloud:Electron Cloud:
 A space in whichA space in which
electrons are likely to beelectrons are likely to be
found.found.
 ElectronsElectrons whirlwhirl about theabout the
nucleus billions of timesnucleus billions of times
in one secondin one second
 They are not movingThey are not moving
around inaround in randomrandom
patterns.patterns.
 Location of electronsLocation of electrons
depends upon how muchdepends upon how much
energyenergy the electron has.the electron has.
The Cloud ModelThe Cloud Model
The Wave Mechanical ModelThe Wave Mechanical Model
AnAn orbitalorbital is described as ais described as a
region in which an electron isregion in which an electron is
most likely to be found.most likely to be found.
Electron Cloud:Electron Cloud:
 Depending on their energy they are locked into aDepending on their energy they are locked into a
certain area in the cloud.certain area in the cloud.
 Electrons with theElectrons with the lowestlowest energy are found inenergy are found in
the energy levelthe energy level closestclosest to the nucleusto the nucleus
 Electrons with theElectrons with the highesthighest energy are foundenergy are found
in thein the outermostoutermost energy levels, farther fromenergy levels, farther from
the nucleus.the nucleus.
IndivisibleIndivisible ElectronElectron NucleusNucleus OrbitOrbit ElectronElectron
CloudCloud
GreekGreek XX
DaltonDalton XX
ThomsonThomson XX
RutherfordRutherford XX XX
BohrBohr XX XX XX
WaveWave XX XX XX

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Atomic Models Through History

  • 1. Models of the AtomModels of the Atom a Historical Perspectivea Historical Perspective Dr. Vijender Singh GDC Memorial Degree College Bahal
  • 2. Atomos: Not to Be CutAtomos: Not to Be Cut The History of Atomic TheoryThe History of Atomic Theory
  • 3. Atomic ModelsAtomic Models  This model of theThis model of the atom may lookatom may look familiar to you. This isfamiliar to you. This is the Bohr model. Inthe Bohr model. In this model, thethis model, the nucleus is orbited bynucleus is orbited by electrons, which areelectrons, which are in different energyin different energy levels.levels.  A model uses familiar ideas toA model uses familiar ideas to explain unfamiliar factsexplain unfamiliar facts observed in nature.observed in nature.  A model can be changed asA model can be changed as new information is collected.new information is collected.
  • 4. The atomicThe atomic model hasmodel has changedchanged throughout thethroughout the centuries,centuries, starting in 400starting in 400 BC, when itBC, when it looked likelooked like aa billiard ballbilliard ball →→
  • 5. Who are these men?Who are these men? In this lesson, we’ll learn about the men whose quests for knowledge about the fundamental nature of the universe helped define our views.
  • 6. DemocritusDemocritus  This is the GreekThis is the Greek philosopher Democritusphilosopher Democritus who began the search forwho began the search for a description of mattera description of matter more thanmore than 24002400 yearsyears ago.ago.  He asked: CouldHe asked: Could matter be divided intomatter be divided into smaller and smallersmaller and smaller pieces forever, or waspieces forever, or was there athere a limitlimit to theto the number of times anumber of times a piece of matter couldpiece of matter could bebe divideddivided?? 400 BC
  • 7. AtomosAtomos  His theory: Matter could notHis theory: Matter could not be divided into smaller andbe divided into smaller and smaller pieces forever,smaller pieces forever, eventually the smallesteventually the smallest possible piece would bepossible piece would be obtained.obtained.  This piece would beThis piece would be indivisible.indivisible.  He named the smallestHe named the smallest piece of matter “atomos,”piece of matter “atomos,” meaning “not to be cut.”meaning “not to be cut.”
  • 8. AtomosAtomos  To Democritus, atomsTo Democritus, atoms werewere smallsmall, hard, hard particles that were allparticles that were all made of the samemade of the same material but werematerial but were differentdifferent shapes andshapes and sizes.sizes.  Atoms wereAtoms were infiniteinfinite inin number, alwaysnumber, always moving and capablemoving and capable of joining together.of joining together.
  • 9. This theory was ignored andThis theory was ignored and forgotten for more thanforgotten for more than 20002000 years!years!
  • 10. Why?Why?  The eminentThe eminent philosophersphilosophers of the time,of the time, AristotleAristotle andand Plato, had aPlato, had a moremore respected,respected, (and ultimately(and ultimately wrongwrong) theory.) theory. Aristotle and Plato favored the earth, fire, air and water approach to the nature of matter. Their ideas held sway because of their eminence as philosophers. The atomos idea was buried for approximately 2000 years.
  • 11.
  • 12. Dalton’s ModelDalton’s Model  In the early 1800s,In the early 1800s, the Englishthe English Chemist JohnChemist John DaltonDalton performed aperformed a number ofnumber of experiments thatexperiments that eventually led toeventually led to the acceptance ofthe acceptance of the idea of atoms.the idea of atoms.
  • 13. Dalton’s TheoryDalton’s Theory  He deduced that allHe deduced that all elementselements are composed ofare composed of atoms. Atoms areatoms. Atoms are indivisible andindivisible and indestructible particles.indestructible particles.  Atoms of theAtoms of the samesame elementelement are exactly alike.are exactly alike.  Atoms ofAtoms of differentdifferent elementselements areare differentdifferent..  CompoundsCompounds are formed byare formed by the joining of atoms of twothe joining of atoms of two or more elements.or more elements.
  • 14. .. This theoryThis theory became onebecame one of theof the foundationsfoundations of modernof modern chemistry.chemistry.
  • 15. Thomson’s Plum PuddingThomson’s Plum Pudding ModelModel InIn 18971897, the, the English scientistEnglish scientist J.J. ThomsonJ.J. Thomson provided the firstprovided the first hint that an atomhint that an atom is made of evenis made of even smallersmaller particles.particles.
  • 16. Thomson’s “Plum Pudding” ModelThomson’s “Plum Pudding” Model Thomson suggested that the electrons in an atom were embedded in a positively charged, diffuse sphere. (Early 20th century) Claim: Atoms contain an equal amount of positive charge as negative charge
  • 17. Thomson ModelThomson Model  He proposed aHe proposed a model of the atommodel of the atom that is sometimesthat is sometimes called the “called the “PlumPlum PuddingPudding” model.” model.  Atoms were madeAtoms were made from a positivelyfrom a positively chargedcharged substancesubstance with negativelywith negatively charged electronscharged electrons scatteredscattered about,about, like raisins in alike raisins in a pudding.pudding.
  • 18. Thomson’s “Plum Pudding” ModelThomson’s “Plum Pudding” Model Reasoning:Reasoning:  Since atoms were electrically neutral butSince atoms were electrically neutral but contained negatively charged electrons, theycontained negatively charged electrons, they must also contain an equal amount of positivemust also contain an equal amount of positive charge.charge.  Thomson had no experimental evidence for hisThomson had no experimental evidence for his model but built on Lord Kelvin’s idea thatmodel but built on Lord Kelvin’s idea that positive charge in an atom was spread evenlypositive charge in an atom was spread evenly and diffusely throughout a spherical shape.and diffusely throughout a spherical shape. (Early 20th century)
  • 19. Thomson ModelThomson Model Thomson studiedThomson studied thethe passagepassage of anof an electric currentelectric current through a gas.through a gas. As the currentAs the current passed throughpassed through the gas, it gave offthe gas, it gave off rays ofrays of negativelynegatively charged particles.charged particles.
  • 20. Thomson ModelThomson Model This surprisedThis surprised Thomson,Thomson, because thebecause the atoms of the gasatoms of the gas were uncharged.were uncharged. Where had theWhere had the negative chargesnegative charges come from?come from? Where did they come from?
  • 21. Thomson concluded that the negative charges came from within the atom. A particle smaller than an atom had to exist. The atom was divisible! Thomson called the negatively charged “corpuscles,” today known as electrons. Since the gas was known to be neutral, having no charge, he reasoned that there must be positively charged particles in the atom. But he could never find them.
  • 22. Rutherford’s Gold FoilRutherford’s Gold Foil ExperimentExperiment  In 1908, theIn 1908, the English physicistEnglish physicist Ernest RutherfordErnest Rutherford was hard at workwas hard at work on an experimenton an experiment that seemed tothat seemed to have little to dohave little to do with unraveling thewith unraveling the mysteries of themysteries of the atomic structure.atomic structure.
  • 23. Rutherford’s experiment InvolvedRutherford’s experiment Involved firing a stream of tinyfiring a stream of tiny positivelypositively chargedcharged particles at a thin sheet ofparticles at a thin sheet of gold foilgold foil (2000 atoms thick)(2000 atoms thick) Rutherford’s Gold FoilRutherford’s Gold Foil ExperimentExperiment
  • 24.  MostMost of the positivelyof the positively charged “bullets” passedcharged “bullets” passed right through the goldright through the gold atoms in the sheet ofatoms in the sheet of gold foilgold foil without changingwithout changing course at all.course at all.  SomeSome of the positivelyof the positively charged “bullets,”charged “bullets,” however, did bouncehowever, did bounce away from the gold sheetaway from the gold sheet as if they had hitas if they had hit somethingsomething solidsolid. He. He knew that positiveknew that positive chargescharges repelrepel positivepositive charges.charges. Rutherford’s Gold FoilRutherford’s Gold Foil ExperimentExperiment
  • 25.
  • 26.  This could only mean that the gold atoms in theThis could only mean that the gold atoms in the sheet were mostlysheet were mostly open spaceopen space. Atoms were. Atoms were notnot a pudding filled with a positively chargeda pudding filled with a positively charged material.material.  Rutherford concluded that an atom had aRutherford concluded that an atom had a small,small, dense, positively charged centerdense, positively charged center thatthat repelledrepelled his positively charged “bullets.”his positively charged “bullets.”  He called the center of the atom the “He called the center of the atom the “nucleusnucleus””  The nucleus isThe nucleus is tinytiny compared to the atom as acompared to the atom as a whole.whole.
  • 27. RutherfordRutherford  Rutherford reasonedRutherford reasoned that all of an atom’sthat all of an atom’s positively chargedpositively charged particles wereparticles were containedcontained in thein the nucleus. Thenucleus. The negatively chargednegatively charged particles wereparticles were scatteredscattered outside theoutside the nucleus around thenucleus around the atom’satom’s edgeedge..
  • 28. Bohr ModelBohr Model In 1913, theIn 1913, the Danish scientistDanish scientist Niels BohrNiels Bohr proposed anproposed an improvement. Inimprovement. In his model, hehis model, he placed eachplaced each electron in aelectron in a specificspecific energyenergy level.level.
  • 29. Bohr ModelBohr Model  According toAccording to Bohr’s atomicBohr’s atomic model, electronsmodel, electrons move in definitemove in definite orbitsorbits around thearound the nucleus, much likenucleus, much like planets circle theplanets circle the sun. These orbits,sun. These orbits, or energyor energy levelslevels,, are located atare located at certaincertain distancesdistances from the nucleus.from the nucleus.
  • 30. This model of the atom isThis model of the atom is still the most famous ofstill the most famous of all models, and though itall models, and though it is not the most accurate,is not the most accurate, it predicts chemicalit predicts chemical reactions very well. (It isreactions very well. (It is important to remember,important to remember, though, that atomsthough, that atoms probably do not reallyprobably do not really look like this.)look like this.)
  • 32. The Wave ModelThe Wave Model  Today’s atomicToday’s atomic model is based onmodel is based on the principles ofthe principles of wavewave mechanicsmechanics..  According to theAccording to the theory of wavetheory of wave mechanics,mechanics, electronselectrons do notdo not movemove about anabout an atom in aatom in a definitedefinite path,path, like thelike the planets around theplanets around the sun.sun.
  • 33. Wave Model of Atoms:Wave Model of Atoms:
  • 34. The Wave ModelThe Wave Model  In fact, it isIn fact, it is impossibleimpossible to determine the exactto determine the exact location of an electron. Thelocation of an electron. The probableprobable location oflocation of an electron is based on how muchan electron is based on how much energyenergy thethe electron has.electron has.  According to the modern atomic model, at atomAccording to the modern atomic model, at atom has ahas a small positively charged nucleussmall positively charged nucleus surrounded by a large region in which there aresurrounded by a large region in which there are enough electrons to make an atom neutral.enough electrons to make an atom neutral.
  • 35. Electron Cloud:Electron Cloud:  A space in whichA space in which electrons are likely to beelectrons are likely to be found.found.  ElectronsElectrons whirlwhirl about theabout the nucleus billions of timesnucleus billions of times in one secondin one second  They are not movingThey are not moving around inaround in randomrandom patterns.patterns.  Location of electronsLocation of electrons depends upon how muchdepends upon how much energyenergy the electron has.the electron has.
  • 36. The Cloud ModelThe Cloud Model
  • 37. The Wave Mechanical ModelThe Wave Mechanical Model AnAn orbitalorbital is described as ais described as a region in which an electron isregion in which an electron is most likely to be found.most likely to be found.
  • 38. Electron Cloud:Electron Cloud:  Depending on their energy they are locked into aDepending on their energy they are locked into a certain area in the cloud.certain area in the cloud.  Electrons with theElectrons with the lowestlowest energy are found inenergy are found in the energy levelthe energy level closestclosest to the nucleusto the nucleus  Electrons with theElectrons with the highesthighest energy are foundenergy are found in thein the outermostoutermost energy levels, farther fromenergy levels, farther from the nucleus.the nucleus.
  • 39. IndivisibleIndivisible ElectronElectron NucleusNucleus OrbitOrbit ElectronElectron CloudCloud GreekGreek XX DaltonDalton XX ThomsonThomson XX RutherfordRutherford XX XX BohrBohr XX XX XX WaveWave XX XX XX

Editor's Notes

  1. Atoms contain an equal amount of positive charge as negative charge (Because atoms have no overall charge but are known to contain negatively charged electrons)
  2. Erwin Schrödinger built upon the thoughts of Bohr yet took them in a new direction.  He developed the probability function for the Hydrogen atom (and a few others).  The probability function basically describes a cloud-like region where the electron is likely to be found.  It can not say with any certainty, where the electron actually is at any point in time, yet can describe where it ought to be.   Clarity through fuzziness, is one way to describe the idea.  The model based on this probability equation can best be described as the cloud model.