Chem 101 Chapter 3: Quantum Mechanics
Chem 101 Chapter 3: Quantum Mechanics CH 101
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This 6 page Class Notes was uploaded by Rebecca de la O on Wednesday September 14, 2016. The Class Notes belongs to CH 101 at University of Alabama - Tuscaloosa taught by Jared Allred in Fall 2016. Since its upload, it has received 12 views.
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Date Created: 09/14/16
Chapter 3 Quantum Mechanics - Quantum mechanics is the physics of subatomic particles (electrons) - Electrons determine the behavior of atoms - Electrons have a wave and particle duality (meaning it displays both those properties) o So does light Light - Light is a form of electromagnetic radiation o Composed of perpendicular oscillating waves (one for the electric field and one for the magnetic field) o The electric field region is where electrically charged particles experience a force o The magnetic field region is where magnetized particles experience a force Waves - a wave is any kind of disturbance or oscillation that travels through matter or space - all waves travel at the same speed in a vacuum - Parts of wave: o Crests – the maximum point/value o Nodes – wherever the point is 0 and changes sign (+ or -) o Trough – lowest point/value o Wavelength – distance between adjacent crests or troughs (typical unit: nm = 1 x 10 m) o Frequency – number of cycles over a period of time - Frequency vs wavelength – they are inversely proportional – o Greater frequency means shorter wavelength and vice versa - Velocity of a wave = frequency x wavelength - Waves experience interference when they interact - If the amplitude of the interacting waves is the same, one of the following can happen: o Constructive interference - waves create a larger wave/amplitude when they interact if they are in phase (crests and trough align with each other) o Destructive interference – waves cancel out when they interact if they are out of phase (crests lines up with the trough of the other wave and vice versa) Electromagnetic spectrum Highest - Radio waves waveleng o Ex. cell phones, AM/FM radio stations th o Frequency is about 10 Hertz - Microwaves Lowest frequenc o Work by rotating molecules in the food to create kinetic and thermal energy y - Infrared radiation o Makes heat visible - Visible region o This is where light is o Intensity (brightness) = amplitude o Wavelengths range from 400 nm to 700 nm o Shorter wave length Violet Blue Green Yellow Orange Red longer Lowest wave length waveleng o We see the light that is reflected, not absorbed, by compounds th - Ultraviolet rays o Sun Highest o Have enough energy to damage biological cells frequenc - X ray y - Gamma rays The Photoelectric Effect - The production of electrons when light is shone onto a material - Classic theory says energy emitted increases with frequency and amplitude but this is wrong! o Intensity doesn’t change threshold (frequency at which electrons are emitted) o Frequency doesn’t affect current except at threshold - The electrons are emitted immediately - no time lag - Increasing the intensity of the light increased the number of photoelectrons, but not their maximum kinetic energy - Red light (low frequency and long wavelength) will not cause the ejection of electrons, no matter what the intensity - Violet light (high frequency and short wavelengths) will eject electrons, even with low intensity Einstein’s Quantum-ish Theory - Electrons are excited in single events by a light particle (photon) - Electrons have a binding energy Φ - Each particle of light carries a discrete amount of energy that depends on frequency not amplitude - Amplitude = number of photons - Kinetic energy of the electron = energy of the photon – binding energy (E = e- hv – Φ) o H = Planck’s constant = 6.626 x 10 -34J/s o v = frequency = energy of the photon Electron diffraction - Waves bend, or diffract, when they encounter an obstacle - When a wave passes through a small opening, it spreads out - If the wave passes through two slits, the resulting waves that spread out on the other end interfere o The interference is caused by each electron interfering itself! Louis de Broglie - Proposed that electrons not only act as particles, but also as waves - An electrons wavelength is related to its kinetic energy (the faster it moves, the higher its energy and the shorter its wavelength h - de Broglie’s relation: = h = Planck’s constant, m = mass, and v = mv velocity (not frequency!) Wave Particle Duality - all particles have wave like properties - an electron, neutron, proton, element all have a wavelength when moving How do we talk about waves? - With quantum mechanics Bohr’s Model - Explained atomic spectra (the spectrum of frequencies of electromagnetic radiation emitted or absorbed during transitions of electrons between energy levels within an atom) - Electrons have a wavelength that needs to be equal to the circumference Erwin Schrodinger - Electrons are like waves - Equation: HΨ = EΨ H= Hamiltonian constant E= energy Ψ= wave function o Solving the equation tells you the structure of the atom o This is where orbitals come from Hydrogen Atom Example - There are an infinite number of wave functions for the hydrogen atom - Categorize by shape: Ψ = s orbital Ψ= p orbital Ψ= d orbital - The gray represents the probability distribution of the electrons and are given by Ψ - Each wave function has 4 numbers associated with it called quantum numbers (n, l, m, l ) s o n (“shell”) = principal quantum number; always a positive integer (0<1); only determines the energy of the wave function (all with the same have the same energy) Higher energy −R H E = n2 RH= Rydberg constant for hydrogen (2.18) Lower energy 1 ∆E = R (H 2 - Energy difference gets smaller with increasing n n final The greater difference results in an emitted photon of greater 1 energy and therefore shorter wavelength 2¿ Transitions between orbitals that are further apart produce light that is higher in energy and therefore shorter in wavelength If electrons move to a higher n, the electrons absorb a photon and is excited to a higher energy (electron gains energy- endothermic) If electrons move to a lower n, light is emitted (electrons lose energy– exothermic) Lower energy is more stable; things want to be in a lower state of energy o l (“subshell”) = angular momentum quantum number; l can be equal to or higher than 0 but must be smaller than n; # of l depends on n Ex. If n=1 then l= 0 If n=2 then l=1 or 0 If n= 3 then l = 2 or 1 or 0 o m l“orbital”) = magnetic quantum number; an integer depending on l (-l ≤ m l 1) The number of possible values for m is thl number of orbitals within a given subshell (orbitals with the same value for n and l). Ex. If l= 2 then m =l-2, -1, 0, 1, 2 5 orbitals If l = 0 then m l 0 1 orbital The s orbital has an l value equal to 1, and there is only one orbital in the s subshell. The s subshell is often approximated as a sphere in shape. The p orbital has an l value equal to 1, and there are three dumbbell-shaped orbitals in the p subshell. The d orbital has an l value equal to 2, and there are five orbitals in the d subshell. The f orbital has an l value equal to 3, and there are seven orbitals in the f subshell +1 −1 o m = spin quantum number; can only be (up) or (down) s 2 2 electrons have an intrinsic spin o To find the number of states, find l and then find m.l Multiply the amount of m l options by 2 (to account for both m s options) o Node = place where an electron will never be found in the probability distribution area (probability function goes to zero) Number of nodes goes up as energy goes up Electron density becomes more spread out as number of nodes goes up too S orbitals P orbital – find electrons along the respective x, y, or z line depending on the kind of p orbital Number of nodes present in this orbital is equal to n-1 Ex. Determine the nodes in the 3pz orbital, given that n = 3 and l= 1 (because it is a p orbital) n-1 3-1=2 nodes o Radial probability tells us where the electron at a certain distance from the nucleus An n s orbital electron has a greater probability of being very close to the nucleus than does an n p orbital electron; an n p orbital electron has a greater probability of being closer to the nucleus than does an n d orbital electron, etc. Within the same number of n, s orbitals will have one more peak than p orbitals; p orbitals will have one more peak than d orbitals; and so on. For orbitals, an increase in the value of n will mean additional peaks
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