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

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 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 CH301 Vanden Bout/LaBrake Fall 2013 Unit2Day2-Crawford Page 1

What are we going to learn today? −The simplest Atom - Hydrogen • 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 CH301 Vanden Bout/LaBrake Fall 2013 QUIZ: CLICKER QUESTION 1 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 10 8 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 CH301 Vanden Bout/LaBrake Fall 2013 Unit2Day2-Crawford Page 2

QUIZ: CLICKER QUESTION 2 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 CH301 Vanden Bout/LaBrake Fall 2013 Exciting Electrons Demo CH301 Vanden Bout/LaBrake Fall 2013 Unit2Day2-Crawford Page 3

Exciting Electrons Demo CH301 Vanden Bout/LaBrake Fall 2013 Exciting Electrons Demo Add electrical energy to various elements: Describe results: CH301 Vanden Bout/LaBrake Fall 2013 Unit2Day2-Crawford Page 4

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* CH301 Vanden Bout/LaBrake Fall 2013 POLLING: CLICKER QUESTION 3 Exciting Electrons Demo WHICH SPECTRUM WOULD YOU EXPECT TO SEE IF WE WERE TO PUT A GRATING BETWEEN YOU AND THE LIGHT SOURCE? A. Unit2Day2-Crawford Page 5

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 POLL: CLICKER QUESTION 4 Exciting which gas leads to emission of the the highest energy visible photons? a) He b) H 2 c)Ne CH301 Vanden Bout/LaBrake Fall 2013 E is proportional to 1/n 2 Where do these Energy levels come from? Unit2Day2-Crawford Page 6

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 n 1 and n 2 are Integers! CH301 Vanden Bout/LaBrake Fall 2013 Unit2Day2-Crawford Page 7

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 n 1 and n 2 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! CH301 Vanden Bout/LaBrake Fall 2013 Bohr ’ s model- solar system -EMPIRICAL Unit2Day2-Crawford Page 8 • ’ • Δ λ

’ • 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 Δ E = h(c/ λ ) CH301 Vanden Bout/LaBrake Fall 2013 BOHR MODEL • 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. http://upload.wikimedia.org/wikipedia/commons/c/cf/Circular_Standing_Wave.gif CH301 Vanden Bout/LaBrake Fall 2013 Unit2Day2-Crawford Page 9

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. CH301 Vanden Bout/LaBrake Fall 2013 Unit2Day2-Crawford Page 10

The Schrödinger Equation allows us to solve for all possible wavefunctions and energies 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 CH301 Vanden Bout/LaBrake Fall 2013 The Hydrogen Atom Simplest of all atomic problems. 1 proton, 1 electron. Function Machine Put that into the Schrödinger (Schrödinger Equation) Equation and solve That will give us the solutions Wavefunctions and energies CH301 Vanden Bout/LaBrake Fall 2013 Unit2Day2-Crawford Page 11

The Hydrogen Atom Function Machine (Schrödinger Equation) That will give us the solutions Infinite number of solutions Which solution are we are interested in? LOWEST ENERGY GROUND STATE ELECTRON CONFIGURATION 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 CH301 Vanden Bout/LaBrake Fall 2013 DIAGRAM SOLUTIONS LOWEST ENERGY ELECTRON TO HIGHEST ENERGY ELECTRON (Draw energy level diagram for hydrogen atom) Unit2Day2-Crawford Page 12

CH301 Vanden Bout/LaBrake Fall 2013 ENERGY • Rydberg-from Bohr model: 2 – 1/n 2  = R (1/n 1 2 ) ( R = 3.29 X 10 15 Hz) • Schrödinger calculated actual energy of the e - in H using his wave equation with the proper expression for potential energy E n = -h R /n 2 = -2.18 x 10 -18 J/n 2 • 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 = ∞ CH301 Vanden Bout/LaBrake Fall 2013 Unit2Day2-Crawford Page 13

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) CH301 Vanden Bout/LaBrake Fall 2013 Unit2Day2-Crawford Page 14

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 ψ 2 • Ψ 2 = probability density – probability that a particle will be found in a region divided by the volume of the region • Ψ 2 = 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 CH301 Vanden Bout/LaBrake Fall 2013 Unit2Day2-Crawford Page 15

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 – m l – 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 CH301 Vanden Bout/LaBrake Fall 2013 Unit2Day2-Crawford Page 16