07 Student Lecture Notes - Atomic Structure

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Table of ContentsChapter 7 - Atomic Structure

I. ELECTROMAGNETIC RADIATION:.............................................................2

THE ELECTROMAGNETIC SPECTRUM.............................................................................................................................2

II. HOW DOES THIS AFFECT OUR STUDY OF CHEMISTRY?...................4

III. EARLY QUANTUM THEORY.......................................................................4

MAX PLANCK(1858-1947), A GERMAN PHYSICIST, ....................................................................................................4LIGHTAS PARTICLES PHOTOELECTRIC EFFECT.........................................................................................................5WAVE PROPERTIESOF MATTER: LOUISDE BROGLIE (1892-1987)..............................................................................6HYDROGEN LINE SPECTRA & THE BOHRMODELOFTHE ATOM.................................................................................7

Johann Balmer (1825-1898) and Johannes Rydberg (1854-1919)..........................................................................7Niels Bohr (1885-1962) A Danish Scientist.............................................................................................................7

IV. THE WAVE MODEL OF THE ATOM........................................................10

HEISENBERG UNCERTAINTY PRINCIPLE......................................................................................................................10Warner Heisenberg (1901-1976)...........................................................................................................................10

Max Born (1882-1970)...........................................................................................................................................10

SCHRDINGERWAVE EQUATION (1926)....................................................................................................................10Erwin Schrdinger (1887-1961), an Austrian Scientist.........................................................................................10

V. QUANTUM NUMBERS...................................................................................11

Orbitals...................................................................................................................................................................12

Orbital Shapes (based on 2nd QN, l).....................................................................................................................12Shells and Subshells...............................................................................................................................................13

Practice with Quantum Numbers...........................................................................................................................13

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Chapter 7 - Atomic StructureThere are periodic trends that can be explained by atomic structure, for which weneed to understand a little physics.

I. Electromagnetic Radiation:

- Energy transport in the form of _______- James Maxwell described radiation in terms of oscillating electro-magnetic fields

- EMR encompasses radio waves, microwaves, IR radiation, visible light, UVradiation, X-rays, -rays; visible tight is a form of _______________

The Electromagnetic Spectrum

In EMR visible light of different v or correspond to different colors.

Wave motion characterized by frequency or wavelength, and the wave velocity.

____________,, is the number of waves or cycles per second that pass a givenpoint in space

Units: s-1 or cycles per sec or Hz

____________, , is the distance from crest to crest in a waveUnits: nm (10-9m) or (angstroms = 10-8cm or 10-10m)

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v and are inversely proportional to each other(as one goes up the other goes down)

c =

Since all EMR travels at the same speed,- If you have a short (like a short step) you

need to take steps more frequently to keepup (have a higher frequency).

- Conversely, if you have a long wavelength, you need to have a smallerfrequency (take fewer steps).

For EMR,- velocity in--vacuum is

c = 2.9979 x 108 m/s, ____________________

Intensity is proportional to the _____________.Energy is inversely proportional to the _____________.

Short wavelengths have high energy.Long wavelengths have low energy.

There are two types of waves:

- ______________ waveslike waves in the ocean any number of cycles are possible

- ______________ waves

like a guitar string only whole numbers of cycles are possible.(This is the type that is applicable to our studies of the atom.)

All forms of Electromagnetic Radiation:

- Travel at the __________________ (2.9979 x 108 m/s)

- Have an ______________ component

- Have a ____________ component

- Have a dual __________ and ________ nature

Lecture Problem #1What is the frequency of light which has a of 100. nm?

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II. How Does This Affect Our Study of Chemistry?

Some properties of matter could not be explained by Rutherfords model of the atom:(Dense positively charged nucleus with e- freely occupying the non-denseexterior.)

1. The presence of ______________rather than a complete spectrumwhen elements were heated.

2. The Ultraviolet Catastrophe

When matter is heated, (stove coils forexample) they give of different colors atdifferent temperatures

(called: black body radiation)

The intensity of the radiation did notcontinue to increase as the frequencyincreased the way that classical physicsof the time predicted.

III. Early Quantum Theory

Max Planck (1858-1947), a German Physicist,

Attempted to explain these phenomena.

In 1900 he theorized that black body radiant energy was __________, and could onlyhave _________________.

He then made the assumption that atoms/molecules absorb or emit energy in smallpackages or ___________.

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Planks Equation for the energy of_____________: =hE

Since therefore

cc ==

hcE =

Where = _____________ of the radiationh = 6.626x10-34Jsec (Plancks Constant)

Lecture Problem #2

How many photons are in 4.00 x 10-17 J of energy produced from orange lightwith a wavelength of 600. nm?

Light as Particles Photoelectric Effect.

Discovered by Albert Einstein in 1905.- If you shine light on a metal, it

will give off an _____________.

- It has to be light of sufficient____________.(You cannot substitute a lot of(high intensity) low energy/longwavelength particles for a fewerhigh energy/short wavelength

particles.

(Just like you cant substitute a bunch of ping-pong balls for a bowling ball!!!)

Einstein explained the photoelectric effect by extending Plancks idea of quantizedblack body radiation to all _______.

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Examples of:Quantized Not Quantized

_____________ __________________________ _____________

Wave Properties of Matter: Louis de Broglie (1892-1987)

- In 1925 de Broglie thought: if light, which is a wave, can have a particlenature, then why cant __________ (especially electrons) have a

___________________?- He used Einsteins and Plancks equations to derive a relationship between the

mass (in kg) of a particle and its wavelength (in m) at a certain velocity (inm/s).

infromEinstePlanckfrom 2mcE

hcE ==

( )___________mc

h

mc

hcmc

hc2

2 fortrueonlyisthis===

If we substitute c with the velocity of the particle:

mv

h:EquationsBroglie'De = Good for the of moving ________.

Lecture Problem #3What is the De Broglie wavelength (in nm) of a hydrogen molecule (m=3.35x10-27 kg)moving at a velocity of 1.84x103m/s ?

We know that a2

2

s

mkgJ

= and h is in units of Jsec

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Hydrogen Line Spectra & The Bohr Model of the Atom

Johann Balmer (1825-1898) and Johannes Rydberg (1854-1919)

- examined the four visible lines in the spectrum of the hydrogen atom.

- played around with these numbers and eventually figured out that all fourwavelengths fit into the Rydberg Equation:

Where R=1.097x107/m (Rydberg Constant)and n=3, 4, 5(for a 1 e-

system)

From this they concluded that for:n=3 red (656.3 nm)n=4 blue-green (486.1 nm)

n=5 blue (434.0 nm)n=6 indigo ???

Lecture Problem #4

Calculate the wavelength of light emitted (in nm) when an electron falls from the n=6to the n=2 level in the hydrogen atom.

Niels Bohr (1885-1962) A Danish Scientist

- In 1913 he proposed a new model of the atom that attempted to better explainatomic line spectra and disproved J.J. Thompsons Plum Pudding model.

- Electrons move in circular ____________ around the nucleus.

- The closer the orbit to the nucleus, the lower its ______________.- Each orbit has a specific energy that has a _______________ value (n).

- The lowest energy orbit is called the _____________________.

- Electrons can move from one orbit to another.Going to a higher energy orbit ______________ energy.

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=

22 n

1

2

1R

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Returning to a lover energy orbit ___________ energy.Emitted energy is usually in the form of _________.

The lines studied by Rydberg andBalmer all ended in n=___ for a

reason.

For nf=2 the E for the transition putthe emitted EMR in the _________

portion of the spectra. These werecalled the ____________ series.


portion of the spectra (large Emeans small ). These were calledthe _____________series.


portion of the spectra (small Emeans long ). These were calledthe _____________series.

Beyond the Paschen series is the Bracket series (nf=4) and Pfund series (nf=5).

Bohr calculated the energy of any given level as: 2nRhc

E = Rhc=1312 kJ/mol

The energy difference between any two levels is given by:

=

2

i

2

f n

1

n

1RhcE If you know the ____________________ involved.

hcE = If you know the _______________ of the emission.

Unfortunately, Bohrs model only successfully explained the spectrum of the H atom.

Efforts were made to modify his theory (e.g., elliptical orbits) but were unsuccessful.

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We had to move to a whole new theory.

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IV. The Wave Model of the Atom

Heisenberg Uncertainty Principle

Warner Heisenberg (1901-1976)

In studying the works of Bohr and DeBroglie concerning the wave nature of theelectron stated that:

Because matter has a particle and wave properties, it is impossible to determine

the exact_____________ and the exact ______________ (or energy, velocity)

of a particle ___________________.

To see something, we must shine light on it, but small particles change position andenergy when struck by photons of light.

Heisenberg related the uncertainty in the position (x) to the uncertainty in themomentum (p) as follows:

( )( ) 3.14159constant;sPlanck'hwhere4

hpx ==>

and ( ) mvmp ==

Max Born (1882-1970)

Interpreted Heisenbergs Uncertainty Principle as:

If we choose to know the __________of an electron in an atom with only a small

uncertainty, we must accept a relatively large uncertainty in its ___________ in

the space around an atoms ____________.

This means that we can only develop areas of high ________________ of finding anelectron of a given energy in a certain ____________ of space.

Schrdinger Wave Equation (1926)Erwin Schrdinger (1887-1961), an Austrian Scientist

Developed a mathematical wave function (H)(psi) to describe the ____________for finding a given electron for the hydrogen atom in certain regions of space.

The equation is long and complex, but includes _________ important variables:

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V. Quantum Numbers

The three variables that come out of the wave equation are: n, l, ml

n These - are quantum variables- have a restricted set of allowed values

-known as quantum numbers .

l

ml

Different solutions were attempted for the wave equation and allowed values werefound to be:

QN Dependence Possible Values

n independent 1, 2, 3, etc. in integers

l dependent on ___ 0 to (n-1) in integers

ml dependent on ___ - l to + l in integers

There are sets of possible quantum numbers

Lecture Problem #5

Try writing the possible sets of n, l, and ml that can be obtained when n=3.

n l ml

The solutions to the wave equation (2) were plotted to see what the affect of the

different variables was on the probability distribution.

Symbol Name Affectn primary QN The ______of the probability region (the energy level)l angular momentum

QN The __________of the probability regionm

lmagnetic QN The _____________in space of the probability region

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Orbitals

The density of the probability points varies withthe distance from the nucleus.- The density is not homogeneous.- The probability region extends to infinity (but

probability gets very small).- We enclose the 90% probability area in a surface

known as _____________.

Orbital Shapes (based on 2nd QN, l)

When l =0 the orbital is _________________Known as an ___ orbital.

- There are ___ nodal planes.- There is ___ lobe

When l =1, the orbital looks like a _____________Known as a ___ orbital.

- There is ___ nodal plane.- There are ___ lobes

When l =2, the orbital looks like a double dumbbell or a dumbbell with a doughnut.Known as a ___ orbital.

- There are ___ nodal plane.- There are ___ lobes

(or 2 lobes and adoughnut)

When l =3 (see bottom

right for shape)Known as a ___ orbital.

- There is ___ nodalplane.

- There are ___ lobes

(after f comes g, h, i, etc)

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Shells and Subshells

A shell is a grouping of orbitals with the same values ____ .

A subshell is a grouping of orbitals with the same values of ________.e.g. 3p (a set of 3 orbitals) or 4d (a set of 5 orbitals)

Within each shell there are ____ subshells.e.g. when n=1 there is 1 subshell (1s)

n=2 there are 2 subshells (2s, 2p)n=3 there are 3 subshells (3s, 3p, 3d)n=4 there are 4 subshells (_______________)

Practice with Quantum Numbers

When n=4 what are the possible values of l?

When l=2, what are the possible values of ml?

For a 4s orbital, what are the possible values of n, l, ml?

For a 3f orbital, what are the possible values of n, l, ml?

What is wrong with each set of QNs?n=2, l=2, ml=0n=3, l=0, ml=-2n=0, l=0, ml=-1

07 Student Lecture Notes - Atomic Structure

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