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11
Quantum MechanicsQuantum Mechanics
Chapters 4 & 5Chapters 4 & 5
22
WAY WAY BACK IN WAY WAY BACK IN TIME... TIME...
Greek philosopher Greek philosopher Democritus (460-Democritus (460-370 BCE.) 370 BCE.)
substances that substances that comprised nature comprised nature – empty spaceempty space – tiny particlestiny particles
““atoms”atoms”
33
Democritus Democritus
different kinds of atoms existed different kinds of atoms existed not able to be broken down by not able to be broken down by
ordinary means ordinary means
44
Aristotle Aristotle
More popular More popular a contemporary of Democritus a contemporary of Democritus matter was a continuous matter was a continuous
substance which he called "hyle“substance which he called "hyle“ this idea was accepted without this idea was accepted without
support for nearly two thousand support for nearly two thousand years.years.
55
pseudo- science pseudo- science
explained natural phenomena in explained natural phenomena in philosophical ways philosophical ways – without experimentation without experimentation – without logicwithout logic
maggots come from rotting meat maggots come from rotting meat frogs cause warts frogs cause warts
66
Isaac Newton, Robert Isaac Newton, Robert Boyle and John Dalton Boyle and John Dalton Questioned natural occurrences Questioned natural occurrences conducted experiments conducted experiments
– controlled variables controlled variables made observations made observations collected data collected data data and observations used to data and observations used to
support hypothesessupport hypotheses
77
John Dalton John Dalton
matter is particulate in nature matter is particulate in nature atoms of a single element are atoms of a single element are
identicalidentical atoms of different elements are atoms of different elements are
different from each otherdifferent from each other Dalton's hypothesis explained the Dalton's hypothesis explained the
observationsobservations first modern atomic theoryfirst modern atomic theory
88
J.J. ThomsonJ.J. Thomson
Are atoms really the smallest Are atoms really the smallest particles?particles?
Cathode ray tubes Cathode ray tubes Rays originated at the cathode Rays originated at the cathode
(negative electrode) and traveled (negative electrode) and traveled toward the anode (positive electrode). toward the anode (positive electrode).
Produced rays composed of negatively Produced rays composed of negatively charged subatomic particles charged subatomic particles – he called particles electrons (he called particles electrons (ee-). -). – mathematically calculated the electron's mathematically calculated the electron's
mass to charge ratio mass to charge ratio
99
Oil Drop ExperimentOil Drop Experiment
Robert Millikan Robert Millikan determined the charge of a single determined the charge of a single
electron (-1) electron (-1) Oil Drop ExperimentOil Drop Experiment
1010
Thomson AtomThomson Atom
Plum Pudding ModelPlum Pudding Model
ElectronsElectrons
1111
Atomic ResearchAtomic Research
Ernest Rutherford Ernest Rutherford – Niels BohrNiels Bohr– Hans GeigerHans Geiger– Ernest MarsdenErnest Marsden
Experiment to study structure of Experiment to study structure of atomatom– Gold Foil ExperimentGold Foil Experiment
1212
Gold Foil ExperimentGold Foil Experiment Ernest Rutherford Ernest Rutherford
positively charged helium nuclei (alpha () particles) positively charged helium nuclei (alpha () particles) propelled at high speed toward a thin sheet (tissue propelled at high speed toward a thin sheet (tissue paper-like) of gold foil surrounded by a fluorescent paper-like) of gold foil surrounded by a fluorescent screenscreen
1313
Experimental Results:Experimental Results:
1. Most of particles pass straight 1. Most of particles pass straight through foilthrough foil
2. Some particles are slightly 2. Some particles are slightly deflecteddeflected
3. A few particles (1 per 8000) 3. A few particles (1 per 8000) are deflected greatly. Nearly are deflected greatly. Nearly bounce back to origin.bounce back to origin.
1414
Conclusions based on Conclusions based on experimental data:experimental data: 1. The atom is 1. The atom is mostly space.mostly space.
2. 2. Mild deflectionMild deflection was caused by was caused by repulsion of similarrepulsion of similar electrostatic electrostatic chargecharge. Therefore, the atom has a . Therefore, the atom has a positive region. 'Protons“positive region. 'Protons“
3. The 3. The positive corepositive core is is very smallvery small (1 (1 x 10x 10-12-12 of total atomic volume) and of total atomic volume) and contains contains most of the atom's most of the atom's massmass. . 'Nucleus''Nucleus'
1515
Rutherford AtomRutherford Atom
The Atom is mostly empty The Atom is mostly empty space…..space…..
1616
1717
Eugene Goldstein Eugene Goldstein
showed that protons created rays in a showed that protons created rays in a cathode ray tube just as the electrons cathode ray tube just as the electrons had donehad done
traveled in the opposite direction. traveled in the opposite direction. (anode to cathode) (anode to cathode)
concluded that a proton is equal but concluded that a proton is equal but opposite in charge to the electron, or opposite in charge to the electron, or 1+, and approximately 1836 times 1+, and approximately 1836 times more massive more massive
1818
Thomson's observation Thomson's observation
Atoms that areAtoms that are– chemically identical can have chemically identical can have
variable massvariable mass
1919
James Chadwick James Chadwick
credited with the discovery of the credited with the discovery of the neutral subatomic particle - the neutral subatomic particle - the neutronneutron
Walter Bothe obtained initial evidence Walter Bothe obtained initial evidence nearly two years before Chadwick's nearly two years before Chadwick's experiments experiments
Neutrons have a mass nearly identical Neutrons have a mass nearly identical to that of the proton, but no electrical to that of the proton, but no electrical charge. charge.
2020
Explanation lies with Explanation lies with the neutrons the neutrons
IsotopesIsotopes– Atoms of the same element containing Atoms of the same element containing
different numbers of neutrons.different numbers of neutrons. NuclideNuclide
– a particular isotope a particular isotope Each isotope acts the same in Each isotope acts the same in
chemical reactionchemical reaction Each nuclide will produce a product of Each nuclide will produce a product of
different mass. different mass.
2121
Hydrogen isotopesHydrogen isotopes
Proton + Neutron Electron -
Protium 1 proton, 1 electron
Deuterium 1 proton, 1 electron, 1 neutron
Tritium 1 proton, 1 electron, 2 neutrons
2222
TO SUMMARIZE... TO SUMMARIZE...
The atom is the smallest particle of The atom is the smallest particle of matter that cannot be chemically matter that cannot be chemically subdivided. subdivided.
Composed of two Composed of two regionsregions and three and three primary primary subatomic particlessubatomic particles. . – Nucleus Nucleus
very small very small positively chargedpositively charged dense. dense.
– Protons Protons – NeutronsNeutrons
Electron Cloud Electron Cloud – ElectronsElectrons
orbit the nucleus. orbit the nucleus. Small point-like negative chargesSmall point-like negative charges
2323
IN PERFECT BALANCE IN PERFECT BALANCE
The atom is electrically neutralThe atom is electrically neutral contain equal number of:contain equal number of:
– protons (positive charges) and protons (positive charges) and – electrons (negative charges).electrons (negative charges).
2424
Remind you of Remind you of anything?anything?
2525
Niels BohrNiels Bohr
1913 1913
Introduced ‘Planetary Model’Introduced ‘Planetary Model’
2626
Planetary ModelPlanetary Model
Gravity and InertiaGravity and Inertia
2727
Solar SystemSolar System AtomAtom
Attractive force:Attractive force:– GravityGravity– Pulls planet Pulls planet
toward suntoward sun Repulsive force:Repulsive force:
– InertiaInertia– Pushes planet in Pushes planet in
a straight line a straight line away from sunaway from sun
Attractive force:Attractive force:+ / - charges+ / - charges– + nucleus pulls + nucleus pulls
– electrons – electrons toward ittoward it
Repulsive force:Repulsive force:
2828
It Ought to Go SPLAT!It Ought to Go SPLAT!
“A charged particle constrained to move in curved path … radiates energy according to Maxwell equations.”
Some basic principles of synchrotron radiation.(document prepared by Antonio Juarez-Reyes, AMLM group, 2001)
Electrons – constant orbit Energy drain
and the atom goes SPLAT!SPLAT!
2929
Electromagnetic Electromagnetic RadiationRadiation
3030
Electromagnetic Electromagnetic RadiationRadiation c = 3.0 X 10c = 3.0 X 108 8 m/sm/s
Wavelength = λ Frequency = f (υ)
3131
Electromagnetic Electromagnetic RadiationRadiation Louis de Louis de
BroglieBroglie Dual Nature Dual Nature
ofof LightLight
Wave NatureWave Nature– Travels through space Travels through space
in wavesin waves– Travels at speed of Travels at speed of
light (c)light (c)
Particle NatureParticle Nature– Interacts with matter Interacts with matter
as a particleas a particle– Quanta (unit of Quanta (unit of
energy) transferred energy) transferred to matter in packets to matter in packets of light (photons)of light (photons)
3232
3333
Electromagnetic Electromagnetic RadiationRadiation
Light Light →→
3434
Electromagnetic Electromagnetic RadiationRadiation
Light Light → → ExcitedExcited atomic atomic
statestate
3535
Electromagnetic Electromagnetic RadiationRadiation
ee-- jumps to jumps to
Higher EnergyHigher Energy
levellevel
Light → Light → ExcitedExcited atomic atomic
statestate
3636
Electromagnetic Electromagnetic RadiationRadiation
ee-- jumps to jumps to e- jumps to
Higher EnergyHigher Energy Lower EnergyLower Energy
levellevel levellevel
Light → Light → ExcitedExcited atomic atomic →→→→→→→→→→→→
statestate
3737
Electromagnetic Electromagnetic RadiationRadiation
ee-- jumps to jumps to e- jumps to
Higher EnergyHigher Energy Lower EnergyLower Energy
levellevel levellevel
Light → Light → ExcitedExcited atomic atomic →→→→→→→→→→→→
statestate
3838
Electromagnetic Electromagnetic RadiationRadiation ee-- jumps to jumps to e- jumps to
Higher EnergyHigher Energy Lower EnergyLower Energy
levellevel levellevel
Light Light →→ExcitedExcited atomic atomic →→→→→→ Atom in Ground State→→→→→→ Atom in Ground State
statestate
photon releasedphoton released
3939
Electromagnetic Electromagnetic RadiationRadiation ee-- jumps to jumps to e- jumps to
Higher EnergyHigher Energy Lower EnergyLower Energy
levellevel levellevel
Light Light →→ExcitedExcited atomic atomic →→→→→→ Atom in Ground State→→→→→→ Atom in Ground State
statestate
photon releasedphoton released
Bright-line SpectrumBright-line Spectrum
4040
Electromagnetic Electromagnetic RadiationRadiation Speed of waveSpeed of wave
c=fc=fλλ solving for frequencysolving for frequency
cc=f =f
λλ
cc==
λλ
ch=ch=
E=
Energy of photon Energy of photon
E=hfE=hfsolving for frequencysolving for frequency
EE=f=f
hh
EE
hh
EEλλ
chch
λλ
4141
Electromagnetic Electromagnetic RadiationRadiation Irwin SchrodingerIrwin Schrodinger Developed the ‘Wave Developed the ‘Wave
Equation’ Equation’ to support de Broglie’s idea to support de Broglie’s idea
of the dual nature of lightof the dual nature of light
4242
Quantum LeapQuantum Leap
Bohr’s Planetary Model is used to Bohr’s Planetary Model is used to explain the spectral lines explain the spectral lines produced by atoms.produced by atoms.
Quantum leap animationQuantum leap animation
4343
Quantum LeapQuantum Leap
TheThe color color of light indicates its of light indicates its wavelengthwavelength
A particular wavelength has a A particular wavelength has a definite definite frequencyfrequency
A particular wavelength has a A particular wavelength has a definite definite amount ofamount of energyenergy
4444
Riding the Wave Riding the Wave (Equation(Equation))
The Wave Equation The Wave Equation – confirmed Bohr’s theory of confirmed Bohr’s theory of
quantized energy levels.quantized energy levels. Treating electrons as waves, Treating electrons as waves,
explains why the tiny negative explains why the tiny negative electrons are not drawn into the electrons are not drawn into the more massive and positive more massive and positive nucleusnucleus
4545
Riding the WaveRiding the Wave
“A charged particle constrained to move in curved path … radiates energy according to Maxwell equations.”
Some basic principles of synchrotron radiation.(document prepared by Antonio Juarez-Reyes, AMLM group, 2001)
As the e- approach the As the e- approach the nucleus, their wavelengths nucleus, their wavelengths become shorter.become shorter. E = E = chch λλ
4646
Solar SystemSolar System AtomAtom
Attractive force:Attractive force:– GravityGravity– Pulls planet Pulls planet
toward suntoward sun
Repulsive force:Repulsive force:– InertiaInertia– Pushes planet in Pushes planet in
a straight line a straight line away from sunaway from sun
Attractive force:Attractive force:+ / - charges+ / - charges– + nucleus pulls + nucleus pulls
– electrons – electrons toward ittoward it
Repulsive force:Repulsive force:– Energy produced Energy produced
form the shorter form the shorter λλ pushes the e pushes the e-- away from the away from the nucleusnucleus
4747
QUANTUM MECHANICSQUANTUM MECHANICS
Electrons do not obey the laws of Electrons do not obey the laws of classical or Newtonian physicsclassical or Newtonian physics
A new science to describe the A new science to describe the laws of small particles was laws of small particles was established established
4848
LOOK! IT ISN'T THERE!LOOK! IT ISN'T THERE!Uncertainty principleNot possible to locate an electron's exact position Position and momentum cannot be determined at the same time
to determine one you effect a change in the other
Electrons - only "seen” when they jump from a higher to lower energy level.
once electron is "seen," its direction and speed are different from what they were prior to observation.
Determining position changes its momentum. Applies to electron when it is considered a particle
Werner Heisenberg
4949
WAVE REVIEWS!WAVE REVIEWS!
Irwin SchrodingerIrwin Schrodinger Wave equation Wave equation
– helps locate probable regions of helps locate probable regions of electron population if considered it electron population if considered it to be like a wave. to be like a wave.
– general paths of the electrons general paths of the electrons around the nucleus can be around the nucleus can be determineddetermined
5050
5151
MAP IT OUT!MAP IT OUT!
Electrons may be described by a set of four quantum numbers which serve as 3-D for electron location.
5252
D.C. Map ActivityD.C. Map Activity
FindFind– Union StationUnion Station– Nat’l Air & Space Nat’l Air & Space
MuseumMuseum– Watergate ComplexWatergate Complex– CapitolCapitol– Ford’s TheaterFord’s Theater– White HouseWhite House– Lincoln MemorialLincoln Memorial– Kennedy CenterKennedy Center
A-B 5A-B 5++
C-D 4C-D 4
A-B 0A-B 0 C 5C 5 B 3-4B 3-4 B 2B 2 C 1C 1 B 0B 0
5353
The Quantum NumbersThe Quantum Numbers principle quantum number (n)principle quantum number (n)
– n = 1, 2, 3...n = 1, 2, 3...– Distance of electron from nucleus.Distance of electron from nucleus.
– Electrons exist ONLY in the energy levels. Electrons exist ONLY in the energy levels. – No electrons have energies to exist between energy levels No electrons have energies to exist between energy levels
[nodes].[nodes]. aangular momentumngular momentum ( (azimuthal) quantum number (l)azimuthal) quantum number (l)
– l = s, p, d, fl = s, p, d, f– Shape of paths, subshells, sublevels, Shape of paths, subshells, sublevels,
magnetic quantum number (m)magnetic quantum number (m)– m = 1, 3, 5, 7m = 1, 3, 5, 7– Spatial orientation to x, y, z axesSpatial orientation to x, y, z axes
spin quantum number (s)spin quantum number (s)– s = clockwise, counterclockwises = clockwise, counterclockwise– Electron spinElectron spin
5454
FIRST PRINCIPLE of FIRST PRINCIPLE of QUANTUM MECHANICSQUANTUM MECHANICS Only specific energy levels are Only specific energy levels are
possible for electrons. possible for electrons. The principle quantum number that The principle quantum number that
corresponds to the energy levels corresponds to the energy levels begins with 1, 2, 3, etc. beginning with begins with 1, 2, 3, etc. beginning with the level closest to the nucleus the level closest to the nucleus – K energy level is 1K energy level is 1– L energy level is 2L energy level is 2– M energy level is 3M energy level is 3– N energy level is 4, etc. N energy level is 4, etc.
5555
SECOND PRINCIPLE of SECOND PRINCIPLE of QUANTUM MECHANICSQUANTUM MECHANICS The maximum number of electrons The maximum number of electrons
that can occupy and energy level is that can occupy and energy level is given by the equationgiven by the equation
2(n)2(n)22 = maximum number of e-= maximum number of e-– n is the principle quantum number of the n is the principle quantum number of the
energy level.energy level.– Principle quantum number is 2, the Principle quantum number is 2, the
electron maximum is 2(2)electron maximum is 2(2)22 = 8 = 8– Principle quantum number is 3, the Principle quantum number is 3, the
electron maximum is 2(3)electron maximum is 2(3)22 = 18 = 18
5656
DIVIDE and CONQUER!DIVIDE and CONQUER!
energy levels are actually several energy levels are actually several closely bound bands of energy closely bound bands of energy
Each of the bands represents a sub Each of the bands represents a sub level level
The number of sublevels is the same The number of sublevels is the same as the principle quantum numberas the principle quantum number
It is represented by the It is represented by the angular angular momentum numbersmomentum numbers – s, p, d, and f.s, p, d, and f.
5757
KK energy level energy level – principle quantum number is principle quantum number is 11. . – 1 sub level, 1 sub level, ss
LL energy level energy level – principle quantum number is principle quantum number is 22. . – 2 sublevels, 2 sublevels, s, ps, p
MM energy level energy level – principle quantum number is principle quantum number is 33. . – 3 sublevels, 3 sublevels, s, p, ds, p, d
NN energy level energy level – principle quantum number isprinciple quantum number is 4 4– 4 sublevels 4 sublevels s, p, d, f.s, p, d, f.
The energy within a level varies. The energy within a level varies. Lowest EnergyLowest Energy Highest EnergyHighest Energy ss >>> >>> pp >>> >>> dd >>> >>> ff
5858
Sublevels have Sublevels have characteristic shapes characteristic shapes
ss
5959
pp
6060
dd
6161
ff
6262
Magnetic Quantum Magnetic Quantum Number Number 1, 3, 5, 71, 3, 5, 7 represents the represents the numbernumber of of
different paths (orbits) that the different paths (orbits) that the electron can take in relationship electron can take in relationship to the three axes of space to the three axes of space
6363
Wolfgang Pauli Wolfgang Pauli
electron spectra affected by electron spectra affected by magnetic fields magnetic fields
indicated that the electrons could indicated that the electrons could be spinning in two different be spinning in two different directions within the orbital directions within the orbital – clockwise clockwise – counterclockwise counterclockwise
6464
Pauli Exclusion Pauli Exclusion PrinciplePrinciple
Spinning in one direction causes a Spinning in one direction causes a magnetic field that is attracted to the magnetic field that is attracted to the north pole of a magnetnorth pole of a magnet
Spinning in the opposite direction Spinning in the opposite direction causes it to be attracted to a south polecauses it to be attracted to a south pole
If two electrons occupy the same If two electrons occupy the same orbital then they must spin in opposite orbital then they must spin in opposite directionsdirections
If they did not they would repel each If they did not they would repel each other as two like magnetic poles repel other as two like magnetic poles repel each other. each other.
6565
North PoleNorth Pole
South PoleSouth Pole
6666
Energy Levels are Energy Levels are Subdivided Subdivided
ENERGY LEVELS
SUBLEVEL SUB SHELL s p d f
ORBITALS
1 1 2 3 1 2 3 4 5
1 2 3 4 5 6 7
1 2 1 21 21 2 1 2 1 2 1 2 1 2 1 2
1 21 21 21 21 21 2 1 2
ELECTRON PAIRS
6767
HierarchyHierarchy
no two electrons in same atom no two electrons in same atom can have same set of four can have same set of four quantum numbers. quantum numbers.
What is the maximum number of What is the maximum number of quantum numbers that can be quantum numbers that can be shared by two electrons?shared by two electrons?
33
6868
Summary ChartSummary Chart
E N E R G Y L E V E L
P R IN C IP L EQ U A N T U M N O . S U B L E V E L S
O R B IT A LP E R S U B L E V E L
O R B IT A LP E R L E V E L
E L E C T R O N SP E R S U B L E V E L
E L E C T R O N SP E R L E V E L
K 1 s 1 1 2 2
L 2 s 1 4 2 8 p 3 6
M 3 s 1 9 2 1 8p 3 6d 5 1 0
N 4 s 1 1 6 2 3 2p 3 6d 5 1 0f 7 1 4
6969
I'D RATHER STAY I'D RATHER STAY SINGLESINGLE most stable state of an atom - most stable state of an atom -
ground stateground state actual arrangement of the actual arrangement of the
electrons in atom referred to as electrons in atom referred to as thethe electron configurationelectron configuration
7070
Hund's RuleHund's Rule
electrons arrange themselves in such electrons arrange themselves in such a way as to MAXIMIZE THE NUMBER a way as to MAXIMIZE THE NUMBER OF UNPAIRED ELECTRONS in a sub OF UNPAIRED ELECTRONS in a sub levellevel
Only after one electron occupies each Only after one electron occupies each of the sublevel’s orbitals do the of the sublevel’s orbitals do the electrons begin to pair up and share electrons begin to pair up and share the same orbitalthe same orbital
ee- - spin oppositely when in same spin oppositely when in same orbital orbital
7171
NucleusNucleus
K Energy LevelK Energy Level
OUTERMOSOUTERMOST Energy T Energy
LevelLevel
NEXT to the NEXT to the OUTERMOSOUTERMOS
T Energy T Energy LevelLevel22ndnd from the from the
OUTERMOST OUTERMOST Energy LevelEnergy Level
7272
POSTULATES of POSTULATES of QUANTUM MECHANICSQUANTUM MECHANICS1.1. The K energy level is the most tightly bound in The K energy level is the most tightly bound in
any atom.any atom.2.2. The outermost energy level NEVER has more The outermost energy level NEVER has more
than than 8 electrons.8 electrons. 3.3. The next to the outermost level NEVER has The next to the outermost level NEVER has
more than more than 18 electrons.18 electrons.4.4. IF the next to the outermost level does not IF the next to the outermost level does not
contain its maximum number of electrons (18 contain its maximum number of electrons (18 e-), THEN the outermost energy level can hold e-), THEN the outermost energy level can hold no more than 2 electrons.no more than 2 electrons.
5.5. IF the second from the outermost energy level IF the second from the outermost energy level does not contain its maximum amount of does not contain its maximum amount of electrons (2n2), THEN the next to the outermost electrons (2n2), THEN the next to the outermost energy level can hold energy level can hold no more than 9 electrons.no more than 9 electrons.
7373
The The Aufbau PrincipleAufbau Principle
Experimental data indicates that Experimental data indicates that sublevels within the energy levels sublevels within the energy levels sometimes overlap the sublevels of sometimes overlap the sublevels of other energy levels other energy levels
electrons electrons fill the subshells of the fill the subshells of the lowest energies firstlowest energies first
Since overlapping occurs, a means of Since overlapping occurs, a means of remembering the order of sub level remembering the order of sub level energies is helpful energies is helpful
7474
Aufbau Diagram Aufbau Diagram (from German (from German Aufbauprinzip,Aufbauprinzip, “building-up principle”) “building-up principle”)
Electrons enter Electrons enter atom in this orderatom in this order
Electons are Electons are removed from removed from atom in the atom in the reverse orderreverse order
Last in first out.Last in first out.
7575
ORBITAL NOTATIONORBITAL NOTATION
Example: Oxygen Example: Oxygen 8 protons, 8 electrons, 8 neutrons8 protons, 8 electrons, 8 neutrons
Notice the application of Hund's Rule, where Notice the application of Hund's Rule, where unpaired electrons are maximized.unpaired electrons are maximized.
7676
ELECTRON ELECTRON CONFIGURATION CONFIGURATION
NOTATIONNOTATION compare this method to the orbital notation.compare this method to the orbital notation.
1s1s22 2s 2s22 2p 2p44
7777
ELECTRON DOT ELECTRON DOT NOTATIONNOTATION
shows only the electrons in the outer shows only the electrons in the outer energy level (valence electrons)energy level (valence electrons)
the ethe e-- that are involved in chemical that are involved in chemical reactions reactions
illustrates the electrons that bond illustrates the electrons that bond with other atoms with other atoms
outer (valence) energy level can outer (valence) energy level can hold no more than hold no more than eight electronseight electrons (2nd postulate of quantum (2nd postulate of quantum mechanics) mechanics)
7878
7979
Oxygen Oxygen 8 protons, 8 8 protons, 8 electronselectrons
chemical symbol is chemical symbol is written in the center written in the center of the notation of the notation
right of the symbol right of the symbol represents the s represents the s orbital orbital
top, left and bottom top, left and bottom represent each of the represent each of the three orbitals in the p three orbitals in the p sub level, sub level, respectively. respectively.