CHM11-3LectureUnit#3(1)

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GENERAL CHEMISTRY 1

LECTURE UNIT No. 3

(ELECTRONIC STRUCTURE OF ATOM)

Engr. Edgie L. EstopaceSchool of Chemical Engineering and ChemistryMapua Institute of Technology



2

CONTENT

1. Quantum Theory2. Photoelectric effect

3. Bohr’s Theory

4. Dual Nature of the Electrons

5. Quantum Mechanics

6. Quantum Numbers

7. Electronic Configuration



The Electromagnetic Spectrum

• Visible light is a small portionof the electromagneticradiation spectrum detected byour eyes.

• Electromagnetic radiationincludes radio waves,microwaves and X-rays.

Described as a wavetraveling through space.

There are two componentsto electromagnetic radiation,an electric field andmagnetic field.



The Wave Nature of Light

• Wavelength, , is thedistance between twocorresponding points on awave.

• Amplitude is the size or “height” of a wave.

• Frequency, , is thenumber of cycles of thewave passing a given point

per second, usuallyexpressed in Hz.



Higher T = shorter λ (higher E ) maximum.

• Couldn’t explain with classical physics.

As T ↑, the wavelength

of maximum intensityshifts toward the blue

Planck’s Quantum Theory



Classical theory:

no restriction on the E emitted by hotatoms.

didn’t fit experimental data.

Planck: atoms emit E in packets (E is quantized)

each packet has a minimum energy

• a quantum of energy• E quantum = h

radiation = h c/λradiation

(h = Planck’s constant = 6.626x10-34 J s)

Planck’s Quantum Theory




• The fourth variable of light is velocity.

All light has the same speed in a vacuum.

c = 2.99792458 x 108 m/s

The product of the frequency and wavelength isthe speed of light.

Frequency is inversely proportional to wavelength.

c




• Refraction is the bending of light when it passes from

one medium to another of different density. Speed of light changes.

Light bends at an angle depending on itswavelength.

Light separates into its component colors.




• Electromagnetic radiation can be categorized in

terms of wavelength or frequency.

Visible light is a small portion of the entireelectromagnetic spectrum.



Example Problem 6.1

• Neon lights emit an orange-red colored glow. This

light has a wavelength of 670 nm. What is thefrequency of this light?



The Particulate Nature of Light

• Photoelectric effect: light striking a metal surface

generates photoelectrons.

The light’s energy is transferred to electrons inmetal.

With sufficient energy, electrons “break free” of the metal.

Electrons given more energy move faster (havehigher kinetic energy) when they leave the metal.




• Photoelectric effect isused in photocathodes.

Light strikes thecathode at frequency

. Electrons areejected if exceedsthe threshold value

0.

Electrons arecollected at theanode.

Current flow is used



Photoelectric Experiments

a) For > 0, the number of electrons emitted is independentof frequency.

Value of 0 depends on metalused.

b) As light intensity increases, thenumber of photoelectronsincreases.

c) As frequency increases, kineticenergy of emitted electronsincreases linearly.

d) The kinetic energy of emittedelectrons is independent of light




• The photoelectric effect is not explained using a wave

description but is explained by modeling light as aparticle.

• Wave-particle duality - depending on the situation, light isbest described as a wave or a particle.

Light is best described as a particle when light isimparting energy to another object.

Particles of light are called photons.

Neither waves nor particles provide an accuratedescription of all the properties of light. Use the modelthat best describes the properties being examined.




• The energy of a photon (E) is proportional to the

frequency ( ).

and is inversely proportional to the wavelength( ).

h = Planck’s constant = 6.626 x 10-34 J s

E h

hc



Example Problem 6.2

• The laser in a standard laser printer emits light with

a wavelength of 780.0 nm. What is the energy of aphoton of this light?




• Binding Energy - energy holding an electron to a

metal.

Threshold frequency, o - minimum frequency of light needed to emit an electron.

For frequencies below the threshold frequency, noelectrons are emitted.

For frequencies above the threshold frequency,

extra energy is imparted to the electrons askinetic energy.

•E photon = Binding E + Kinetic E

This explains the photoelectric effect.



Example Problem 6.3

• In a photoelectric experiment, ultraviolet light with a

wavelength of 337 nm was directed at the surface of a piece of potassium metal. The kinetic energy of theejected electrons was measured as 2.30 x 10-19 J.What is the electron binding energy for potassium?



Atomic Spectra

• Atomic Spectra: the particular pattern of

wavelengths absorbed and emitted by an element.

Wavelengths are well separated or discrete.

Wavelengths vary from one element to the next.

• Atoms can only exist in a few states with veryspecific energies.

When light is emitted, the atom goes from ahigher energy state to a lower energy state.



Atomic Spectra

• Electrical current dissociates molecular H2 intoexcited atoms which emit light with 4

wavelengths.



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Atomic Spectra and the Bohr Atom

• Every element has a unique spectrum.

• Thus we can use spectra to identify elements.

This can be done in the lab, stars, fireworks,

etc.



The Bohr Atom

• Bohr model - electrons orbitthe nucleus in stable orbits.Although not a completelyaccurate model, it can beused to explain absorptionand emission.

Electrons move from lowenergy to higher energyorbits by absorbingenergy.

Electrons move from highenergy to lower energyorbits by emitting energy.

Lower energy orbits arecloser to the nucleus dueto electrostatics.



The Bohr Atom

• Excited state: grouping of electrons that is not at the

lowest possible energy state.

• Ground state: grouping of electrons that is at thelowest possible energy state.

Atoms return to the ground state by emittingenergy as light.



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• The Rydberg equationis an empirical

equation that relatesthe wavelengths of the lines in thehydrogen spectrum.

hydrogeof spectrumemission

in thelevelsenergytheof

numberstherefer tosn’

nn

m101.097R

constantRydbergtheisR

n

1

n

1R

1

21

1-7

2

2

2

1



25


• SP3. What is the wavelength of light emitted when

the hydrogen atom’s energy changes from n = 4 to n= 2?

22 1-7

2

2

2

1

12

41

21m101.0971

n

1

n

1R1

2nand4n

2

2

2

1

12

n

1

n

1R

1

2nand4n

16

1

4

1m101.097

1

41

21m101.0971

n

1

n

1R1

2nand4n

1-7

22 1-7

2

2

2

1

12



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• In 1913 Neils Bohr incorporated Planck’squantum theory into the hydrogen spectrumexplanation.

• Here are the postulates of Bohr’s theory.

1. Atom has a number of definite and discrete

energy levels (orbits) in which an electron

may exist without emitting or absorbing

electromagnetic radiation.

As the orbital radius increases so does the energy

1<2<3<4<5......



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2. An electron may move from one discreteenergy level (orbit) to another, but, in so doing,monochromatic radiation is emitted or absorbedin accordance with the following equation.

E E

hc hE E-E

12

12

Energy is absorbed when electrons jump to higher orbits.

n = 2 to n = 4 for example

Energy is emitted when electrons fall to lower orbits.

n = 4 to n = 1 for example



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3. An electron moves in a circular orbit about thenucleus and it motion is governed by theordinary laws of mechanics and electrostatics,with the restriction that the angularmomentum of the electron is quantized (canonly have certain discrete values).

angular momentum = mvr = nh/2

h = Planck’s constant n = 1,2,3,4,...(energylevels)

v = velocity of electron m = mass of electronr = radius of orbit



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• Light of a characteristic wavelength (andfrequency) is emitted when electrons move fromhigher E (orbit, n = 4) to lower E (orbit, n = 1).

This is the origin of emission spectra.

Light of a characteristic wavelength (andfrequency) is absorbed when electron jumps from

lower E (orbit, n = 2) to higher E (orbit, n= 4)

– This is the origin of absorption spectra.

http://localhost/var/www/apps/conversion/tmp/PowerPoint%20Media/Movies/07M07AN1.MOV





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• Bohr’s theory correctly explains the H emissionspectrum.

• The theory fails for all other elements becauseit is not an adequate theory.



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The Wave Nature of the Electron

• In 1925 Louis de Broglie published his Ph.D.dissertation.

A crucial element of his dissertation is thatelectrons have wave-like properties.

The electron wavelengths are described by thede Broglie relationship.

particleof velocityv

particleof massm

constantsPlanck’h

mvh







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• De Broglie’s assertion was verified by Davisson &

Germer within two years.• Consequently, we now know that electrons (in fact -

all particles) have both a particle and a wave likecharacter.

This wave-particle duality is a fundamentalproperty of submicroscopic particles.



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• Example 5-9. Determine the wavelength, in m, of

an electron, with mass 9.11 x 10-31

kg, having avelocity of 5.65 x 107 m/s. Remember Planck’s constant is 6.626 x 10-34 Js which is

also equal to 6.626 x 10-34 kg m2 /s2.

m1029.1m/s1065.5kg109.11

smkg10626.6

mv

h

11

731-

2234

m/s1065.5kg109.11

smkg10626.6

mv

h

731-

2234



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• SP4. Determine the wavelength, in m, of a 0.22caliber bullet, with mass 3.89 x 10-3 kg, having avelocity of 395 m/s, ~ 1300 ft/s.

You do it!

m1031.4

m/s953kg103.89

smkg10626.6mv

h

34

3-

2234

m/s953kg1089.3

smkg10626.6mv

h

3-

2234

• Why is the bullet’s wavelength so small compared to the

electron’s wavelength?



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The Quantum Mechanical Picture of the Atom

• Werner Heisenberg in 1927 developed the conceptof the Uncertainty Principle.

• It is impossible to determine simultaneously both

the position and momentum of an electron (or anyother small particle).

Detecting an electron requires the use of electromagnetic radiation which displaces the

electron!•Electron microscopes use this phenomenon



The Quantum Mechanical Model of the Atom

• Quantum mechanical model replaced the Bohr model

of the atom.

Bohr model depicted electrons as particles incircular orbits of fixed radius.

Quantum mechanical model depicts electrons aswaves spread through a region of space(delocalized) called an orbital.

The energy of the orbitals is quantized like theBohr model.



The Quantum Mechanical Model of the Atom

• Diffraction of electrons shown in 1927.

Electrons exhibit wave-like behavior.

• Wave behavior described using a wave function, the

Schrödinger equation.

H is an operator, E is energy and is the wavefunction.

H E



Potential Energy and Orbitals

• Total energy for electrons includes potential and

kinetic energies. Potential energy more important in describing

atomic structure; associated with coulombicattraction between positive nucleus and negative

electrons.

• Multiple solutions exist for the wave function for anygiven potential interaction.

n is the index that labels the different solutions.

H n

E n

i l d O bi l




• n can be written in terms of two components.

Radial component, depends on the distance fromthe nucleus.

Angular component, depends on the direction ororientation of electron with respect to the nucleus.

P i l E d O bi l




• The wave function may have positive and negative

signs in different regions. Square of the wave function, 2, is always positive

and gives probability of finding an electron at anyparticular point.

• Each solution of the wave function defines an orbital.

Each solution labeled by a letter and numbercombination: 1s, 2s, 2 p, 3s, 3 p, 3d , etc.

An orbital in quantum mechanical terms is actuallya region of space rather than a particular point.

Q N b



Quantum Numbers

• Quantum numbers - solutions to the functions used

to solve the wave equation.

Quantum numbers used to name atomic orbitals.

Vibrating string fixed at both ends can be used toillustrate a function of the wave equation.

Q N b



Quantum Numbers

• When solving the Schrödinger equation, three

quantum numbers are used.

Principal quantum number, n (n = 1, 2, 3, 4, 5, … )

Secondary quantum number, l

Magnetic quantum number, ml

Q N b



Quantum Numbers

• The principal quantum number, n, defines the shell in

which a particular orbital is found.

n must be a positive integer

n = 1 is the first shell, n = 2 is the second shell,etc.

Each shell has different energies.

Q t N b



Quantum Numbers

• The secondary quantum number, l, indexes energy

differences between orbitals in the same shell in anatom.

• l has integral values from 0 to n-1.

l specifies subshell

Each shell contains as many l values as its value of n.

Q t N b



Quantum Numbers

• The energies of orbitals are specified completelyusing only the n and l quantum numbers.

In magnetic fields, some emission lines split intothree, five, or seven components.

A third quantum number describes splitting.

Q t N b



Quantum Numbers

• The third quantum number is the magnetic quantum

number, ml.

ml has integer values.

ml may be either positive or negative.

ml’s absolute value must be less than or equal to l.

For l = 1, ml = -1, 0, +1

Q t N b



Quantum Numbers

• Note the relationship between number of

orbitals within s, p, d , and f and ml.

E l P bl 6 5



Example Problem 6.5

• Write all of the allowed sets of quantum numbers (n,

l, and ml) for a 3p orbital.

Vi li i O bit l



Visualizing Orbitals

• s orbitals are spherical

• p orbitals have two lobes separated by a nodal plane.

A nodal plane is a plane where the probability of finding an electron is zero (here the yz plane).

• d orbitals have more complicated shapes due to thepresence of two nodal planes.

Vi li i O bit l




• Nodes are explained using the Uncertainty Principle.

It is impossible to determine both the position andmomentum of an electron simultaneously and withcomplete accuracy.

An orbital depicts the probability of finding anelectron.

• The radial part of the wave function describes how

the probability of finding an electron varies withdistance from the nucleus.

Spherical nodes are generated by the radialportion of the wave function.

Visuali ing Orbitals




• Cross sectional views of the 1s, 2s, and 3s orbitals.

The Pauli Exclusion Principle and Electron Configurations




• The spin quantum number, ms, determines thenumber of electrons that can occupy an orbital.

ms = ±1/2

Electrons described as “spin up” or “spin down”.

An electron is specified by a set of four quantumnumbers.





• Pauli Exclusion Principle - no two electrons in anatom may have the same set of four quantumnumbers.

Two electrons can have the same values of n, l,and ml, but different values of ms.

Two electrons maximum per orbital.

Two electrons occupying the same orbital are spin

paired.

Orbital Energies and Electron Configurations




• Electrons in smaller orbitals are held more tightlyand have lower energies.

Orbital size increases as the value of n increases.

True for hydrogen atoms, but not entirely true formultielectron atoms.

•As nuclear charge increases, orbital size decreases.

•Electrons interact with other electrons as well as thepositively charged nucleus.





• For electrons in larger orbitals, the charge “felt” is acombination of the actual nuclear charge and theoffsetting charge of electrons in lower orbitals.

The masking of the nuclear charge is calledshielding.

Shielding results in a reduced, effective nuclearcharge.





• The energy ordering for atomic orbitals is 1s, 2s, 2 p,3s, 3 p, 4s, 3d , 4 p, 5s, 4d , 5 p, 6s, 4f , 5d , 6 p, 7s, 5f ,6d , and 7 p.

An orbital’s size and penetration when treatedquantitatively produces the order of filling

represented.

• Electronic configurations are written in order of energy for atomic orbitals.

Hund’s Rule and the Aufbau Principle



Hund s Rule and the Aufbau Principle

• Aufbau principle - when filling orbitals, start with thelowest energy and proceed to the next highestenergy level.

• Hund’s rule - within a subshell, electrons occupy themaximum number of orbitals possible.

• Electron configurations are sometimes depicted usingboxes to represent orbitals. This depiction showspaired and unpaired electrons explicitly.

Example Problem 6 6



Example Problem 6.6

• What is the electron configuration for the sulfur

atom?





• A simplified depiction uses superscripts to indicatethe number of electrons in an orbital set.

1s2 2s2 2 p2 is the electronic configuration forcarbon.

• Noble gas electronic configurations are used as ashorthand for writing electronic configurations.

Relates electronic structure to chemical bonding.

Electrons in outermost occupied orbitals give riseto chemical reactivity of an element.

[He] 2s2 2 p2 is the shorthand for carbon





• The inner electrons, which lie closer to the nucleus,are referred to as core electrons.

Core electrons can be represented by the noble gaswith the same electronic configuration.

• The outer electrons are usually referred to as valenceelectrons.

Valence electrons are shown explicitly when a noblegas shorthand is used to write electronicconfigurations.

Valence electrons determine reactivity.

Example Problem 6 7



Example Problem 6.7

• Rewrite the electron configuration for sulfur using the

shorthand notation.

The Periodic Table and Electron Configurations




• The periodic table and the electronic configurationspredicted by quantum mechanics are related.

The periodic table is broken into s, p, d , and f blocks.

Elements in each block have the same subshell forthe highest electron.

Structure of periodic table can be used to predictelectronic configurations.





• The shape of the periodic table can be broken down intoblocks according to the type of orbital occupied by thehighest energy electron in the ground state.

• We find the element of interest in the periodic table andwrite its core electrons using the shorthand notationwith the previous rare gas element. Then we determinethe valence electrons by noting where the element sitswithin its own period in the table.

Electron Configurations of Transition Metals



4th period and heavier elements

• Pick the noble-gas core.

• Add ns

• Add (n – 1)d (d “steps down”)

• Add np


Complete 5s and 4d . 2 e- into 5 p:

[Kr] 4d 10 5s2 5p2

Sn (5th period, group 4A). Noble-gas core: [Kr]




[Ar] 3d 10 4s1Cu has lower E with filled d -block and half-filled s-block

Ni (4th; 8B; 8 e- into 3d )

Cu (4th; 1B; 9 e- into 3d )

Tc (5th; 7B; 5 e- into 4d ) [Kr] 4d 5 5s2

[Ar] 3d 8 4s2

[Ar] 3d 9 4s2





Sc3d1 4s2

Y4d1 5s2

La5d1 6s2

Ti3d2 4s2

Zr4d2 5s2

Hf 5d2 6s2

V3d3 4s2

Nb4d4 5s1

Ta5d3 6s2

Cr 3d5 4s1

Mo

4d5 5s1

W5d4 6s2

Mn3d5 4s2

Tc

4d5 5s2

Re5d5 6s2

Fe3d6 4s2

Ru4d7 5s1

Os5d6 6s2

Co3d7 4s2

Rh4d8 5s1

Ir5d7 6s2

Ni3d8 4s2

Pd

4d10

Pt5d9 6s1

Cu3d10 4s1

Ag

4d10 5s1

Au5d10 4s1

Zn3d10 4s2

Cd

4d10 5s2

Hg5d10 6s2

Note: ½ filled and filled shells have extra stability


Ion Electron Configurations




Same approach.

Positive ion: remove one e- for each “+”

Negative ion: add one e- for each “-”

S2- (16 + 2) = 18 e-

S [Ne] 3s 2 3p 4

S2- [Ne] 3s 2 3p 6 or [Ar]

Rb+ (37 - 1) = 36 e-

Rb [Kr] 5s 1

Rb+ [Kr] or [Ar] 3d 10 4s 2 4p 6




Isoelectronic = equal number of e-.

“A-group” ions usually adopt the nearestnoble-gas configuration…

… many ions areisoelectronic.

[He] 2s 2

2p 6

O2-

F-

Ne Na+

Mg2+

Al3+

[Ne] 3s 2 3p 6 S2- Cl- Ar K+ Ca2+


Transition Metal Ions



Transition Metal Ions

When filled, E ns > E (n -1)d .

ns e

-

are lost first.

Fe [Ar] 3d 6 4s2 → Fe2+ [Ar] 3d 6

Mn [Ar] 3d 5 4s2 → Mn2+ [Ar] 3d 5

→ Fe3+

[Ar] 3d 5

→ Mn4+ [Ar] 3d 3

→ Mn7+ [Ar]

Example Problem 6.8



Example Problem 6.8

• Use the periodic table to determine the electron

configuration of tungsten (W), which is used in thefilaments of most incandescent lights.



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End of Lecture Unit No. 3

• The study of variousspectra is one of the

fundamental tools thatchemists apply tonumerous areas of their work.

CONTENT



72

CONTENT

1. Quantum Theory

2. Photoelectric effect

3. Bohr’s Theory

4. Dual Nature of the Electrons

5. Quantum Mechanics6. Quantum Numbers

7. Electronic Configuration



GENERAL CHEMISTRY 1

LECTURE UNIT No. 3

(ELECTRONIC STRUCTURE OF ATOM)

Engr. Edgie L. EstopaceSchool of Chemical Engineering and ChemistryMapua Institute of Technology

CHM11-3LectureUnit#3(1)

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