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CHAPTER4
Electronic Structure of Atom
From Indivisible to QuantumMechanical Model of the Atom
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Classical ModelClassical Model
Democritus
Dalton
ThomsonRutherford
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DemocritusDemocritus
Circa 400 BC
Greek philosopher
Suggested that all matter iscomposed of tiny, indivisible
particles, called atoms
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Dalton’s Atomic Theory (1808)Dalton’s Atomic Theory (1808)
1. All matter is made of tiny indivisible particles calledatoms.
2. Atoms of the same element are identical. Theatoms of any one element are different from those
of any other element.3. Atoms of different elements can combine with one
another in simple whole number ratios to formcompounds.
4. Chemical reactions occur when atoms areseparated, joined, or rearranged; however, atomsof one element are not changed into atoms of another by a chemical reaction.
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J.J. Thomson (1897)J.J. Thomson (1897)
Determined the charge to massratio for electrons
Applied electric and magnetic
fields to cathode rays (waves)“Plum pudding” model of theatom
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Rutherford’s Gold Foil ExperimentRutherford’s Gold Foil Experiment
(1910)(1910)
Alpha particles (positively chargedhelium ions) from a radioactive source
was directed toward a very thin goldfoil.
A fluorescent screen was placed behindthe Au foil to detect the scattering of
alpha (α ) particles.
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Rutherford’s Gold Foil ExperimentRutherford’s Gold Foil Experiment
(Observations)(Observations)
Most of the α -particles passedthrough the foil.
Many of the α -particles deflectedat various angles.
Surprisingly, a few particles were
deflected back from the Au foil.
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Rutherford’s Gold FoilRutherford’s Gold FoilExperiment (Conclusions)Experiment (Conclusions)
Rutherford concluded that most of themass of an atom is concentrated in a
core, called the atomic nucleus.The nucleus is positively charged.
Most of the volume of the atom is
empty space.
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Shortfalls of Rutherford’sShortfalls of Rutherford’s
ModelModel
Did not explain where the atom’snegatively charged electrons arelocated in the space surrounding its
positively charged nucleus.We know oppositely charged particlesattract each other
What prevents the negative electronsfrom being drawn into the positivenucleus?
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Bohr Model (1913)Bohr Model (1913)
Niels Bohr (1885-1962), Danishscientist working with Rutherford
Proposed that electrons must haveenough energy to keep them inconstant motion around the
nucleusAnalogous to the motion of theplanets orbiting the sun
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Planetary ModelPlanetary Model
The planets are attracted to thesun by gravitational force, they
move with enough energy toremain in stable orbits around thesun.
Electrons have energy of motionthat enables them to overcome theattraction for the positive nucleus
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Think about satellites….Think about satellites….
We launch a satellite into spacewith enough energy to orbit the
earth The amount of energy it is given,determines how high it will orbit
We use energy from a rocket toboost our satellite.
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Electronic Structure of Electronic Structure of AtomAtom
Waves-particle duality
Photoelectric effect
Planck’s constantBohr model
de Broglie equation
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Radiant EnergyRadiant Energy
Radiation ≡ the emission of energy in various forms
A.K.A. Electromagnetic Radiation
Radiant Energy travels in the form of waves that have bothelectrical and magnetic impulses
Electromagnetic Radiation ≡ radiation that consistsof wave-like electric and magnetic fields in space,including light, microwaves, radio signals, and x-rays
Electromagnetic waves can travel through emptyspace, at the speed of light (c=3.00x108m/s) orabout 300million m/s!!!
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WavesWaves
Waves transfer energy from one place to
another • Think about the damage done by waves during
strong hurricanes.• Think about placing a tennis ball in your bath tub, if
you create waves at one it, that energy istransferred to the ball at the other = bobbing
Electromagnetic waves have the same
characteristics as other waves
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Wave CharacteristicsWave Characteristics
avelength, λ (lambda) ≡ distance betweensuccessive points
10m
2m
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Wave CharacteristicsWave Characteristics
Frequency, ν (nu) ≡ the number of complete wave cycles to pass a given point
per unit of time; Cycles per second
t=0 t=5 t=0 t=5
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Units for FrequencyUnits for Frequency
1 cycle/ss-1
hertz, Hz
Because all electromagnetic waves travelat the speed of light, wavelength isdetermined by frequencyLow frequency = long wavelengths
High frequency = short wavelengths
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WavesWaves
Amplitude ≡ maximum height of a wave
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WavesWaves
Node ≡ points of zero amplitude
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ElectromagneticElectromagneticSpectrumSpectrum
Radio & TV, microwaves, UV,infrared, visible light = all are
examples of electromagneticradiation (and radiant energy)
Electromagnetic spectrum: entire
range of electromagnetic radiation
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Electromagnetic SpectrumElectromagnetic Spectrum
1024 1020 1018 1016 1014 1012 1010 108 106
Gamma Xrays UV Microwaves FM AMIR
Visible Light
Frequency Hz
10-16 10-9 10-8 10-6 10-3 100 102Wavelength m
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NotesNotes
Higher-frequency electromagnetic waveshave higher energy than lower-frequencyelectromagnetic waves
All forms of electromagnetic energyinteract with matter, and the ability of thesedifferent waves to penetrate matter is a
measure of the energy of the waves
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What is your favorite radioWhat is your favorite radio
station?station?
Radio stations are identified bytheir frequency in MHz.
We know all electromagneticradiation(which includes radiowaves) travel at the speed of
light.What is the wavelength of yourfavorite station?
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Velocity of a WaveVelocity of a Wave
Velocity of a wave (m/s) = wavelength (m) xfrequency (1/s)c = λ ν c= speed of light = 3.00x108 m/sEg: My favorite radio station is 105.9 Jamming Oldies!!! What is thewavelength of this FM station?
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Wavelength of FMWavelength of FM
Answer:
c = λ ν
c= speed of light = 3.00x108 m/s
ν = 105.9MHz or 1.059x108Hz
λ = c/ ν = 3.00x108 m/s = 2.83m
1.059x1081/s
What does the electromagneticWhat does the electromagnetic
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What does the electromagneticWhat does the electromagneticspectrum have to do withspectrum have to do withelectrons?electrons?
It’s all related to energy - energyof motion (of electrons) and
energy of light
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LightLight
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States of ElectronsStates of Electrons
When current is passed through a gas at alow pressure, the potential energy (energydue to position) of some of the gas atomsincreases.
Ground State: the lowest energy state of anatom
Excited State: a state in which the atom hasa higher potential energy than it had in itsground state
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Excited State
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Absorbance and Emission
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Absorbance and Emission
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Quantization
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Neon SignsNeon Signs
When an excited atom returns toits ground state it gives off the
energy it gained in the form of electromagnetic radiation!
The glow of neon signs, is an
example of this process
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White LightWhite Light
White light is composed of all of thecolors of the spectrum = ROY G BIV
When white light is passed through aprism, the light is separated into aspectrum, of all the colors
What are rainbows?
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Line-emission SpectrumLine-emission Spectrum
When an electric current ispassed through a vacuum tube
containing H2 gas at low pressure,and emission of a pinkish glow isobserved.
What do you think happens whenthat pink glow is passed througha prism?
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Hydrogen’s Emission SpectrumHydrogen’s Emission Spectrum
The pink light consisted of just a few specificfrequencies, not the whole range of colors as withwhite light
Scientists had expected to see a continuousrange of frequencies of electromagnetic radiation,because the hydrogen atoms were excited bywhatever amount of energy was added to them.
Lead to a new theory of the atom
h d l f d
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Bohr’s Model of HydrogenBohr’s Model of HydrogenAtomAtom
Hydrogen did not produce a continuousspectrum
New model was needed: Electrons can circle the nucleus only in
allowed paths or orbits When an e- is in one of these orbits, the
atom has a fixed, definite energy e- and hydrogen atom are in its lowest
energy state when it is in the orbit closestto the nucleus
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Bohr Model Continued…Bohr Model Continued…
Orbits are separated by empty space,where e- cannot exist
Energy of e- increases as it moves to
orbits farther and farther from thenucleus
(Similar to a person climbing a ladder)
B h M d l d H d
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Bohr Model and HydrogenBohr Model and Hydrogen
SpectrumSpectrum
While in orbit, e- can neither gain or lose energyBut, e- can gain energy equal to the differencebetween higher and lower orbitals, and thereforemove to the higher orbital (Absorption)
When e- falls from higher state to lower state, energyis emitted (Emission)
Bohr’s CalculationsBohr’s CalculationsBased on the wavelengths of hydrogen’s line-emission spectrum, Bohr calculated theenergies that an e- would have in the allowedenergy levels for the hydrogen atom
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Photoelectric EffectPhotoelectric Effect
An observed phenomenon, early 1900sWhen light was shone on a metal, electronswere emitted from that metal
Light was known to be a form of energy,
capable of knocking loose an electron from ametal
Therefore, light of any frequency could supplyenough energy to eject an electron.
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Photoelectric Effect : Situation
Light strikes the surface of a metal(cathode), and e- are ejected. Theseejected e- move from the cathode to the
anode, and current flows in the cell. Aminimum frequency of light is used. If the frequency is above the minimum andthe intensity of the light is increased,
more e- are ejected.
Photoelectric EffectPhotoelectric Effect
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Photoelectric EffectPhotoelectric Effectcont.cont.
Observed: For a given metal, noelectrons were emitted if the light’sfrequency was below a certainminimum, no matter how long thelight was shone
Why does the light have to beof a minimum frequency?
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Explanation….
Max Planck studied the emission of lightby hot objectsProposed: objects emit energy in small,
specific amounts = quanta(Differs from wave theory which would say objects emitelectromagnetic radiation continuously)
Quantum: is the minimum quantity of energythat can be lost or gained by an atom.
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Planck’s EquationPlanck’s Equation
E radiation = Planck’s constant xfrequency of radiation
E = h ν
h = Planck’s constant= 6.626 x 10-34 J•sWhen an object emits radiation, there
must be a minimum quantity of energythat can be emitted at any given time.
Ei t i E d Pl k’Ei t i E d Pl k’
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Einstein Expands Planck’sEinstein Expands Planck’s
TheoryTheory
Theorized that electromagneticradiation had a dual wave-particlenature!
Behaves like waves and particles Think of light as particles that eachcarry one quantum of energy =photons
PhotonsPhotons
Photons: a particle of electromagneticradiation having zero mass and carrying aquantum of energy
Ephoton = h ν
Back to PhotoelectricBack to Photoelectric
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Back to PhotoelectricBack to PhotoelectricEffectEffect
Einstein concluded: Electromagnetic radiation is
absorbed by matter only in wholenumbers of photons
In order for an e- to be ejected, thee- must be struck by a single
photon with minimum frequency
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Example of Planck’s Equation
CD players use lasers that emit red light with a λ of 685 nm. Calculate the energy of one photon.
Different metals require different minimumfrequencies to exhibit photoelectric effect
Answer
Ephoton = h ν
h = Planck’s constant = 6.626 x 10-34 J•s
c = λ ν
c = speed of light = 3.00x108 m/s
ν = (3.00x108 m/s)/(6.85x10-7m)
ν = 4.37x1014 1/s
Ephoton = (6.626 x 10-34 J•s)(4.37x1014 1/s)
Ephoton = 2.90 x 10-19
J
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Wave Nature of Electrons
We know electrons behave as particlesIn 1925, Louis de Broglie suggested thatelectrons might also display waveproperties
de Broglie’s EquationA free e- of mass (m) moving with avelocity (v) should have an associated
wavelength: λ = h/mvLinked particle properties (m and v) witha wave property (λ )
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Example of de Broglie’s Equation
Calculate the wavelength associated withan e- of mass 9.109x10-28 g traveling at40.0% the speed of light. [Hint.: 1 J = 1 kgm2/s2]
v=(3.00x108m/s)(.40)=1.2x108m/s
λ = h/mv
λ =
(6.626 x 10-34
J•
s) =6.06x10-12
m (9.11x10-31 kg)(1.2x108m/s)
Remember 1J = 1(kg)(m)2/s2
Answer:
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Wave-Particle DualityWave-Particle Duality
de Broglie’s experimentssuggested that e- has wave-likeproperties.
Thomson’s experimentssuggested that e- has particle-likeproperties
measured charge-to-mass ratio
uantum mec an ca
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uantum mec an camodel
SchrÖdinger
Heisenberg
PauliHund
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Where are the e- in the atom?
e- have a dual wave-particle nature
If e- act like waves and particles at thesame time, where are they in the atom?
First consider a theory by Germantheoretical physicist, Werner Heisenberg.
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Heisenberg’s IdeaHeisenberg’s Ideae- are detected by their interactions withphotonsPhotons have about the same energy as e-Any attempt to locate a specific e- with aphoton knocks the e- off its courseALWAYS a basic uncertainty in trying to locatean e-
Heisenberg’s Uncertainty Principle
Impossible to determine both theposition and the momentum of an e- inan atom simultaneously with great
certainty.
SchrÖdinger’s Wave
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SchrÖdinger s WaveEquation
An equation that treated electrons in atomsas waves
Only waves of specific energies, andtherefore frequencies, provided solutions tothe equation
Quantization of e- energies was a naturaloutcome
Solutions are known as wave functions
Wave functions give ONLY the probability of finding and e- at a given place around thenucleus
e- not in neat orbits, but exist in regions
called orbitals
SchrÖdinger’s WaveEquation
SchrÖdinger’s Wave
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SchrÖdinger s WaveEquation
Here is the equationDon’t memorize this or write it down
It is a differential equation, and we needcalculus to solve it
-h = (ә2 Ψ )+ (ә2Ψ )+( ә2Ψ ) +Vψ =Eψ
8(π)2m (әx2) (әy2) (әz2 )
Scary???
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Probability ≡ likelihoodOrbital ≡ wave function; region in spacewhere the probability of finding an electron ishighSchrÖdinger’s Wave Equation states thatorbitals have quantized energiesBut there are other characteristics to
describe orbitals besides energy
Definitions
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Quantum NumbersQuantum Numbers
Definition: specify the properties of atomic orbitals and the properties of electrons in orbitals
There are four quantum numbers
The first three are results fromSchrÖdinger’s Wave Equation
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Quantum Numbers (1)
Principal Quantum Number, n
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Quantum Numbers
Principal Quantum Number, n Values of n = 1,2,3,… ∞
Positive integers only! Indicates the main energy level
occupied by the electron
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Quantum Numbers
Principal Quantum Number, n Values of n = 1,2,3,… ∞
Describes the energy level, orbitalsize
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Quantum Numbers
Principal Quantum Number, n Values of n = 1,2,3,… ∞
Describes the energy level, orbitalsize As n increases, orbital size
increases.
Principle Quantum
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Principle QuantumNumber
n = 1
n=2
n=3
n=4n=5n=6
Energy
Principal Quantum
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Principal QuantumNumber
Pr nc p e uantum
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Pr nc p e uantumNumber
More than one e- can have the samen value
These e- are said to be in the same e-shell
The total number of orbitals that existin a given shell = n2
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Quantum Numbers (2)
Angular momentum quantum number,l
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Quantum Numbers
Angular momentum quantumnumber, l
Values of l = n-1, 0
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Quantum NumbersQuantum Numbers
Angular momentum quantumnumber, l
Values of l = n-1, 0 Describes the orbital shape
Q N b
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Quantum Numbers
Angular momentum quantumnumber, l Values of l = n-1, 0
Describes the orbital shape Indicates the number of sublevel
(subshells)( except for the 1st main energy level, orbitals of
different shapes are known as sublevels or subshells)
* Shape of the “volume” of space that
the e-
occupies
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Orbital Shapes
For a specific main energy level, the number of orbital shapes possible is equal to n.Values of l = n-1, 0 Eg. Orbital which n=2, can have one of two shapes
corresponding to l = 0 or l=1
Depending on its value of l, an orbital isassigned a letter.
O bit l Sh
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Orbital ShapesAngular magnetic quantum number, l
If l = 0, then the orbital is labeled s.
s is spherical.
If l = 1, then the orbital is labeled p.
p is “dumbbell” shape
If l = 2, the orbital is labeled d .
“double dumbbell” or four-leaf clover
If l = 3, then the orbital is labeled f .
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Orbital
Shapes
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Energy Level and Orbitals
n=1, only s orbitalsn=2, s and p orbitals
n=3, s, p, and d orbitals
n=4, s,p,d and f orbitals
Remember: l = n-1
Value of l 0 1 2 3 Type of orbital s p d f
Energy Level Transitions
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Energy Level Transitions
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Atomic Orbitals
Atomic Orbitals are designated by theprincipal quantum number followed byletter of their subshell
Eg. 1s = s orbital in 1st main energy level Eg. 4d = d sublevel in 4th main energy level
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Quantum Numbers (3)
Magnetic Quantum Number, ml
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Quantum Numbers
Magnetic Quantum Number, ml
Values of ml= +l…0…-l
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Quantum Numbers
Magnetic Quantum Number, ml
Values of ml= +l…0…-l
Describes the orientation of theorbitalAtomic orbitals can have the same
shape but different orientations
* orientation of the orbital in space
Magnetic Quantum
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ag e c Qua uNumber
s orbitals are spherical, only oneorientation, so m=0
p orbitals, 3-D orientation, so m=-1, 0 or 1 (x, y, z)
d orbitals, 5 orientations, m= -2,-1,
0, 1 or 2
Magnetic Quantum Number,
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g Q ,ml
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Quantum Numbers (4)
Electron Spin Quantum Number,ms
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Quantum Numbers
Electron Spin Quantum Number,ms
Values of ms= +1/2 or –1/2
e- spin in only 1 or 2 directions A single orbital can hold a maximum
of 2 e-, which must have oppositespins
O bit l ShO bit l Sh
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Orbital ShapesOrbital Shapes
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1) s orbitals(l = 0 )
O bit l ShO bit l Sh
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2) p orbitals(l = 1 )
Orbital ShapesOrbital Shapes
Orbital ShapesOrbital Shapes
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3) d orbitals(l = 2 )
Orbital ShapesOrbital Shapes
orientation of the orbital in space, ml
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ml = -1 ml = 0 ml = 1
ml = -2 ml = -1 ml = 0 ml = 1 ml = 27.6
Spin quantum numberSpin quantum number
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p qp qmmss
ms = +½ or -½
ms = -½ms = +½
7.6
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