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Chem 101 Chapter 3: Quantum Mechanics

by: Rebecca de la O

Chem 101 Chapter 3: Quantum Mechanics CH 101

Marketplace > University of Alabama - Tuscaloosa > CH 101 > Chem 101 Chapter 3 Quantum Mechanics
Rebecca de la O

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Light Waves Wave Particle Duality Frequency Wavelength Bohr's Model Hydrogen Atom Orbitals
General Chemistry
Jared Allred
Class Notes
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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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