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Unit2Day2-Crawford Monday, September 23, 2013 4:15 PM Vanden - - PDF document

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Unit2Day2-Crawford Monday, September 23, 2013 4:15 PM Vanden Bout/LaBrake/Crawford CH301 Why are there no blue fireworks? LIGHT, ELECTRONS & QUANTUM MODEL UNIT 2 Day 2 CH302 Vanden Bout/LaBrake Fall 2013 Important Information EXAM

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CH302 Vanden Bout/LaBrake Fall 2013

Vanden Bout/LaBrake/Crawford CH301 Why are there no blue fireworks? LIGHT, ELECTRONS & QUANTUM MODEL UNIT 2 Day 2

CH301 Vanden Bout/LaBrake Fall 2013

Important Information

EXAM GRADES WERE GREAT! EXAM WRAPPER – QUEST LM – BONUS POINTS LM12 & 13 due today 9AM HW04 due today 9AM LM14, 15 & 16 due Th 9AM Laude Lecture 2 & 3 LMs

Unit2Day2-Crawford

Monday, September 23, 2013 4:15 PM Unit2Day2-Crawford Page 1

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CH301 Vanden Bout/LaBrake Fall 2013

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

CH301 Vanden Bout/LaBrake Fall 2013

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

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CH301 Vanden Bout/LaBrake Fall 2013

The Rydberg formula is an empirically derived relationship between the difference between the inverse square of integer values and emission spectral lines. A) True B) False

QUIZ: CLICKER QUESTION 2

CH301 Vanden Bout/LaBrake Fall 2013

Exciting Electrons Demo

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CH301 Vanden Bout/LaBrake Fall 2013

Exciting Electrons Demo

CH301 Vanden Bout/LaBrake Fall 2013

Exciting Electrons Demo

Add electrical energy to various elements: Describe results:

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CH301 Vanden Bout/LaBrake Fall 2013

Exciting Electrons Demo

CH301 Vanden Bout/LaBrake Fall 2013

Exciting Electrons Demo Think Like a Chemist

HH HH 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.

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CH301 Vanden Bout/LaBrake Fall 2013

Exciting Electrons Demo

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

CH301 Vanden Bout/LaBrake Fall 2013

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

POLL: CLICKER QUESTION 4

E is proportional to 1/n2 Where do these Energy levels come from?

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CH301 Vanden Bout/LaBrake Fall 2013

Where do these Energy levels come from?

CH301 Vanden Bout/LaBrake Fall 2013 CH301 Vanden Bout/LaBrake Fall 2013

Rydberg Formula

Mathematician Balmer noted a pattern 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!

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CH301 Vanden Bout/LaBrake Fall 2013

Rydberg Formula

Discrete lines = Discrete Energies

Particular wavelengths correspond to transitions between different energy levels. NOT ALL ENERGIES ARE POSSIBLE! What is the energy difference between the n=1 and n=2 states Negative corresponds to emission Positive to absorption n1 and n2 are Integers!

CH301 Vanden Bout/LaBrake Fall 2013

THIS INTERPRETATION OF THE LINE SPECTRA ALLOWED SUGGESTED THAT THE ENERGIES OF THE ELECTRONS MUST BE QUANTIZED!

Bohr’s model- solar system -EMPIRICAL

  • ’
  • Δ

λ

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CH301 Vanden Bout/LaBrake Fall 2013

’

  • Bohr’s theory allowed for the calculation of an energy level
  • Or the calculation of the emitted wavelength upon release of energy

when an electron transitions from higher to lower energy

ΔE = h(c/λ)

CH301 Vanden Bout/LaBrake Fall 2013

  • Bohr model was not working well for an

atom with more than one electron. It treated the electron as a particle. de Broglie had shown that electrons have wave properties. 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

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

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CH301 Vanden Bout/LaBrake Fall 2013

Wave-Particle Duality

Small (low mass) “particles” have wave-like properties They are neither described as particles or waves They have characteristics of each We saw the same issue for “light” Seems like a wave, but the energy (photon) appears particle-like

CH301 Vanden Bout/LaBrake Fall 2013

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 tiny particles with vanishingly small mass and momentum. It is what it is.

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CH301 Vanden Bout/LaBrake Fall 2013

Wave functions – Tell us about “where” the electron is. (the probability of finding the particle at a given position) Energies– Tell us about the energy of the electron The Schrödinger Equation allows us to solve for all possible wavefunctions and energies

CH301 Vanden Bout/LaBrake Fall 2013

The Hydrogen Atom

Simplest of all atomic problems. 1 proton, 1 electron.

Put that into the Schrödinger Equation and solve

Wavefunctions and energies

Function Machine (Schrödinger Equation) That will give us the solutions

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CH301 Vanden Bout/LaBrake Fall 2013

The Hydrogen Atom

Infinite number of solutions Which solution are we are interested in? LOWEST ENERGY GROUND STATE ELECTRON CONFIGURATION

Function Machine (Schrödinger Equation) That will give us the solutions

CH301 Vanden Bout/LaBrake Fall 2013

Where is the Energy?

Two key ideas from Quantum Mechanics, systems are described by Energies– Tell us about the energy of the electron

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

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CH301 Vanden Bout/LaBrake Fall 2013 CH301 Vanden Bout/LaBrake Fall 2013

ENERGY

  • Rydberg-from Bohr model:

 = R(1/n1

2 – 1/n2 2)

(R = 3.29 X 1015 Hz)

  • Schrödinger calculated actual

energy of the e- in H using his wave equation with the proper expression for potential 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 until freedom – ionization n = ∞ Unit2Day2-Crawford Page 13

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CH301 Vanden Bout/LaBrake Fall 2013

Exciting Electrons Demo

SUMMARIZE THE SIMILARITIES AND DIFFERENCES BETWEEN THE PHOTOELECTRIC EFFECT AND THE EMISSION SPECTRA OF EXCITED ELEMENTS

CH301 Vanden Bout/LaBrake Fall 2013

Where is the particle?

Two key ideas from Quantum Mechanics, systems are described by Wave functions – Tell us about “where” the electron is. (the probability of finding the particle at a given position)

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CH301 Vanden Bout/LaBrake Fall 2013

WAVE FUNCTION

  • Schrödinger replaced precise

trajectory of a particle with a wave function.

  • Born interpretation of the

wave function- the probability of finding the particle in a region is proportional to the value of ψ2

  • Ψ2 = probability density –

probability that a particle will be found in a region divided by the volume of the region

  • Ψ2 = 0 indicates node

CH301 Vanden Bout/LaBrake Fall 2013

Physical Model – Quantum Mechanics Electrons are they particles? Are they waves? Neither! They are strange quantum mechanical things that appear to us sometimes as being particles and sometimes as waves

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CH301 Vanden Bout/LaBrake Fall 2013

SOLUTIONS: Atomic Orbitals

  • Apply wave function to e- in 3-D

space, bound by nucleus.

  • Solutions to these wave equations

are called orbitals.

  • Wave function squared gives the

probability of finding the electron in that region in space.

  • Each wave function is labeled by

three quantum numbers,

– n – size and energy – l – shape – ml – orientation

CH301 Vanden Bout/LaBrake Fall 2013

Shapes are hard to draw

At the moment we really care about the wavefunction squared often called the probability density. Radial probability density is the probability of finding the electron at some distance from the nucleus

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CH301 Vanden Bout/LaBrake Fall 2013

Hydrogen Like atoms

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

POLL: CLICKER QUESTION 5

A B

CH302 Vanden Bout/LaBrake Fall 2013

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

  • rbital

l = 0,1,2…n-1 n different values of l for any given n

  • rbitals 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 – magnetic quantum number – indicates the orientation of the angular momentum around the nucleus distinguishes the different orbitals within a subshell ml=l, l-1…, -l there are 2l + 1 values of ml for a given value of l

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CH301 Vanden Bout/LaBrake Fall 2013

Classify the solutions

Classify our wavefunction solutions based upon both Energy - principle quantum number n “Shape” - angular momentum quantum number l

CH301 Vanden Bout/LaBrake Fall 2013

Shapes are hard to draw

How do we draw three dimensional functions? It is hard. http://winter.group.shef.ac.uk/orbitron/

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CH301 Vanden Bout/LaBrake Fall 2013

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

CH301 Vanden Bout/LaBrake Fall 2013

Probability density of s orbital

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CH301 Vanden Bout/LaBrake Fall 2013

Solutions Shapes (where is the electron?) These are the n = 2 solutions, which one of these is not like the others?

CH301 Vanden Bout/LaBrake Fall 2013

p-orbitals

Probability distribution of p

  • rbital

3 different orientations

  • f p subshell, denoted

by the three values of ml

d-orbitals

Probability distribution distribution of d

  • rbital

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CH301 Vanden Bout/LaBrake Fall 2013

Probability distribution distribution of d

  • rbital

5 different orientations of d

  • rbitals denoted by 5 different

values of ml

CH301 Vanden Bout/LaBrake Fall 2013

f-orbitals

7 different

  • rientations of f
  • rbitals denoted by

the seven different values for ml Unit2Day2-Crawford Page 21

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CH301 Vanden Bout/LaBrake Fall 2013

  • The location of an

electron in a H atom is described by a wave function known as an atomic orbital, each

  • rbital is designated by a

set of three quantum numbers and fall into shells and subshells

quantum numbers – orbital notation

CH301 Vanden Bout/LaBrake Fall 2013

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 location

  • n the diagram.

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CH301 Vanden Bout/LaBrake Fall 2013

Electronic Configuration and Quantum Numbers for H

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

QUIZ: CLICKER QUESTION 5

CH301 Vanden Bout/LaBrake Fall 2013

Electronic Configuration and 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? QUIZ: CLICKER QUESTION 6

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CH301 Vanden Bout/LaBrake Fall 2013

Electronic Configuration and Quantum Numbers for H

What are all the possible quantum numbers for an electron located in a 2d orbital of a H atom? QUIZ: CLICKER QUESTION 7

CH301 Vanden Bout/LaBrake Fall 2013

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

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CH301 Vanden Bout/LaBrake Fall 2013

Learning Outcomes

Understand QM is a model and that solutions to the Schrödinger equation yield wave functions and energies Understand that the wave function can be used to find a radial distribution function that describes the probability

  • f an electron as a function of distance away from the nucleus

List, define and describe the three quantum numbers for the H-atom wave functions and know what possible combinations of quantum numbers are allowed. Define the atomic orbital names based on quantum numbers

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