Quantum Theory Structure of an atom What we are going to learn this chapter Properties of waves and electromagnetism Bohr’s theory of a hydrogen atom and its relation to emission lines Debroglie wavelengths Quantum numbers Electron distribution Electron configurations Many important theories and principles Plank’s quantum theory Einstein’s photoelectric effect Heisenberg uncertainty principle Schrodinger wave equation The Birth of Quantum Mechanics Before 1900 atoms and molecules were regarded as rebounding balls. This is the basis of theories such as the ideal gas law and works well to describe macroscopic phenomena After 1900 Max Planck (nobel prize 1918) discovered that atoms or molecules only emit energy in discrete levels or “quanta” Energy was NOT continuous and this turned physics upside down. We have no right to assume that any physical laws exist, or if they have existed up to now, that will continue to exist in a similar manner in the future. -Max Planck Development of Atomic Models Thomson: The plum pudding model postively charged jellylike blob, with suspended electrons Rutherford: nuclear model all positive charge in the nucleus negative charge surrounding it: Bohr model: expansion of Rutherford’s ideas. Electromagnetic radiation Electromagnetic radiation is a form of energy. That has wavelike properties. Heat microwaves xrays What Else? sunlight Properties of Waves Examples of Transverse Waves Examples of Longitudinal Waves Transverse waves- Frequency Frequency (ν) (pronounced nu) is equal to the _______________________________________ In equation form ν=c/λ Units of ν is _____________(pronounced ______) Units of λ is distance, visible light is around nm (nanometers) Electromagnetic Waves Electromagnetic waves have and electric component and a magnetic component Two components have same wavelength and frequency, in perpendicular planes http://hyperphysics.phy-astr.gsu.edu/ Be sure you can identify: Amplitude Wavelength (λ) Frequency Travel at 2.9989x108m/s (the speed of light c) Electromagnetic Spectrum As wavelength increases what happens to frequency? does it: A) Increase B) Decrease Decrease Answer the Following: Which has greater frequency red light or blue light? Which has greater energy? Blue Blue Does blue light have greater speed than red light? NO! all have same speed Example Exercise The wavelength of green light from a traffic signal is centered at 522 nm. What is the frequency of this radiation. Known: c= 3.00x108m/s λ=522 nm ν=c/λ Then fill into equation First convert λ to meters Fix sig figs and check for units Another Example The frequency of radiation from your microwave is 120 GHz. Find the wavelength of the microwaves. Similar at home exercise: The wavelength of radiation when you get an xray is 10.0 nm. Find the wavelength of the xrays. In Class Quiz The frequency of red light from a traffic signal is centered at 4.11x1014Hz. What is the wavelength of this radiation? A) 1.37x106 m B) 1.37x106 nm C) 730 nm D) 7.30x10-7nm Planck’s Quantum Theory When solids are heated they emit __________ Attempts to explain this up until Plank failed at either very high or low wavelengths. Planck discovered molecules can only emit light at specialized energies or “_________” A “__________” is the smallest quantity of energy and is equal to: h=6.626x10-34 J*s Example Exercise What is the energy of green traffic light in the previous example. (λ=522nm) Known: c= 3.00x10-8m/s λ=522 nm=5.22x10-7m Another Example The frequency of radiation from your microwave is 120 GHz. Find the energy of the microwaves. To do at home: The wavelength of red light from a traffic signal is centered at 730 nm. What is the energy of this radiation. The frequency of radiation of an xray is 3x1016 Hz. Find the energy of the xrays. Black Body Radiation Blackbody radiation depends only on temperature of object Given this information about a light bulb, why are incandescent bulbs inefficient light sources? 2700-3300K Example Exercise What is the wavelength of the brightest part of the light from our next closest star, Proxima Centauri? Proxima Centauri is a red dwarf star about 4.2 light years away from us with an average surface temperature of 3,042 Kelvin. Light: A wave or a particle. Wave Both ~300B.C Aristotle ~1600 A.D. R. Descartes ~400B.C ~1000 A.D. Democritus Alhazen ~1700 A.D. Robert Hooke ~1700 A.D. Sir Isaac Newton ~1800 A.D. Thomas Young ~1700 A.D. C. Huygens Albert Einstein ~1900 Particle Photoelectric Effect Ejection of _________ from the surface of a metal or other material when shines on it. Energy of _______________must be higher than “_______” energy or no photon will be ejected. This ________________is called the “________________” Ex: Violet light can eject electrons from potassium, but red light can’t. Use E=hν to determine threshold frequency. Shows _______________________ http://phet.colorado.edu/en/simulation/photoelectric Photoelectric Effect What do you think happens if the intensity of light is increased but the frequency of the electrons stay the same? If the photon is exactly the energy of the work function the electrons will be knocked loose If the energy of the photon is higher the electrons will acquire _________________________ _________________________ Photoelectric effect example problem The work function for calcium is 4.34x10-19 J. What is the minimum frequency of light for the photoelectric effect for calcium. Then calculate the kinetic energy of the ejected electron if the light of frequency 1.00x1015 s-1 is used for irradiating the metal. Photoelectric Effect: A second look at the equation Ek=hν - Φ y= mx + b Before threshold frequency ___________________is present After threshold frequency the relationship is _____________ Photo Electric Effect Extra Notes: Rephrasing of what I said just for you The idea here is that given one photon you are transferring that energy into the electrons in the metal. If you put exactly the amount of energy in it needed to eject an electron (aka the work function, aka Φ or W) then there is no energy left over for it to move (aka have kinetic energy) However if the photon has more energy than the work function, it transfers that in the form of movement (aka kinetic energy) You Try Similar at home Exercise: You Try: The work function for magnesium is 5.9x10-19J. Calculate the minimum frequency of light required to eject electrons from magnesium. Then calculate the kinetic energy of the ejected electron if the light of frequency 1.00x1015 s-1 is used for irradiating the metal Wave Interference Constructive Waves with same phase interfere ________________ They ______ Waves with different phase interfere ________________ They _________ Destructive Double Split Experiment: Young Wave or Particle? Summary: Experiments show it has properties of both. Photo electric effect: Particle like Double split experiment wavelike This is true of very small matter Largest so far to have measurable wave-like properties is those with mass 1610 amu DeBroglie Wavelength: Describing matter as a wave. De Broglie expanded wave particle duality from light to matter. Here is equal to the velocity of the particle, not the frequency. Often you’ll find the velocity using the kinetic energy. Example Problems: DeBroglie Wavelength Find the DeBroglie wavelength of an electron with a K.E. of 2.56x1027J. Why can’t we see the waves of macroscopic matter? (hint :A baseball weights 0.145kg and it moves around 27 m/s.) Heisenberg Uncertainty Principle It is impossible to know simultaneously both the momentum (p) and the position (x) of a particle with certainty. The uncertainty values are related by: (momentum=mass*velocity) If your uncertainty of momentum decreases your measurements of position will _______________ and vice versa. What happens to the uncertainty in position if your uncertainty in velocity decreases? Heisenburg Uncertainty Principle Examples: You are pulled over by a police officer for speeding, and try to escape a ticket by claiming if he knew where you are, he can’t possibly know how fast you were going. The officer says, “well, I knew where you were within 0.5 m, your car probably weighs around 1300kg, so I know your velocity within…….” Wavefunctions, Energy levels, and particles in a box Ψ Is the “______________” Describes the __________________. Its just a symbol for a mathematical function Different particles have different wavefunctions Ψ2 is the “_______________” The probability of finding the ________________________ Technically “__________________” probability of finding a particle divided by the volume. Wavefunctions, Energy levels, and particles in a box Some questions for you. Ψ is a function, so at any point can we absolutely determine the sign. Is itAlways Positive Always Negative Can be both Ψ2 Is the square of that function so can we absolutely determine the sign. Is itAlways Positive Always Negative Can be both Nodes A node occurs when Ψ is _____ When this happens, what is Ψ2 equal to? __________ So what is the probability that the electron is at a node? _____________ Number of nodes is equal to n-1 Um….what was that again:An example. Lets take an example where Ψ is a number (to make it simple). We’ll say 0.44cm-3 So then Ψ2=0.20cm-3. Ψ So the wavefunction is equal to 0.44cm-3 Ψ2 and the probability density is equal to 0.20cm-3 . What is the probability of finding the particle within 3cm3? 0.2cm-3 * 3cm3=0.6 or 60% 0cm3 3cm3 X Schrödinger Equation The “hat” on the H indicates it’s an ____________. Can use to find _________________ We will use the results of this, not the actual equation. Particle in a Box. Set up: A single particle is in a box. Only certain ______________ are allowed. Energy is “__________” Real life relation: String anchored at two points. Particle in a Box: Solutions Solution to Shrodinger equation: L is the ______________. n is the _______________ it is an integer. Particle in a Box Example: Use the solutions to the Schrödinger equation for a particle in a box to estimate the value of the wavelength of an electron in a helium atom given that the approximate radius of a helium atom is 100. pm. Bohr model of the atom Before this arose they knew there were electrons traveling around a proton filled nucleus. Laws of physics said electrons should spiral into nucleus. Bohr said energy levels are ________________ Only works for _____________ Energy difference is given by: Rh=2.18x10-18J n= 1,2,3…… “_________________________”. Energy levels Z=atomic number A Hydrogen Atom Two different ways of thinking about it. Rydberg equation Was discovered by analyzing line spectra Schrodinger equation Solving the particle in a box problem in three dimensions Same results from either equation. Rydberg’s was determined first, then Shrodinger’s results agreed. Also true for “hydrogen-like” atoms. 1 electron atoms. We’ll start with Schrödinger Results from solving the Shrodinger equation for the hydrogen atom Z is the atomic number me is the mass of an electron e is the charge of an electron or proton h is Planks constant r is atomic radius Agrees with experimental results Stair and Ball Analogy Bohr Model Energy Levels The energy of a given energy level is given as: • So the difference in energy is Rydberg Equation If the energy of a given energy level is defined as En=-Rh(1/n2). We can find the difference in energy shells by Enf-Eni Change= __________________ __________________________ Filling the above equations into Change= Final-initial …and finally rearranging Either of these are often shown in text books. Use whichever you prefer but be sure not to mix them up. One has a negative one does not. Rydberg's constant is experimental value Sign Conventions for Energy: *common error causes* A free electron has ΔE= ΔE is + Energy of levels are negative, most negative and therefore lowest energy is n=1 ΔE is positive if going from ___________ energy shell i.e. ground state to anything, 25 ect… Words such as “photon absorbed” will be used. ΔE is negative if going from _____________ i.e. anything to ground state, 52 ect… Words such as “photon emitted” will be used. E=hν=hc/λ This energy is the energy of __________________. This must always be ______________! ΔE is - Example Problems Rydberg Equation A photon that is emitted when a hydrogen undergoes a transition to n=2 is of the frequency 6.17x1014 s-1. Find the initial energy level. What is the wavelength of a photon emitted during a transition from the n=5 to n=2 state in a hydrogen atom? Lasers Light Amplification by Stimulated Emission of Radiation. http://www.infoplease.com/images/ESCI112LASERS003.gif Example Problem Rydberg Equation A monochromatic beam of light with a total energy of 2.5J contains 8.56x10-4 mols of photons. What is the wavelength of the beam. Emission Series Emission Series: Another Look (Hydrogen) What do we use Emission Spectra for? Emission Spectra is unique to individual elements Spectra can be collected and matched to known emission spectra to determine the element present. Flame tests Hydrogen Emission Spectra Fe Emission Spectra Flame test Emission/Absorption Spectra Lines in visible region shown above (Hydrogen shown) Also some occur in other spectral regions and aren’t seen without detectors Emission Spectra: Applications in Astronomy •Spectra is collected •Compared to known ions •Temperatures known Time to regress to our 5 yr old selves Why is the grass green? Why is the sky blue? Why is the sun yellow? The grass is green because… What happens if you shine green light on the plants? What happens if you shine red light on the plants? Why is the Sky Blue? Previous Slide Lecture Summary Long wavelength Red and orange light travels relatively unperturbed through the atmosphere. Shorter wavelengths get scattered turning the sky blue. As it travels farther much of the blue light interferes with each other cancelling each other out and making the sky paler. During sunset the light has to travel so far through the atmosphere that most of the blue light is completely scattered and interfered away. Leaving only the reds/oranges and yellows to reach your eyes. Other Transitions Schrodinger Equation Eψ=Hψ Ψ is the “__________”- complex function of space and time. Describes particle. Ψ ____________________ |Ψ2| is the “_____________________” These probability densities make up “____________” which describe ______________________________________________. Technically this is only good for one electron atoms but there are good approximations for many electron systems. Atomic Orbitals Exact solutions to the Schrödinger equation for hydrogen like atoms Approximate solutions to the Schrodinger equation for atoms with more than one electron. Shows where the ______________________________. Technically extend to infinity, normally drawn where there is a 90% probability of finding the electron Atomic Orbitals Wavefunctions s 1s 2s px 1p py 3s pz 3p dxy 3d dyz dzx dx2-y2 dy2 You don’t need to know these wavefunction equations, won’t need to use them. Just FYI so you know what they look like. Quantum Numbers Describes the distribution of electrons. The combination of them all specifies the wavefunction. You can think of it as an address to an electron Analogy: Finding Person on Campus Building number 403 Room number 1100 Row F Chair 1 Male or Female Quantum numbers n l ml ms Quantum Number- Principle Quantum Number ______________________- “n” Can have any positive integer. We saw this in the ____________ as the energy levels. 1,2,3….∞ Quantum Number- Angular Momentum Quantum Number Angular Momentum Quantum Number- “l” Distinguishes the orbitals of different shape. Values have letters associated with them. 0=s, 1=p, 2=d, 3=f, 4=g,…….. These are associated with the atomic orbitals we just discussed. Can be any integer from 0 to n-1. n 1 2 3 4 allowed values of l Question: For the 4th energy shell, what are the orbitals present? Quantum Numbers- Magnetic Quantum Number Magnetic Quantum number- “ml” (read as m sub l) Distinguishes orbitals that have same n and l (same energy and shape) but having a different orientation. Allowed values are from –l…0…l Table of Allowed Values for 1-4 energy levels n 1 2 3 4 l ml Lets fill in the numbers for the n=3 energy level. Quantum numbers s l=0 ml=0 p l=1 ml= -1 0 1 l=2 ml= 2 -1 0 1 2 d ***The quantum numbers ml here doesn’t necessarily relate to the exact orbital its under, don’t worry about memorizing which goes where. Wavefunctions s 1s 2s px 1p py 3s pz 3p dxy 3d dyz dzx dx2-y2 dy2 You don’t need to know these wavefunctions equations, won’t need to use them. Just FYI so you know what they look like. Quantum numbers- spin quantum number Spin quantum number- “ms” (read this as m sub s) Distinguishes spin axis of electron. (also shown as spin up or spin down on diagrams) Allowed values for each orbital are +1/2 or -1/2. Question- How many electrons are allowed per individual orbital? State whether each of the sets of quantum numbers is permissible for an electron, if not explain why. Example 1: n=1, l=1, ml=0, ms=+1/2 Example 2: n=3, l=1, ml=-2, ms=-1/2 Example 3: n=2, l=1, ml=0, ms=+1 Example 4: n=3, l=2, ml=-2, ms=-1/2 Shielding and Penetration Orbitals with radial probability closer to the nucleus are more penetrating. The closer, more penetrating orbitals are shielding the further orbitals from the nucleus. Energies of Orbitals Hydrogen Everything other than Hydrogen Ect….to infinity Ect….to infinity E Questions: What is the difference between the two? Why do you think hydrogen is different? Here I have draw hydrogen with atomic orbitals higher than 1. Is this correct? Why or why not? Energies in Relation to Periodic Table Electron Configuration Pauli Exclusion Principle states that no two electrons can have all four quantum numbers be the same. Fill in electrons in order of energy levels. Each orbital holds 2 electrons. Right Diagram for Carbon Hund’s rule- Fill across degenerate energy levels before filling orbital. Write electron configuration as follows: 1s22s22p2 Example: Write electron configuration for Cobalt Diamagnetism vs Paramagnetism ______________ has unpaired electrons Carbon Drawn Toward magnets _____________ has paired electrons. Slightly Repelled by magnets Neon Electron configurations of ions Simply add or subtract electrons based on the charge of the ion Example: Ca to Ca2+ Ca 1s22s22p63s23p64s2 or ___________ Electron configurations of ions Simply add or subtract electrons based on the charge of the ion Example:Ca to Ca2+ Ca2+ 1s22s22p63s23p6 or ________________ _________________ Electron configurations of ions Simply add or subtract electrons based on the charge of the ion Example:Cl to Cl1- Cl 1s22s22p63s23p5 or [Ne] 3s23p5 _________________ Electron configurations of ions Simply add or subtract electrons based on the charge of the ion Example:Cl to Cl1- Cl- _________________ Electron Configurations Exceptions Half filled and full filled orbitals are more stable. To get d orbitals to this stability promote electrons from s orbitals When valence d orbitals have electrons and you need to make an positive ion, remove from valence s orbitals first. Fs also have a bunch of exceptions, don’t worry about these. If I ask for an electron configuration from the F block, just follow the rules Question: Why can we be so fluid with our exchange of electrons from the s and d orbitals? Electron configurations of ions Simply add or subtract electrons based on the charge of the ion Example: Co to Co2+ Co 1s22s22p63s23p64s23d7 or ____________ Take away two electrons Where are we taking them from? Electron configurations of ions add or subtract electrons based on the charge of the ion Example: Co to Co2+ Co2+ 1s22s22p63s23p63d7 or [Ar] 3d7 Take away two electrons _________________ Electron configurations of ions Example:Cr to Cr1+ Electron configuration of neutral chromium requires promotion of electron Cr To give stable half shell Electron configurations of ions Example:Cr to Cr1+ Electron configuration of neutral chromium requires promotion of electron to give stable half shell Cr 1s22s22p63s23p64s13d5 or _____________ Then take away electron from 4s shell Electron configurations of ions Example:Cr to Cr1+ Electron configuration of neutral chromium requires promotion of electron to give stable half shell Cr1+ 1s22s22p63s23p63d5 or _____________ Then take away electron from 4s shell You Try Use what we just learned about Chromium to write the electron configuration of Cu and Cu1+. Electron configurations of ions Example:Cu to Cu1+ Electron configuration of neutral copper requires promotion of electron to give stable full shell Cu Then take away electron from 4s shell Electron configurations of ions Example:Cu to Cu1+ Electron configuration of neutral copper requires promotion of electron to give stable half shell Cu1+ Then take away electron from 4s shell Discussion Question Using the logic we just worked out why do Cr, Mo, W, Cu, Ag and Au all form +1 ions? Switching Gears….. Periodic Trends Atomic Radius Ionic Radius Ionization Energy Electron Affinity What we are going to learn! Some history about the periodic table development Trends: using the periodic table to predict Ionization energy, electron affinity, atomic radius, effective nuclear charge and electro negativity. Instead of 1.21, directly, we’ll just talk about some interesting elements. Development of the Periodic Table Electronegativity Electronegativity Effective Nuclear Charge Effective Nuclear Charge Increases __________________ Vertical Trend doesn’t make a lot of sense to discuss here so we will ignore it Nuclear charge felt by an electron when both the actual _____________________and the _______________ of other electrons are taken into account. Core electrons shield the ______________. Reason behind many of the other trends! Atomic Radius Increases down a group Increasing amount of ___________ increases size. Increases right to left across a period Due to ________________________________, holds electrons closer Examples Rank the following in order of increasing radius Li, C, F Li, K, Rb Ba, Se, F Would you be asked to rank, Be, Al, Ge? Or similar? Ionic Radius Cations are smaller More positive is smaller. _____ is smaller than ______ Anions are bigger More negative is bigger. _____is larger than ______ Higher effective nuclear charge when electrons are removed, lower when electrons are added. Example: S2-, Draw an arrow from the smallest to largest species in the following isolectronic series Cl-, Ar, K+, Ca2+ First: what is this “isoelectronic” word iso=_________ electronic: sounds sort of like electron so…… isoelectronic= ___________________ More examples Rank the following in order from smallest to largest: Li+, Be2+, F- Cu+, Cu2+, K+ Cl-, F-, Br- and another: Given the following pictures of ionic compounds match the pictures with the ions: Na+, Mg2+, Cl-, O2- Pink Purple Blue Green First Ionization Energy Minimum energy required to remove an electron from its ground state General Trends with exceptions Exceptions come from getting half and fully filled subshells: You need to know these! What is the electron configuration of Be, B, N, O? Use this to explain the higher ionization energy. F N Cl O Be C P Mg B S Al Be: N: B: O: Examples: Rank the following in order from lowest to highest first ionization energy. First some normal ones He, Ne, Ar Now some exceptions: Li, Be, B C, N, O B, Li, Ne Second and Third Ionization Energy First is always the _________. 2nd 1st 3rd Nuclear charge** doesn’t change, so each electron feels more of a positive pull. **Notice this says nuclear charge, not effective nuclear charge e eg. Electron Affinity Cl + e Cl Electron Affinity General trends, but has a fair amount of exceptions Lets look at some values Positive electron affinities means its exothermic Electron Affinity Why do group 2A (alkaline earth) an 7A (halogens) form stable atomic anions? (aka -1 ions) High effective nuclear charge means ______________. One more electron fills the shell, this adds __________ F: F-: Na: Na-: Filled sub-shells are stable. Why do the noble gasses and not form stable atomic anions? Ne: 1s22s22p6 Already has a filled shell. Already stable, adding an electron isn’t energetically favor. N: 1s22s22p3 Have a filled half shell, adding another electron causes ______________________________. Electronegativity (Chapter 2.12) Ability of an atom to attract electrons _______________________________________________ Not as many important exceptions, mostly involving the d block. We won’t worry about them. Why aren’t there as many exceptions with these? Electronegativity and Electron affinity O atoms are electronegative Same general trend Both involve ability of an atom to _______________ CO2 Electronegativity is that ability while _________, attracts shared ______________ e- Electron affinity is that ability of an _______________. eg. Cl + e- high electron affinity Cl- Inert Pair Effect Tendency of heavier atoms to form ions with a difference in charge of two. Use electron configurations to explain. Sb Sb: Sb3+: Sb5+: Pb Pb: Pb2+: Pb4+: Do the rest at home for practice! Diagonal Relationship Diagonal bands going down and right have similar properties. Look at radii and ionization energies and explain. General Trends in Chemical Properties Understand why the groups in general form certain ions. Understand why trends occur including reactivity in section 1.21 What follows is a smatterering of interesting aspects of elements I think is pertinent to real life. Silicone as a basis for life? Smallest element with same valence electron structure as carbon Many similar properties to carbon Probably not as likely as SciFi makes it out to be Doesn’t bind with as many atoms Doesn’t make double or triple bonds, severely limiting chemistry Si chains with H are unstable in water. Si chains with O are more stable, but still not as stable as carbon. Noble Gases He: refrigerant for super conducting magnets like in MRIs: used in scuba diving and blimbs. Many uses where you need an “inert” atmosphere, chemistry, lightbulbs, storage ect….. “Neon” lights, which are really many elements. Interesting tidbit: Argon means “the lazy one” in greek. He Ne Ar Kr Xe
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