electromagnetic spectrum - made of electromagnetic radiation (forms of energy that exhibit wavelike...

ELECTRONS IN ATOMS

Wave description of light

Electromagnetic spectrum - made of electromagnetic radiation (forms of energy that exhibit wavelike behavior as they travel through space)

Electromagnetic waves - combination of electrical and magnetic fields which travel at the speed of light

c = 300 x 108 msec

Wavelength λ (lambda) ndash usually measured in

nm or Aringngstroms (Aring)

Relative sizes of wavelengths

FrequencyFrequency ν (Greek letter nu) (or f) ndash

units are usually cyclessec sec ndash1 or Hertz (Hz)

c = λ ν = 30 x 108 msec

wwwatmoswashingtonedu~hakim301handoutshtml

The Photoelectric effectThe emission of electrons from ametal when lightshines on themetal The number of electrons and theirenergies dependson the brightnessof the incidentlight

httpwwwastrovirginiaeduclassoconnellastr30imphotoelectric-effect-2jpg

Max Planck (1900)

He suggested that the object emits energy in small specific amounts called quanta A quantum is the minimum quantity of energy that can be lost or gained by an atom He proposed E = h ν where E = energy in Joules ν = frequency and h = Planckrsquos constant

6626 x 10-34 Jmiddots

E = h ν

What is a Joule

James Prescott Joule

A Joule is the derived unit of energy in the SI system It is the energy exerted by a force of one Newton acting to move an object through a distance of one meter

I Joule = Force x distance = 1 Newton-meter = (mass x acceleration) x

meter=

kgmiddot ms2 m = kgm2s2

Einstein and wave-particle duality (1905)

abyssuoregonedu~jsimageswave_particlegif

Light ndash particle and waveEach particle of lightcarries a quantum ofenergy which Einsteincalled photons A photon isa particle of

electromagneticradiation having zero

massand carrying a quantum ofenergy

For an electron to be ejected from the surface of a metal the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal

Spectroscopy

The Hydrogen-atom Bright Line-Emission Spectrum

Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation

ΔEphoton = E2-E1

Bohr (Niels) Model of the Atom - 1913 The allowed

orbits have specific energies given by a simple formula En = (-RH) n = 1234

RH is the Rydberg constant

218 x 10-18 J

Evidence for Electrons in Fixed-Energy Levels

The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines

The concept of electron energy levels is supported by spectral lines

Combining equationsGiven E = h ν and ΔE = E2-E1

combining them results in

ν = ΔE = ( RH) (1 - 1 )

h h n2i n2

f

Further simplification

ΔE = ( RH) (1 - 1 )

n2i n2

f

Bohr Model of the atom Electrons in hydrogen atoms exist in

only specified energy states Electrons in hydrogen atoms can absorb

only certain specific amounts of energy and no others

When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons

Different photons produce different color lines as seen in a bright line-emission spectrum

The main problem was that this explanation could not explain the behavior of any other element besides hydrogen

What led to quantum theory

The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory

If electrons behave as both particles

and waves where are they located in

an atom

Heisenberg Uncertainty Principle (1927)

It is impossible to determine simultaneously both

the position and velocity of an electron or any

other particle (Δp) (Δ x) = h (Planckrsquos constant)

Δp = uncertainty in momentumΔx = uncertainty in position

The Quantum Model of the Atom

1924 Louis de Broglie

Electrons should beconsidered as wavesconfined to the spacearound the nucleus

httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml

Derivation of the de Broglie wavelength equation

Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]

mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]

λ

mv2 = hv λ

Substitute rearrange solve for λ = hv and simplify even further mv2

λ = h This is the de Broglie wavelength

mv equation

Germer and DavissonDe Brogliersquos equation was applicable to

anyobject not just atoms The wave

propertiesof electrons were demonstrated in 1927

by Germer and Davisson (US) usingdiffraction by crystals

This technique is used today in electron microscopy

Erwin Schroumldinger and thewave mechanical model

(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2

Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved

Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals

Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation

Principal quantum number (n) ndash the main energylevel occupied by the electron

n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2

Orbital (or azimuthal) quantum number (l) or angular momentum

quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for

sharpprincipal diffuse and fundamental These

words were used to describe different series of spectral

linesemitted by the elements

Orbital quantum number

Letter designation

Number of orbitals

Number of electrons per sublevel

0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14

Magnetic and spin quantum numbers

Magnetic quantum number (ml) ndash indicates the

orientation of an orbital around the nucleusValues range from ndashl to +l (defines how

many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates

the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12

Principal quantum number


Magnetic quantum number

Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)

n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12

n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1

+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12

n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2

+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12

n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3

+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12

s orbital

p orbitals

d orbital

s

f orbitals

Electron configuration notation Long hand configuration (always

start with 1s) Short hand or noble gas

configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration

Orbital diagramnotation configuration

Electron configurations- rules

Aufbau principle

An electron occupies thelowest energyorbital that canreceive it

Diagonal Rule

Ord

er

of

orb

ital fi

llin

g

Energy in orbital filling

Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron

andall electrons in singly occupied orbitalsmust have the samespin

Pauli Exclusion principle

no two electrons in the same atomhave the same set of four

quantumnumbers The first three may bethe same but the spin must beopposite

Order of orbital filling

httpintrochemokstateeduWorkshopFolderElectronconfnewhtml

Example 1Boron ndash atomic number 5 Longhand 1s22s22p1

Shorthand [He]2s22p1

Orbital diagram

1s 2s 2p

Example 2Polonium ndash atomic number 84Longhand

1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4

Shorthand [Xe] 6s24f145d106p4

Orbital diagram

Exceptions to the Aufbau principle

For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2

3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5

For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2

3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1

3d10

Degenerate orbitalsa group of orbitals with the same

energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4

Mo and W are similar

Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9

Ag and Au are similar

Additional Definitions

Paramagnetic An atom has unpaired

electrons in its electron configuration

(Look at its orbital diagram)

Diamagnetic All electrons in an atom

are paired (Look at its orbital diagram)

Ion Configurations

Electrons will be added to or taken away from

orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)

ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes

1s22s22p63s23p6

Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6

Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec

The Photoelectric effect

Max Planck (1900)

What is a Joule


Light ndash particle and wave

Spectroscopy


Energy of photons emitted

Bohr (Niels) Model of the Atom - 1913


Combining equations

Bohr Model of the atom


If electrons behave as both particles and waves where are they




Germer and Davisson

Erwin Schroumldinger and the wave mechanical model

Wave functions = orbitals

Quantum numbers

Orbital (or azimuthal) quantum number (l) or angular momentum q


Slide 30

s orbital

p orbitals

d orbitals

f orbitals

Electron configuration notation


Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations


Electromagnetic spectrum - made of electromagnetic radiation (forms of energy that exhibit wavelike behavior as they travel through space)

Electromagnetic waves - combination of electrical and magnetic fields which travel at the speed of light

c = 300 x 108 msec






c = λ ν = 30 x 108 msec




Max Planck (1900)



E = h ν

What is a Joule




meter=








Spectroscopy



ΔEphoton = E2-E1




218 x 10-18 J






ν = ΔE = ( RH) (1 - 1 )

h h n2i n2

f


ΔE = ( RH) (1 - 1 )

n2i n2

f











an atom













λ

mv2 = hv λ



mv equation







(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2












Letter designation

Number of orbitals


0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations






c = λ ν = 30 x 108 msec




Max Planck (1900)



E = h ν

What is a Joule




meter=








Spectroscopy



ΔEphoton = E2-E1




218 x 10-18 J






ν = ΔE = ( RH) (1 - 1 )

h h n2i n2

f


ΔE = ( RH) (1 - 1 )

n2i n2

f











an atom













λ

mv2 = hv λ



mv equation







(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2












Letter designation

Number of orbitals


0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations



Max Planck (1900)



E = h ν

What is a Joule




meter=








Spectroscopy



ΔEphoton = E2-E1




218 x 10-18 J






ν = ΔE = ( RH) (1 - 1 )

h h n2i n2

f


ΔE = ( RH) (1 - 1 )

n2i n2

f











an atom













λ

mv2 = hv λ



mv equation







(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2












Letter designation

Number of orbitals


0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations

What is a Joule




meter=








Spectroscopy



ΔEphoton = E2-E1




218 x 10-18 J






ν = ΔE = ( RH) (1 - 1 )

h h n2i n2

f


ΔE = ( RH) (1 - 1 )

n2i n2

f











an atom













λ

mv2 = hv λ



mv equation







(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2












Letter designation

Number of orbitals


0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations







Spectroscopy



ΔEphoton = E2-E1




218 x 10-18 J






ν = ΔE = ( RH) (1 - 1 )

h h n2i n2

f


ΔE = ( RH) (1 - 1 )

n2i n2

f











an atom













λ

mv2 = hv λ



mv equation







(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2












Letter designation

Number of orbitals


0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations



ΔEphoton = E2-E1




218 x 10-18 J






ν = ΔE = ( RH) (1 - 1 )

h h n2i n2

f


ΔE = ( RH) (1 - 1 )

n2i n2

f











an atom













λ

mv2 = hv λ



mv equation







(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2












Letter designation

Number of orbitals


0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations




218 x 10-18 J






ν = ΔE = ( RH) (1 - 1 )

h h n2i n2

f


ΔE = ( RH) (1 - 1 )

n2i n2

f











an atom













λ

mv2 = hv λ



mv equation







(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2












Letter designation

Number of orbitals


0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations






ν = ΔE = ( RH) (1 - 1 )

h h n2i n2

f


ΔE = ( RH) (1 - 1 )

n2i n2

f











an atom













λ

mv2 = hv λ



mv equation







(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2












Letter designation

Number of orbitals


0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations











an atom













λ

mv2 = hv λ



mv equation







(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2












Letter designation

Number of orbitals


0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations













λ

mv2 = hv λ



mv equation







(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2












Letter designation

Number of orbitals


0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations







(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2












Letter designation

Number of orbitals


0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations











Letter designation

Number of orbitals


0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations











n = 2 l = 0 (s) l = 1 (p)

ml = 0ml = -1 0 +1


n = 3 l = 0 (s) l = 1 (p)l = 2 (d)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2


n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)

ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3


s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations

s orbital

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations

p orbitals

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations

d orbital

s

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations

f orbitals






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations






Aufbau principle


Diagonal Rule

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations

Ord

er

of

orb

ital fi

llin

g











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations











Orbital diagram

1s 2s 2p




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations




Orbital diagram






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations






3d10












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations












Ion Configurations




1s22s22p63s23p6


Electrons in Atoms


Slide 3


Frequency

c = λ ν = 30 x 108 msec


Max Planck (1900)

What is a Joule



Spectroscopy





Combining equations







Germer and Davisson



Quantum numbers



Slide 30

s orbital

p orbitals

d orbitals

f orbitals



Slide 37


Hundrsquos Rule


Slide 41


Example 1

Example 2


Degenerate orbitals


Ion Configurations

electromagnetic spectrum - made of electromagnetic radiation (forms of energy that exhibit wavelike...

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