chapter 4a_electronic atomic structure

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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.



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



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



Excited State



Absorbance and Emission



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


Describes the energy level, orbitalsize



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Quantum Numbers


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



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 .



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



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


Values of ml= +l…0…-l



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Quantum Numbers


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,



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



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 )





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3) d orbitals(l = 2 )


orientation of the orbital in space, ml



ml = -1 ml = 0 ml = 1

ml = -2 ml = -1 ml = 0 ml = 1 ml = 27.6

Spin quantum numberSpin quantum number



p qp qmmss

ms = +½ or -½

ms = -½ms = +½

7.6

chapter 4a_electronic atomic structure

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