Vanden&Bout/LaBrake& CH301& LIGHT,&ELECTRONS&and&QUANTUM …

CH302 Vanden Bout/LaBrake Fall 2012

Vanden Bout/LaBrake

CH301

LIGHT, ELECTRONS and QUANTUM MODEL

UNIT 2 Day 2

CH302 Vanden Bout/LaBrake Spring 2012

Important InformaKon

EXAM GRADES WERE GREAT! EXAM WRAPPER – QUEST LM – BONUS POINTS

LM13 & 14due Th 9AM


What are we going to learn today?

•  Understand how light can probe electrons in atoms"

•  Recognize that electrons have discrete energy levels in atoms"

•  Predict the energy for transitions of an electron between the energy levels in hydrogen "

•  Relate the empirical model to the theoretical model of the energy levels of electrons in H atom"

•  Solutions to the theoretical model predict electron configuration "

−The simplest Atom - Hydrogen"


What is the energy associated with a photon that has a wavelength of 550 nm?

Plank’s constant = 6.626 X 10-‐34 J * s Speed of light = 2.99 x 108 m/s

A)  414 kJ B)  3.61 x 10-‐37 J C)  3.61 X 10-‐19 J D)  235 J E)  4.14 J

QUIZ: CLICKER QUESTION 1


The Rydberg formula is an empirically derived relaKonship between the difference between the inverse square of integer values and emission spectral lines.

A)  True B)  False



Exciting Electrons Demo"


Exciting Electrons Demo" Think Like a Chemist"

HH HH

H* H*

H* H*

Ne*

Ne*

Ne Ne


Exciting Electrons Demo"POLLING: CLICKER QUESTION 3

WHICH SPECTRUM WOULD YOU EXPECT TO SEE IF WE WERE TO PUT A GRATING BETWEEN YOU AND THE LIGHT SOURCE?

A.

B.


ExciKng which gas leads to emission of the the highest energy visible photons? a) He b) H2 c)  Ne

POLL: CLICKER QUESTION 4


Rydberg Formula "

MathemaKcian Balmer noted a pamern in the frequencies of some of the lines.

Rydberg figured this out with an Empirical model for all the lines for the H-‐atom (simple because there is only one electron)

Convert wavelength to frequency to energy n1 and n2 are Integers!


Rydberg Formula "Discrete lines = Discrete Energies ParKcular wavelengths correspond to transiKons between different energy levels.

NOT ALL ENERGIES ARE POSSIBLE!

What is the energy difference between the n=1 and n=2 states

NegaKve corresponds to emission PosiKve to absorpKon

n1 and n2 are Integers!


E is proporKonal to 1/n2

Where do these Energy levels come from?


Bohr’s model-‐ solar system -‐EMPIRICAL

•  Bohr’s theory allowed for the calculaKon of an energy level

•  Or the calculaKon of the emimed wavelength upon release of energy when an electron transiKons from higher to lower energy

ΔE = h(c/λ)


•  Bohr model was not working well for an atom with more than one electron. It treated the electron as a parKcle. de Broglie had shown that electrons have wave properKes. Schrödinger decided to emphasize the wave nature of electrons in an effort to define a theory to explain the architecture of an atom.

BOHR MODEL

hmp://upload.wikimedia.org/wikipedia/commons/c/cf/Circular_Standing_Wave.gif


Heisenberg Uncertainty Principle

•  Wavelike properKes of very small mamer means that we cannot simultaneously determine the locaKon of the parKcle and exactly how it is moving (momentum).

•  Δp Δx > constant •  Δp Δx > ½ ħ


Wave-‐ParKcle Duality

Small (low mass) “parKcles” have wave-‐like properKes

They are neither described as parKcles or waves They have characterisKcs of each

We saw the same issue for “light”

Seems like a wave, but the energy (photon) appears parKcle-‐like


How do we deal with the new “wave/particle” things? We need a new model!!"

Quantum Mechanics!

It doesn’t make sense! It shouldn’t!

You don’t live in a world of Kny parKcles with vanishingly small mass and momentum.

It is what it is.


Wave funcKons – Tell us about “where” the electron is. (the probability of finding the parKcle at a given posiKon)

Energies– Tell us about the energy of the electron

The Schrödinger EquaKon allows us to solve for all possible wavefuncKons and energies


The Hydrogen Atom"Simplest of all atomic problems. 1 proton, 1 electron.

Put that into the Schrödinger EquaKon and solve

WavefuncKons and energies

FuncKon Machine (Schrödinger EquaKon)

That will give us the soluKons


The Hydrogen Atom"

Infinite number of soluKons Which soluKon are we are interested in? LOWEST ENERGY GROUND STATE ELECTRON CONFIGURATION

FuncKon Machine (Schrödinger EquaKon)

That will give us the soluKons


Where is the Energy?"

Two key ideas from Quantum Mechanics, systems are described by




ENERGY

•  Rydberg-‐from Bohr model: υ = R(1/n12 – 1/n22) (R = 3.29 X 1015 Hz)

•  Schrödinger calculated actual energy of the e-‐ in H using his wave equaKon with the proper expression for potenKal energy En = -‐hR/n2 = -‐2.18 x 10-‐18 J/n2

•  n is principal quantum number which is an integer that labels the different energy levels

•  e-‐ will climb up the energy levels unKl freedom – ionizaKon n = ∞


Where is the particle?"

Two key ideas from Quantum Mechanics, systems are described by




WAVE FUNCTION

•  Schrödinger replaced precise trajectory of a parKcle with a wave funcKon.

•  Born interpretaKon of the wave funcKon-‐ the probability of finding the parKcle in a region is proporKonal to the value of ψ2

•  Ψ2 = probability density – probability that a parKcle will be found in a region divided by the volume of the region

•  Ψ2 = 0 indicates node


" "Physical Model – Quantum Mechanics"

Electrons are they parKcles? Are they waves?

Neither!

They are strange quantum mechanical things that appear to us someKmes as being parKcles and someKmes as waves


DIAGRAM SOLUTIONS LOWEST ENERGY ELECTRON TO HIGHEST ENERGY ELECTRON (Draw energy level diagram for hydrogen atom)


IONIZATION VERSUS PHOTOELECTRIC EFFECT


SOLUTIONS: Atomic Orbitals

•  Apply wave funcKon to e-‐ in 3-‐D space, bound by nucleus.

•  SoluKons to these wave equaKons are called orbitals.

•  Wave funcKon squared gives the probability of finding the electron in that region in space.

•  Each wave funcKon is labeled by three quantum numbers, –  n – size and energy

–  l – shape

–  ml – orientaKon


Atomic Orbitals-‐ Defined by Quantum Numbers

n – principal quantum number-‐specifies the energy of the orbital, All atomic orbitals with the same value of n have the same energy and belong to

the same shell

l – orbital angular momentum quantum number – measure of the rate at which the electron circulates around the nucleus, which defines the shape of the orbital

l = 0,1,2…n-‐1 n different values of l for any given n orbitals of a shell fall into n groups called subshells l=0 is called s-‐orbital l=1 is called p-‐orbital l=2 is called d-‐orbital l=3 is called f-‐orbital

ml – magneKc quantum number – indicates the orienta;on of the angular momentum around the nucleus

disKnguishes the different orbitals within a subshell ml=l, l-‐1…, -‐l there are 2l + 1 values of ml for a given value of l


Classify the solutions"

Classify our wavefuncKon soluKons based upon both

Energy -‐ principle quantum number n

“Shape” -‐ angular momentum quantum number l


Shapes are hard to draw"At the moment we really care about the wavefuncKon squared o�en called the probability density.

Radial probability density is the probability of finding the electron at some distance from the nucleus


Hydrogen Like atoms"

Below is a plot of the radial distribuKon of He+, and H (both have only 1 electron) Which is He+?


Shapes are hard to draw"

How do we draw three dimensional funcKons?

It is hard.

hmp://winter.group.shef.ac.uk/orbitron/


s orbital – actually 1s is “easy” to draw


Probability density of s orbital


Solutions Shapes (where is the electron?)"

These are the n = 2 solutions, which one of these is not like the others?"


p-‐orbitals

Probability distribuKon of p orbital

3 different orientaKons of p subshell, denoted by the three values of ml


d-‐orbitals

Probability distribuKon distribuKon of d orbital

5 different orientaKons of d orbitals denoted by 5 different values of ml


f-‐orbitals

7 different orientaKons of f orbitals denoted by the seven different values for ml


•  The locaKon of an electron in a H atom is described by a wave funcKon known as an atomic orbital, each orbital is designated by a set of three quantum numbers and fall into shells and subshells

quantum numbers – orbital notaKon


Ground state for H

•  Picture shows the difference in energy levels for the first 3 energy levels available for an electron in the H atom. Show the ground state vs an excited state locaKon on the diagram.


Electronic ConfiguraKon and Quantum Numbers for H

State the ground state electron configuraKon and the associated quantum numbers for H.




The three quantum numbers for an electron in a hydrogen atom in a certain excited state are n=4, l=2, ml=-‐1. In what type of orbital is the electron located?




What are all the possible quantum numbers for an electron located in a 2d orbital of a H atom?



What Did We Learn Today?"

Light is a wave with a frequency, speed and wavelength

THIS ALLOWS US TO USE LIGHT TO PROBE THE ENERGY OF ELECTRONS IN MATTER

Developed a physical model that predicts the energy of electron in H atom -‐ QUANTUM


Learning Outcomes"Understand QM is a model and that soluKons to the Schrödinger equaKon yield wave funcKons and energies

Understand that the wave funcKon can be used to find a radial distribuKon funcKon that describes the probability of an electron as a funcKon of distance away from the nucleus

List, define and describe the three quantum numbers for the H-‐atom wave funcKons and know what possible combinaKons of quantum numbers are allowed.

Define the atomic orbital names based on quantum numbers

Vanden&Bout/LaBrake& CH301& LIGHT,&ELECTRONS&and&QUANTUM …

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