SPARKS CH301 Why are there no blue fireworks? LIGHT, ELECTRONS & QUANTUM MODEL UNIT 2 Day 2 LM15, 16 & 17 due W 8:45AM
QUIZ: CLICKER QUESTION Which of these types of light has the highest energy photons? A. Green Light (540 nm or 5.4 x 10-7 m) B. Red Light (650 nm or 6.5 x 10-7 m) C. Radio waves (100 m) D. Ultraviolet (50 nm or 5 x 10-8 m) E. Infrared (3 mm or 3 x 10-6 m)
Quick Review of DNA
Why Should I wear Sunscreen? TYPES of DNA DAMAGE
Why Should you wear Sunscreen? AVOBENZONE common active ingredient, UV max 357 nm Zinc Oxide reflects UV light
QUIZ: CLICKER QUESTION We shine a beam of light with energy 7 ev on a gold surface (Φ = 5.1 ev) and measure the number and KE of electrons that are ejected. If we increase the energy of our incident radiation (the beam of light), what would you expect to happen? A. More electrons would be ejected. B. Fewer electrons would be ejected. C. The ejected electrons would have a higher KE. D. The ejected electrons would have a lower KE. E. Both answers (A) and (C) would be expected.
What are we going to learn today? The Simplest Atom - Hydrogen What do we know about the H electron? 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
Exciting Electrons Demo
Exciting Electrons Demo
Exciting Electrons Demo
Exciting Electrons Demo Think Like a Chemist H H H H H* H* H* H* Ne Ne Ne* Ne*
POLLING: CLICKER QUESTION 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.
POLL: CLICKER QUESTION Based on the colors you see in the demo, exciting which gas leads to emission of the the highest energy visible photons? a) He b) H 2 c) Ne
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!
E is proportional to 1/n 2 Where do these Energy levels come from?
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 For n=2 to n=1 Energy given off or absorbed by atom? Higher E to lower E Delta E = -2.18 x 10^-18 * (1-0.25) Delta E = negative. Negative corresponds to emission Positive to absorption n 1 and n 2 are Integers!
THIS INTERPRETATION OF THE LINE SPECTRA SUGGESTED THAT THE ENERGIES OF THE ELECTRONS MUST BE QUANTIZED! Electrons in hydrogen atoms must have only specific allowed energies because only specific changes in energy (ΔE) are observed.
Bohr s model- solar system -EMPIRICAL 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)
ATOMIC EMISSION LINE SPECTRA hydrogen helium sodium calcium http://astro.u-strasbg.fr/~koppen/discharge/
POLLING: CLICKER QUESTION In order for an electron to move to a different energy level in an atom, what must happen? a. Nothing. Electrons don t move to different energy levels b. The electron must absorb energy c. The electron must give off a photon d. The electron must either absorb or give off energy
POLLING: CLICKER QUESTION You have two samples of the same gas. Sample X has ten times more atoms than sample Y. How will their emission spectra compare? a. Sample X s spectrum will have more colors. b. Sample X s spectrum will have brighter colors. c. Sample X s spectrum will have both more colors and brighter colors. d. We would expect no difference between the two spectra.
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
Heisenberg Uncertainty Principle Wavelike properties of very small matter means that we cannot simultaneously determine the location of the particle and exactly how it is moving (momentum). Δp Δx > constant Δp Δx > ½ ħ
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
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.
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
The Hydrogen Atom Simplest of all atomic problems. 1 proton, 1 electron. Function Machine (Schrödinger Equation) That will give us the solutions Put that into the Schrödinger Equation and solve Wavefunctions and energies
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
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)
Rydberg-from Bohr model: = R(1/n 1 2 1/n 22 ) (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 = -hr/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 = ENERGY
IONIZATION VERSUS PHOTOELECTRIC EFFECT
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)
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
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
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
Atomic orbitals: defined by Quantum Numbers PRINCIPAL quantum number, n. Describes the energy and approximate nuclear distance. Shell n = 1, 2, 3, 4,... ANGULAR MOMENTUM quantum number, l. Describes the shape of the orbital orbitals of a shell fall into n groups called subshells l = 0, 1, 2,...(n-1) l = s, p, d, f,...
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
Hydrogen Like atoms POLLING: CLICKER QUESTION Below is a plot of the radial distribution of He +, and H (both have only 1 electron) Which is He +?
Classify the solutions Classify our wavefunction solutions based upon both Energy - principle quantum number n Shape - angular momentum quantum number l
Shapes are hard to draw How do we draw three dimensional functions? It is hard. http://winter.group.shef.ac.uk/orbitron/
s orbital actually 1s is easy to draw
s-orbitals
Solutions Shapes (where is the electron?) These are the n = 2 solutions, which one of these is not like the others?
MAGNETIC quantum number, m l. indicates the orientation of the angular momentum around the nucleus distinguishes different orbitals within a subshell The number of values of m l gives you the number of orbitals for a given subshell. m l = integers from l through 0 to + l. there are 2l + 1 values of m l for a given value of l
p-orbitals Probability distribution of p orbital 3 different orientations of p subshell, denoted by the three values of m l
A cross section of the electron probability distribution for a 3p orbital.
d-orbitals Probability distribution distribution of d orbital 5 different orientations of d orbitals denoted by 5 different values of m l
f-orbitals 7 different orientations of f orbitals denoted by the seven different values for m l
What Did We Learn Today? LIGHT CAN BE USED 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 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 of 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