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Transcript
Ch 5: Electronic structure (aka Quantum Theory) 5.3: Electromagnetic Radiation (aka “Light”) 5.1 & 5.2: Bohr model & Quantum-mechanical model Review of Basic Atomic Structure 1. PROTONS – in nucleus, determine the identity of an atom (what element it is) 2. NEUTRONS – in nucleus, contribute to mass 3. ELECTRONS – move around in the empty space around the nucleus Determine the way an atom BEHAVES chemically (how it reacts or doesn’t react….) Remember!!!! Models are made to fit the data….. If new data is discovered, models must be changed to fit the new data. Quick Review of older models DATA: Mass conservation experiments MODEL: Dalton’model: Thompson’s 1800-1803 plum-pudding model, 1897 Rutherford’s nuclear atomic model, 1911 So, what new data made it necessary to come up with the QUANTUM ATOMIC MODEL? EVIDENCE: Atomic emission spectra of HYDROGEN SPECTRAL TUBE— tube filled with an element in gas form. When you apply a voltage, it emits light. Here’s a little something to compare with… white, natural sunlight has an emission spectrum like this…. LAB-related question: How do you split up light into its component parts? DISPERSION BY PRISM or USE OF DIFFRACTION GRATING—separates light into its components (what we see as one color may actually be composed of light of various colors) NEW DATA that led to the QUANTUM atomic model ___________’s atomic HYDROGEN emission spectrum is DISCRETE, not CONTINUOUS _______________________ Violet 410nm Blue 434nm Blue-Green 486 nm Red 656nm Balmer Series I don’t get it – why are those LINES such a big deal?! In order to understand WHY/ HOW the emission spectra relates to the the quantum atomic model, you need to understand…. LIGHT aka “Electromagnetic Radiation” INTRODUCTION TO “LIGHT” LIGHT is also known as ELECTROMAGNETIC radiation (EM radiation) ___________________________________. WAVE EM radiation acts like both a _________ and a ____________________________ DISCRETE PARTICLE (i.e. photon) Waves Wave: a rhythmic disturbance in both time and space which transfers energy, but not matter. Wave Categories • Mechanical Waves: require a medium. Examples: • Water waves (Tsunami) & Earthquake waves • Sound waves (speed= 340 m/s in air but varies for different media, faster in solids) • Electromagnetic Waves: do not require a medium. Can travel through space (vacuum). Example: Light from the sun reaches us Note: All EM waves have a speed of 3.00 x 108 m/s when in a vacuum. TYPES OF WAVES 1. TRANSVERSE WAVES - The particles vibrate perpendicular to the direction of the wave's propagation (ex: waves along a string, electromagnetic waves). 2. LONGITUDINAL WAVES - The particle displacement is parallel to the direction of wave propagation (ex: sound) TYPES OF WAVES (cont’d) 3. ELLIPTICAL WAVES Result when longitudinal and transverse waves are superpositioned. (ex: surface water waves) 4. TORSIONAL WAVES http://youtu.be/m686UO68AXI Parts of a wave Wavelength, l ”lambda”: The distance from the crest to crest or trough to trough. Crest: High Point Equilibrium (Baseline) Amplitude, A: The distance from the equilibrium (baseline) to the crest or trough Trough: Low point Low vs. High amplitude In light, amplitude is related to intensity or brightness Frequency the number of waves IN ONE SECOND – Symbol is ν = “nu” – SI unit is Hertz (Hz) or 1/s or s-1 Relationship between Frequency & Wavelength INVERSELY RELATED DECREASES As Wavelength INCREASES, frequency _________ As Wavelength DECREASES, frequency INCREASES _________ EM radiation (low high E) Type of radiation Wavelengths(m) i. Radio 570 - 2.8 TV 5.6 - 0.34 ii. Microwave 0.1 - 0.001 iii. Infrared radiation (IR) 10-3 - 10-7 iv. Visible light red 700x10-9 (700nm) ROYGBIV violet 400x10-9 (400nm) v. Ultraviolet (UV) 10-7 - 10-10 vi. x-rays 10-10 -10-12 vii. Gamma rays less than 10-12 Speed of a Wave speed= distance/time c = l/t c =l ν REFRACTION: When a wave travels from one medium to a different medium, the speed changes, but the frequency stays the same. A wave’s speed is constant in a given medium. In a vacuum, any EM radiation travels at the speed of light: c = 3.00 x 108 m/s Speed of Light – 3.00 x 108 m/s Frequency c = lv (in 1/s or Hz) Wavelength (in m) 1) Find the wavelength of 93.3 MHz in meters 3 x 108 m/s = 93.3 x 106 1/s l (93.3 x 106 1/s) 93.3 x 106 1/s 3.22 m WAVELENGTH CONVERSIONS When you use the formula, λ must be in METERS. Sample conversion: • nanometers to meters (1 nanometer = 10-9 meter) • 600 nm = ? m 600 nm x 10-9 meter = 600 x 10-9 m = 6 x 10-7 m 1 nm You Try: • What is the frequency of a light wave with a wavelength of 550 nm? • What color light is it? (Hint: 400 nm is violet; 700 nm is red) Energy of a wave (measured in joules, J) Frequency E = hn (in 1/s or Hz) Planck’s Constant 6.626 x 10-34 J*s 1) Find the energy of 93.3 MHz in meters E = (6.626 x 10-34 J*s) ( 93.3 x 106 1/s) 6.18 x 10-26 joules Electromagnetic Spectrum Low High Energy: OY G BIV Summary of Light c = ln c l= n c n= l Therefore: wavelength and frequency are inversely proportional. Therefore: energy High frequency = more energy is directly proportional to the Low frequency = less enery frequency. E = hn Questions of the Day 1) List the seven types of EM radiation in order from low to high energy. 2) What’s the relationship btwn. λ & ν? E & ν? 3) What is the lower energy light? One with λ = 450 (violet/ blue) nm or λ = 700 nm (red) 4) Calculate the frequency for yellow light with a wavelength of 589 nm. 8 m/s = (589 x 10-9 m) ν 3 x 10 c = ln 5.09 x 1014 1/s 4) What is the energy of this light? -34 j*s) ( 5.09 x 1014 1/s) E = (6.626 x 10 E = hn 3.37 x 10-19 J QUANTUM ATOMIC THEORY Data: Hydrogen’s Emission Spectrum 1st model: Bohr’s Model Planck’s Equation E=hv E=energy in joules H=planck’s constant=6.63E-34J*s V=frequency (per second or Hz) The energy(E) & the frequency(V) of an electromagnetic wave are directly related. Electromagnetic Wave Equation C=λv C=speed of light=3.00E8m/s λ=wavelength in meters V=frequency (per second or Hz) Frequency & wavelength are inversely related AND wavelength & energy are inversely related. NEW DATA that led to the QUANTUM atomic model ___________’s atomic HYDROGEN emission spectrum is DISCRETE, not CONTINUOUS _______________________ Violet 410nm Blue 434nm Blue-Green 486 nm Red 656nm Balmer Series Quantized vs. Continuous Quantized Continuous • Comes in discrete packages • Example: second hand on clock that “ticks” • STAIRS or LADDER • Flowing • Example: second hand on clock that moves continuously • RAMP or ESCALATOR Quantum theory 1. Electrons can only have certain “allowed” ____________energies. 2. To change (jump) from one “allowed” energy to another “allowed” energy, the electron absorb or emit must _____________the exact difference between these energies—this is called a ___________. QUANTUM Niel Bohr’s atomic model, 1913 (aka planetary model) EACH RING REPRESENTS AN ALLOWED ENERGY LEVEL. • Electrons orbit the nucleus in circular paths (___________) rings or orbits of fixed energy (_________). energy levels • Electrons in rings closer to the nucleus are LOWER ___________in energy. • Electrons in rings farther away from the nucleus are HIGHER in energy. __________ Bohr’s model (electron transitions) • An electron transition from n= 1 to n=3 is a ___________ excitation because the electron goes from having a low energy high energy. • An electron transition from n relaxation = 3 to n=2 is a _________ because the electron goes from having a high energy low energy. • What is shown in this a relaxation picture?_______________ Bohr’s model (energy changes) EXCITATION _____________occurs when an electron __________________ ABSORBS or TAKES IN energy, so that the electron is in an EXCITED STATE _____________. ___________________ RELAXATION occurs when an electron EMITS or GIVES OFF energy. __________________ If the electron relaxes completely, the electron is in GROUND STATE a _________ Excited State & Ground State • Ground state: the lowest possible energy level an electron be in. • Excited state: any energy level higher than the ground state. Bohr Atom Animation • http://higheredbcs.wiley.com/legacy/college/ halliday/0471320005/simulations6e/index.ht m?newwindow=true EXCITATION • Let’s look at the Hydrogen atom • If heat, electricity, or light are absorbed, the electron can move up energy levels (EXCITATION) RELAXATION • As the electron falls back (RELAXATION) to ground state it gives the energy back as light (emission). SERIAL RELAXATION • May fall down in steps • Each with a different energy Calculation of Energy • The energy absorbed or emitted during an excitation or relaxation is equal to the DIFFERENCE ___________________________ between the initial energy level and the final energy level. or difference in energy • ΔE = change _________________________ between two energy levels _____________________ QUANTUM (aka… a “_________________”) E3 – E1 or ΔE = _________ E1 – E3 In this example, ΔE = _______ (the amount absorbed or emitted is the same!) Energy of Emitted Photon Energy of the emitted photon, Ephoton= Difference in energy between two states, E A quantum of energy is the amount of energy required to move an electron from one energy level to another. An Analogy for Bohr’s Model Increasing energy Fifth Fourth Third Second First Nucleus • The energy levels are like the rungs of a ladder, but are NOT equally spaced. • There is no “in between” energy How the Bohr model explains the emission spectrum of H: Absorption vs. Emission spectrum of H ABSORPTION SPECTRUM—black lines represent ENERGY absorbed as electron EXCITES _________________________________ EMISSION SPECTRUM—colored lines represent ENERGY emitted as electron RELAXES __________________________________ Questions of the Day 1) The lowest energy level that an electron occupies is its _______________. 2) When an electron jumps to a higher energy level, we called this level the _________ state. 3) When it jumps back down to a lower energy level, this electron movement is called a __________ and is accompanied by a __________ of energy. 4) Why are there sometimes different energy photons/ wavelengths of light emitted when an electron jumps back down? QUANTUM ATOMIC THEORY Data: Emission Spectrum of OTHER ELEMENTS 2nd model: Wave-Mechanical Model I was the first to come up with QUANTUM ATOMIC MODEL, and the idea of quantized energy levels… Bohr Quick review of Bohr: THE MODEL THE ENERGY DIAGRAM FOR H (quantized energy levels) Why we had to move on…. • Why a new model? -The Bohr model didn’t fit the emission spectra of _____________________. elements other than H -According to classical physics, if Bohr’s planetary atomic model were true, the electron would lose energy as it orbits and spiral into the nucleus, resulting in ____________… UV death… -Also… Bohr had no explanation for WHY _____electrons had quantized energy…. - quantized energy levels But… his idea of ______________________ was VERY IMPORTANT UV DEATH!!!!! Quick review of Bohr: THE MODEL THE ENERGY DIAGRAM FOR H (quantized energy levels) EVIDENCE #1: Emission spectra of OTHER ELEMENTS! E.g. Argon/Neon Spectral Tubes MORE EMISSIONS IN THE VISIBLE RANGE THAN ACCOUNTED FOR BY BOHR’S ENERGY DIAGRAM! •Excited in an electrical discharge •Spectrum: DISCRETE bands of color •Spectrum: DISCRETE bands of orange, yellow and green SPECTRAL TUBE USE OF DIFFRACTION GRATING/ PRISM Line Spectra of Other MORE EMISSIONS THE Elements VISIBLE Every element has itIN own RANGE THAN(DIFFERENT) ACCOUNTEDpattern FOR BYof characteristic BOHR’S ENERGY electron energy levels.DIAGRAM! Therefore, each element emits is own characteristic (DIFFERENT) pattern of light frequencies. Excited Gases & Atomic Structure EVIDENCE #2: Photoelectric effect Every metal has a e e e DIFFERENT Threshold Energy! radiation Surface of metal Observed with METALS; the basis for Solar Energy. If the Ephoton is equal to or greater than the Ethreshold for metal , then an e- is ejected (electrical current!) Before we continue… a quick review!!! • What is the piece of evidence that made it necessary to come up with a new quantum model of the atom? The atomic emission spectra of elements OTHER THAN HYDROGEN. • What does a diffraction grating or prism do? It splits light up into its component parts. • How is the atomic emission spectra for elements different from the atomic emission spectrum for white light/ sunlight? The elements have spectra that have discreet bands of colored light; sunlight has a spectra that is continuous. Before we continue… a quick review!!! • With what type of elements is the photoelectric effect observed? It is observed with metals • What is the photelectric effect? It is the observation when LIGHT that has an energy equal or greater to a certain threshold energy shines on a metal, electrical current is produced. If it doesn’t have enough energy, no current is produced. Ideas that led to the Quantum Mechanical Model 1920’s 1. Louis de Broglie (electron has wave properties, “Wave-Particle Duality of Matter”) 2. Werner Heisenberg (“Uncertainty Principle”) 3. Erwin Schrodinger (mathematical equations using probability, quantum numbers quantitatively describe electron as a wave “Schrodinger’s wavefunctions”) Hullo! Louis de Broglie Ideas Wave-mechanical model : 1. DeBroglie’s wave-particle duality for matter (1923) • states that all matter has ____________properties…. wave-like especially when particles are very small and very electrons fast….. like ____________ • thought of the electrons as __________________ standing waves Why standing waves? • Because standing waves are quantized too… You see this: but not this: De Broglie wavelength •Since light waves have a particle behavior (as shown by Einstein in the Photoelectric Effect), then particles could have a wave behavior. De Broglie wavelength (in m) l= h mv Mass (in kg) Planck’s Constant 6.626 x 10-34 J*s Velocity (in m/s) Example: • Determine the de Broglie wavelength for an electron moving at a speed of 9. x 106m/s. (me= 9.1 x 10 -31 kg) Remember h=6.7 x 10-34 JS Answer: 8.18 x 10 -11 m Werner Heisenberg Ideas Wave-mechanical model : 2. Heisenberg’s Uncertainty Principle • states that you cannot precisely know the Position, x and the _________ Velocity, v of any particle __________ simultaneously…. as you determine one, it’s harder to determine the other • THEREFORE, any accurate atomic model must deal with ______________ probability Erwin Schrodinger Ideas Wave-mechanical model: 3. Schrodinger’s Wavefunctions, 1925 • came up with mathematical functions called wavefunctions, Ψ(r) to describe the electrons as ____________________ waves rather than particles…. • FINALLY!!!! something mathematical that could be used probability (although if to calculate an electron’s _____________ we’re talking about waves, it might be better to think of intensity it as an electron’s _____________. radial wavefunctions, Ψ(r) -describe an electron as a wave radial probability plots, [Ψ(r)]2 Probability Curve for Hydrogen When the probability plots are graphed…. • Instead of rings, you get orbitals…. of space where most of • ORBITALS: regions ____________________________ the electron’s wave is found (A region in space _______________________________________ in which there is high probability of finding an _______________________________________ electron.)… There are 4 major types. _______________________________________ NOTICE! Energy is still quantized—but there are no more rings! aka “Electron Cloud” The electron cloud represents positions where there is probability of finding an electron. The higher the electron density, the higher the probability that an electron may be found in The Electron Cloud for a Sodium ion that region. The Orbital (aka “Electron Cloud”) for Hydrogen 90% probability of finding the electron within this space examples of “s” orbitals “spherical” three “p” orbitals “dumbbell shaped” http://www.rmutphysics.com/CHARUD/scibook/crystal-structure/porbital.gif five “d” orbitals “clovershaped” seven “f” orbitals “multi-lobed” W-M model structure ORBITALS – a region of space where there is a high probability of finding an electron (of a certain energy). Each orbital can hold 2 electrons MAX. (4 shapes you need to know – s, p, d, f) SUBSHELLS – all orbitals with the SAME SHAPE in a particular shell (distance of the orbital’s outer edge from the nucleus) SHELLS/ ENERGY LEVELS “n” – all subshells of a given size (distance from the nucleus) – the MAXIMUM number of electrons in a shell is 2n2 Schrodinger’s Quantum Wave-mechanical model • Mathematically generated by thinking of the electron as a wave and location as wave intensity or probability • Electrons have signs, nodes where they change signs because electron position or amplitude has sign… Wave-mechanical vs. Bohr 1. Electrons are located in specific energy levels. To go from one level to another, the exact different (aka “quantum”) must be absorbed or emitted (similar to Bohr). 2. There is no exact path around the nucleus. (different from Bohr) 3. The model estimates the probability of finding an electron in a certain region of space. (different from Bohr) Energy level diagram aka ATOMIC ORBITAL _________________ DIAGRAM _________________ _________________ -each _______ dash represents an orbital -each level is a ________ of orbitals subshell with a particular energy RULES: PRINCIPLE 1. AUFBAU _________________—electrons fill in lower energy levels FIRST. EXCLUSION PRINCIPLE 2. PAULI _________________________—an orbital can hold only 2 electrons, and they must have opposite spins. No 2 electron in an atom can share the same set of four quantum numbers. __ HUND’S RULE 3. _______________—in a set of SAME ENERGY degenerate (___________)orbitals, the electrons will fill the orbitals in a way that would give the maximum number of parallel spins. One electron has to go in each degenerate orbital before e-’s pair up __ __ __ not __ __ __ Blocks in the Periodic Table Orbital Diagram/ Notation for Carbon Orbital Notation (ON) • Another word for “Atomic Orbital Diagram,” shows the electrons in their orbitals, from low to high energy Carbon: 1s __ 2s__ 2p __ __ __ Electron Configuration (ECN) • An quicker way of describing the atomic orbital diagram Carbon: 1s22s22p2 (the superscripts add up to the number of electrons in an atom) Info given by ON or ECN • The energy of the electrons in an atom or ion • The probable location (orbital) of the electrons in an atom or ion Important Terms • “VALENCE” electrons – electrons farthest away from the nucleus (highest shell) • “CORE” or “KERNEL” electrons – electrons closer to the nucleus (lower shells) Important Terms • “PARAMAGNETIC” ECN or ON -having unpaired electrons, responds to a magnetic field (paramagnetic substances tend to be colorful) • “DIAMAGNETIC” ECN or ON -having only paired electrons, does NOT respond to a magnetic field (diamagnetic substances tend to be white/ clear) What you need to know about the wave-mechanical model (NOW): • what a wave function is (in general) and how its square gives the probability density plot • what an orbital is (as opposed to Bohr’s orbits/ rings) • names, shapes, and number of 4 orbital types • how to fill in atomic orbital diagrams… • Next…. Electron configurations Abbreviated/ Noble Gas Shorthand ECN or ON 1. Find the noble gas BEFORE the element and put it in [ ]. This represents most (or sometimes all) of the “CORE” electrons 2. Continue the ECN or ON from the noble gas. Ex. Mg 1s2 2s2 2p6 3s2 Shorthand: [Ne] 3s2 SPECIAL ECNs & ONs • If an element has 1 less e- than a HALF or FULL “d” or “f” SUBSHELL, 1 e- is taken from the valence “s” and placed in the “d” or “f” to make it half or fully filled • There is special stability from half or fully filled “d” or “f” subshells…. THE ECN or ON of CATIONS • Only METALS form CATIONS • CATIONS – remove electron(s) from the highest shell first (preferably the highest energy subshells first) – electrons are NOT removed from the core! Ex. Mg+2 (remove 2 electrons) Mg : 1s2 2s2 2p6 3s2 Mg+2 : 1s2 2s2 2p6 Ex. Pb+4 (remove 4 electrons) Pb: [Xe] 6s2 4f14 5d10 6p2 Pb+4 : [Xe] 4f14 5d10 THE ECN or ON of ANIONS • ONLY NONMETALS FORM ANIONS • ANIONS – add electron(s) Ex. N-3 (add 3 electrons) N: 1s2 2s2 2p3 N-3 : 1s2 2s2 2p6 Important Terms • “ISOELECTRONIC” -having the same electron configuration as another atom or ion -3 E.G. N is “isoelectronic” with -2 O and with Ne. Four Quantum Numbers Influence the orbital defined by a particular wavefunction Describe ONE particular electron 1. Principal Quantum Number 2. Orbital Quantum Number 3. Magnetic Quantum Number 4. Spin Quantum Number Principal Quantum Number, n • Indicates main energy levels n = 1, 2, 3, 4… • Each main energy level has “n” possible sublevels/ subshells Ex. The 1st energy level has 1 possible subshell (s) The 2nd energy level has 2 possible subhells (s,p) The 3rd energy level has 3 possible subshells (s, p, d) Orbital Quantum Number, ℓ (Angular Momentum Quantum Number) • Indicates shape of orbital sublevels • ℓ can equal integers {0 n-1} ℓ sublevel #orbitals #electrons 0 s 1 2 1 p 3 6 2 d 5 10 3 f 7 14 Magnetic Quantum Number, ml • Indicates the orientation of the orbital in space. • ml can equal integers { - ℓ + ℓ} • The number of values represents the number of orbitals. Ex. If ℓ = 2, then we are looking at a “d” subshell ml = {-2,-1,0,1,2} = 5 values so 5 different orientations or orbitals for the “d” subshell Electron Spin Quantum Number, (ms or s) • Indicates the spin of the electron (clockwise or counterclockwise). • Values of ms: +1/2, -1/2 (spin up or spin down, respectively) Example: • List the values of the four quantum numbers for electrons in the 3d sublevel. • Answer: n=3 l=2 ml = -2,-1, 0, +1, +2 ms = +1/2, -1/2 for each pair of electrons