electronic structure of atoms unit 7 electronic structure of atoms chm 1045: general chemistry and...

ElectronicStructureof Atoms

Unit 7Electronic Structure

of Atoms

CHM 1045: General Chemistry and Qualitative Analysis

Dr. Jorge L. AlonsoMiami-Dade College –

Kendall CampusMiami, FL

Textbook Reference:

•Module #9


Atoms and Electromagnetic RadiationAtoms absorb and emit energy, often in the form of electromagnetic radiation

(visible light, microwaves, radio & TV waves, u.v., infrared,etc)

{Fireworks}


The Nature of Light Energy(1) White Light is not white,

VIB G.Y O RSpectroscope

ed

range

ellow

reen

lue

iolet

ndigo

(3) Light does not travel in truly straight lines, it travels in waves

(2) Light is electrical and magnetic (electromagnetic)

it is colored: the Spectrum:

{3D-Wave}


Light Energy as Waves: two important characteristics

1. wavelength (): the distance (m) between corresponding points on adjacent waves

For waves traveling at the same velocity, the longer the wavelength,

the smaller the frequency

Knowing and , you calculate the speed of light !

= high

= low

1

(c)constant

c (1/sec) (m)

2. frequency () or (f ): the number of waves passing a given point per unit of time (1/s = s1-)

short

long

Speed (c) = wave length (λ) x frequency ()m/sec = m x 1/sec

SPEED = DISTANCE x PER UNIT TIME


Electromagnetic RadiationA form of energy characterized by waves (or pulses) of

varying frequencies ( and wavelengths ().

{Wavelength of v. l.}

c

c

{3D-Wave}

{*Light Waves}


Electromagnetic Radiation• Speed of Light: All

electromagnetic radiation travels at the same velocity (c), 3.00 108 m/s.

Einstein’s Theory of Special Relativity: Energy and mass are different forms of the same thing

mc2

Frequency (f )

1 α

c

Problem: What is the wavelength of a photon of light that has a frequency of 3.8 x 109 s-1 ?

c

c

1-9

-18

s 10 x 3.8

s m 10 x 00.3 = 7.89x10-2 m


The Nature of Energy:Discrete vs. ContinuousDigital:

0110100101001Analog

Waves:Quanta (Photon):

Eggs:

Water:

particles


{Photoelectric Effect}

Energy as a Particle (Photon, Quanta)

When light energy shines on a metal, an electron current is generated.

Light is behaving as a particle (photon)

that knocks-off valence electrons from the metal.

waves

particles

Light Energy


Energy from electrons comes in discrete quantities (bundles) that are whole number multiples of h

• The wave nature of light does not explain how an object can glow when its temperature increases.

{Metals & EM Radiation}

Planck concluded that energy (E) is proportional to frequency

where h is Planck’s constant, 6.63 10−34 J-s.

• Max Planck explained it by assuming that energy comes in packets called quanta (energy bundle, photon). Max Planck (1848-1947)

hEFor any particular frequency () there is a particular bundle of Energy (E) that exists as a discrete quantity (quanta) that is a multiple of Planck’s constant (h).

Energy as a Particle (Photon, Quanta)

1

2


The Nature of Energy Since c = then

c

h

Problem: What is the wavelength (in Å) of a ray whose energy is 6.16 x 10-14 erg? {Note: Modules use erg =10-7 Joule}

c

h E

Therefore, if one knows the wavelength of light, one can calculate the energy in

one photon, or packet, of that light.


The Nature of EnergyE = h

c

h

Problem: What is the wavelength (in Å) of a ray whose energy is 6.16 x 10-21 Joules? {Note: Modules use erg =10-7 Joule}

E

ch

Joules

m21-

834-

10 x 16.6

sec/10 x 0.3 Joules.sec10 x 63.6

m-510 x 3.23

m-510 x 3.23 Å? Å10 x 23.310

Å1 510-

m


c =

c

h h E

c

(1) Waves

(2) Particle (Photon, Quanta)

Energy as……

ΔE =h

mc2

(3) Matter

E


The Wave-Particle Duality of Matter

• Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties.

=h

mv

(where h is Planck’s constant, 6.63 10−34 J-s, and v is velocity of light)

{ElectonWaves}• Electromagnetic radiation can behave as a particle or as wave phenomena

• He demonstrated that the relationship between mass (m) and wavelength () was:

velocity (v) ∝

1 m

= eq given


The Wave Nature of MatterProblem: An electron has a mass of 9.06 x 10-25 kg and

is traveling at the speed of light. Calculate its wavelength?

=h

mvm x102.44

m/s)10 x (3.00 x ) kg 10 x 9.06(

)/10 x 63.6( 18-825-

-34

sJ

J = Joule = kg.m2

Problem: What is the wavelength of a 70.0 kg skier traveling down a mountain at 15.0 m/s?

=h

mvm x10 6.31

m/s) (15.0 x ) 0.70(

)/10 x 63.6( 37--34

kg

sJ


The Nature of EnergyWhite Light’s Continuous Spectrum:

VIB G.Y O R


{Flame Tests.Li,Na,K} {Na,B} {AtomicSpectra}

Substances both absorb and emit only certain Discrete Spectra

The Nature of Energy


• Niels Bohr adopted Planck’s assumption and explained atomic phenomena in this way:

1. Electrons in an atom can only occupy certain orbits (corresponding to certain energies, frequencies and wavelengths, because E=h=h c/λ).

3. Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by

E = h

2. Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.

The Bohr “Planetary” Model of the Atom (1913)

1st EL f = 4

2nd EL f = 5


The Bohr Model of the Atom

The larger the fall the greater the energy{ExcitedElectrons*}

Which series releases most energy?


The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the

RH ( )1nf

2

1ni

2-

where RH is the Rydberg constant, 2.18 10−18 J, and ni and nf are the initial and final energy levels of the electron. Z is the atomic number

1

Rydberg formula for hydrogen (1885)

Rydberg formula for hydrogen-like elements (He+, Li 2+, Be3+ etc., )

1

Atomic Spectra & Bohr Atom


if

-18-18

E E 10 x 2.180

- 10 x 2.180

E

2

i

2

f n

J

n

J

E = RH ( )1nf

2

1ni

2-

where RH is the Rydberg constant, 2.18 10−18 J, and ni and nf are the initial and final energy levels of the electron.

10 x 2.180

E-18

n 2n

Joule

= eq given

Since energy and wavelength are mathematically related, the Rydberg Equation can also be expressed in terms of energy:

The energy possessed by an electron at a particular energy level (En) can be expressed as:

Atomic Spectra & Bohr Atom

= ( )RH

nf2

RH

ni2

-

1


Atomic Spectra and the Bohr AtomProblem: How much energy (J) is liberated when an

electron changes from n = 4 to n = 2? What is the wavelength (m) of the light emitted?

E

ch

J10x 4088.0

s/m10x 0.3 J.s10x 63.6

18-

834-

c

c

h E

E E E if

2

-18

2

-18 10 x 2.180 -

10 x 2.180

if n

J

n

J

c

h

2

i

-18

2

f

-18

4

J10x 2.180 -

2

J10x 2.180

Jx -18-18-18 10 4088.0 J) 10 x (0.1362- J) 10 x (0.545 E

To convert energy to wavelength, we must employ the equations:

m10x 4.865 -7


Atomic Spectra and the Bohr Atom

m10x 4.865 -7

Notice that the wavelength calculated from the Rydberg equation matches the wavelength of the green colored line in the H spectrum.

J10 x 4088.0 E -18


2006 (B)

Ele 1

Ele 2


Heisenberg’s Uncertainty Principle• Heisenberg showed that the more

precisely the momentum of a particle is known, the less precisely is its position known:

• In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!

(x) (mv) h4


Quantum Model of the Atom• Max Planck (energy quanta, Planck’s constant)• Albert Einstein (energy and frequency) • Niels Bohr (electrons and Spectra) • Louis de Broglie (particle-wave duality of matter)• Werner Heisenberg (electron uncertainty)• Erwin Schrödinger (probability wave function, the four

quantum numbers)• Jörge L. Alônsø (diagrammatic quantum mechanical

atomic model)

Solvay Conference in Brussels 1911

Prof. Alonso


Energy Levels =

1, 2, 3, etc

Sublevel Orbital

types = s, p, d, f

Orbital cloud orientation (x, y, z, etc)

Electron pair spin in Orbital cloud (2e- ea)

1s

2s 2px

2py

2pz

3py

3px

3pz

3s

3dxy3dxz

3dyz

3dx2

y2

3dx2

1

2

3 4


Quantum Numbers

• Describe the location of electrons within atoms.

• There are four quantum numbers: Principal = describes the energy level (1,2,3,etc)Azimuthal = energy sublevel, orbital type (s2, p6,

d10, f14)Magnetic = orbital orientation or cloud (2

electrons on each cloud) Example: three p clouds: px, py, pz

Spin = which way the electron is spinning (↑↓)


Electron Configuration, Orbital Notation and Quantum Numbers

1s2 2s2 2p6 3s23p63d10 4s24p64d104f14

Principal (n)= energy level Azimuzal () = sublevel orbital type

Magnetic (ml) = orbital cloud orientation (2e-

per orbital)

Spin (ms) = electron + or -


Electron ConfigurationTwo issues:

(1)Arrangement of electrons within an atom

1s2 2s2 2p6 3s23p63d10 4s24p64d104f14

(2) Order in which electrons fill the orbitals

1s22s22p63s23p64s23d104p65s24d105p66s24f14

Aufbau Process: Using Periodic Table Sub-blocks:


Schrödinger (1926)Bohr (1913)

Historic Development of Atomic Theory


The Schrödinger Equation

• is the imaginary unit, (complex number whose square is a negative real

number)

• is time, • is the partial derivative with respect to t, • is the reduced Planck's constant (Planck's constant divided by 2π),

• ψ(t) is the wave function,

• is the Hamiltonian (a self-adjoint operator acting on the state space).

ψ(t)

i

t


Quantum Mechanics• Developed by Erwin Schrödinger, it

is a mathematical model incorporating both the wave & particle nature of electrons.

• The wave function is designated with a lower case Greek psi ().

• The square of the wave function, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.

{QuantumAtom}


• Solving the wave equation gives a set of wave functions , or orbitals, and their corresponding energies.

• Each orbital describes a spatial distribution of electron density.

• An orbital is described by a set of three quantum numbers.

The Schrödinger Equation

ψ(t )


Principal Quantum Number, n

• The principal quantum number, n, describes the energy level on which the orbital resides.

• The values of n are integers ≥ 0.

1 2 3


Azimuthal Quantum Number,

• This quantum number defines the shape of the orbital.• Allowed values of are integers ranging from 0 to n − 1.• We also use letter designations:

Value of 0 1 2 3

Type of orbital s p d f

= 0 = 1 = 2 = 3


Magnetic Quantum Number, ml

• Describes the three-dimensional orientation of the orbital.

• Values are integers ranging from -l to l:

−l ≤ ml ≤ l.

• Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.

0 -1+1

0


Values of Quantum Numbers

• Principal Quantum #: values of n are integers ≥ 0. • Azimuthal Quantum #: values of are integers ranging from 0 to n − 1.• Magnetic Quantum #: values are integers ranging from - to :

− ≤ ml ≤ .


s Orbitals ( = 0)

Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.

{RadialElectronDistribution}


s Orbitals ( = 0)

• Spherical in shape.

• Radius of sphere increases with increasing value of n.

{1s} {2s} {3s}


p Orbitals ( = 1)

• Have two lobes with a node between them.

{pz}{px} {py}{www.link}

0 -1+1


“P” orbital electrons arerepelled by the “S” orbitalelectrons and so spend moretime further from the nucleus.

“P” orbital electrons alsorepel from each others’ sublevels, so they run alongthe axes.

2s

2p

1s

Orbital Overlap: 1s2 2s2 2p6


d Orbitals ( = 2)

•Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.

{www.link}{*Orbitals.s.p.d}01

-1 2 -2


f Orbitals ( = 3)

• There are seven f orbitals per n level.The f orbitals have

complicated names.They have an = 3m = -3,-2,-1,0,+1,+2,

+3 7 values of m

The f orbitals have important effects in the lanthanide and actinide elements.

{www.link.f}

0

1 -1

-22

-33


Energies of Orbitals

• For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.

• That is, they are degenerate (collapsed).


Energies of Orbitals

• As the number of electrons increases, though, so does the repulsion between them.

• Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.

{E.L. vs FillingOrder}


Electron Configuration & Periodic Table


Spin Quantum Number, ms

• 1920s: it was discovered that two electrons in the same orbital do not have exactly the same energy.

The “spin” of an electron

describes its magnetic

field, which affects its energy.

{e-spin}


Electron Configurations

• Distribution of all electrons in an atom.

• Consist of Number denoting the

energy level. Letter denoting the type

of orbital. Superscript denoting the

number of electrons in those orbitals.


Orbital Diagrams

• Each box represents one orbital.

• Half-arrows represent the electrons.

• The direction of the arrow represents the spin of the electron.


Basic Principles of Electron Configuration Notations

• Pauli Exclusion Principle

• Hund’s Rule of Maximum Multiplicity• Alonso’s Rules of the Stability of Degenerate Orbitals


Pauli Exclusion Principle

• No two electrons in the same atom can have exactly the same energy (identical sets of quantum numbers)

Only two electrons can occupy an orbital and they must have opposite spins.


Hund’s Rule of Maximum Multiplicity

“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”

{Electron Configuration} {Electron Configuration2}

One electron fills each orbital before a second of opposite spin accompanies it.


Alonso’s Rules of the Stability of Degenerate Orbitals

Completely Filled Completely Filled

Completely Filled Half Filled

Half Filled Half Filled

Completely Filled Not even Half Filled

s d

Phenomenon also occurs between degenerate s and f orbitals

Most Stable Electron

Configuration


Periodic Table and Electron

Configuration

{e- filling order}


1s

2s2p

3s3p

3d4s

Electronic configuration : 1s2

Nitrogen

2s22p3

FeMnVTiScK

Na

ZnCuNiCr Co

Mg

Ca

Be

H

As

O

S

Se

F

Cl

BrGa

C

Si

Ge

N

P

He

Ne

Ar

Kr

1 2 GROUP 3 4 5 6 7 0

Li

Al

B

1

2

3

4

Hund’s Rule


Neon

1s

2s2p

3s3p

3d4s

1s2Electronic configuration: 2s22p6

FeMnVTiScK

Na

ZnCuNiCr Co

Mg

Ca

Be

H

As

O

S

Se

F

Cl

BrGa

C

Si

Ge

N

P

He

Ne

Ar

Kr

1 2 GROUP 3 4 5 6 7 0

Li

Al

B

1

2

3

4

Hund’s Rule


1s

2s2p

3s3p

3d4s

1s2Electronic configuration: 2s22p6 3s2 3p6 4s2 3d3

Vanadium

FeMnVTiScK

Na

ZnCuNiCr Co

Mg

Ca

Be

H

As

O

S

Se

F

Cl

BrGa

C

Si

Ge

N

P

He

Ne

Ar

Kr

1 2 GROUP 3 4 5 6 7 0

Li

Al

B

1

2

3

4

[Ne]

[Ar]


Chromium

1s

2s2p

3s3p

3d4s


Notice that one of the 4s electronshas been transferred to 3d so that 3d is now a half filled shell with extrastability. 4s and 3d contain onlyunpaired electrons.

FeMnVTiScK

Na

ZnCuNiCr Co

Mg

Ca

Be

H

As

O

S

Se

F

Cl

BrGa

C

Si

Ge

N

P

He

Ne

Ar

Kr

1 2 GROUP 3 4 5 6 7 0

Li

Al

B

1

2

3

4

[Ne]

[Ar]


1s

2s2p

3s3p

3d4s


Nickel

FeMnVTiScK

Na

ZnCuNiCr Co

Mg

Ca

Be

H

As

O

S

Se

F

Cl

BrGa

C

Si

Ge

N

P

He

Ne

Ar

Kr

1 2 GROUP 3 4 5 6 7 0

Li

Al

B

[Ne]

1

2

3

4

[Ar]


1s

2s2p

3s3p

3d4s

1s2Electronic configuration: 2s22p6 3s2 3p6 4s13d10

Copper

Notice that again one of the 4s electronshas been promoted to 3d so that 3d is now a completely filled shell with extrastability.

FeMnVTiScK

Na

ZnCuNiCr Co

Mg

Ca

Be

H

As

O

S

Se

F

Cl

BrGa

C

Si

Ge

N

P

He

Ne

Ar

Kr

1 2 GROUP 3 4 5 6 7 0

Li

Al

B

1

2

3

4


Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.

Some Anomalies


Some AnomaliesElectron configuration for copper is[Ar] 4s1 3d5

rather than the expected[Ar] 4s2 3d4.

•This occurs because the s and d orbitals are very close in energy.


Some Anomalies• These anomalies also occur in f-block atoms, as well.


Electron Configuration

1s2 2s2 2p6 3s2 3p6 4s2 3d6

1s2 2s2 2p6 3s2 3p6 3d6 4s2

[Ar] 4s2 3d6

[Ar] 4s0 3d6

Fe

Identify elements which posses the following electron configurations:

Fe

Fe

Fe2+

[Ne] 3s2 3p6 Write Elect-Config for S2-

{Aufbau order of filling}

{Energy level order}

{Previous Nobel Gas Abbreviation}

{Cations formed by removal of outermost electrons}


Periodic Table and Electron

Configuration

{e- filling order}


Transition Metals

1234567

Have additional electrons, but they are in an energy level that is lower than the valence electrons.

Uses dots to represent Valence Electrons = those in outermost

Energy Level


Electrons behave as waves (like standing waves above) and particles.

Electron position cannot be pinned down.

Electons don’t follow orbits, but rather orbitals describe their paths.


The Energy of Electromagnetic Waves

Einstein concluded that energy (E) is proportional to frequency

where h is Planck’s constant, 6.63 10−34 J-s.

Energy from electrons comes in whole number multiples of h = eq given

hE


The Bohr Model of the Atom (1913)


The Nature of Energy

• One does not observe a continuous spectrum, as one gets from a white light source.

• Only a line spectrum of discrete wavelengths is observed.


Atoms and Electromagnetic Radiation

Atoms absorb and emit energy, often in the form of electromagnetic radiation (light, microwaves, radio & TV waves, u.v., infrared,etc)

•To understand the electronic structure of atoms, one must understand the nature of waves.

electronic structure of atoms unit 7 electronic structure of atoms chm 1045: general chemistry and...

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