Last material covered before midterm #1
Last material covered before midterm #1 CHEM 1B
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This 10 page Class Notes was uploaded by Stacy Vargas on Thursday October 15, 2015. The Class Notes belongs to CHEM 1B at University of California - Santa Cruz taught by Roberto Bogomolni in Fall 2015. Since its upload, it has received 19 views. For similar materials see CHEM 1B in Chemistry at University of California - Santa Cruz.
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Date Created: 10/15/15
129 The Characteristics of Hydrogen Qrbitals When the Schrodinger equation is solved for the hydrogen atom you nd many wave functionOrbitals that satisfy it Each orbital is characterized by a set of which arise when the boundary conditions are applied is related to the size and energy of the orbital 0 As n increases the orbital becomes larger and the electron spends more time away farther from the nucleus An increase of n indicates there is higher energy because the electron is less tightly bound to nucleusDtherefore the energy is negative integral values from O to n 1 for each value of n this number relates to the angular momentum of an electron in a given orbital 0 Dependence of wave functions on I determine the shapes of the atomic orbitals 0 Value of for a particular orbital is commonly assigned a letter Os 1Dp 2jd 3Df can have integral values between I and including zero 0 This value relates to the orientation in the space of the angular momentum associated with the orbital Refer to table below The rst four levels of orbitals in hydrogen are listed with their quantum numbers set of orbitals with a given value of uantun t Numbers for the Firat Four Lavela cat i42riizaitala in the Hydrogen tth Dtbitall Ht imb of it Designation mg 39 ll39bll ll n 1 539 3E i l F ilii l1i i l mr f tjngci i 3 ii i Tha labels 5E El and I are used liar 1 j 1 31 hlE t l iEal f The originally 1 1Er 1 j referred 1E chara ten tiij Di linEE rt 439 nbaemretj in the Htgi 39iit Electra 5 1 g 1 WHILE sharpie p principal ti itali use r l 1 l fundamental Balsam ftha lattars 3 g 3 i m m m Emmy became alphabetic gr n Haltipping l t39ai l39llljl39l I5 resemeci 213 a symbol for i value angular momentum Ntirnhnr tit bital per EL bahell mlhm H m l o The 3 types of representations for hydrogen ls 25 and 3s orbitals are illustrated in the image below 0 Note the 25 and 3s orbitals contain areas of high probability separated by areas of zero probability 0 Note Characteristic is a spherical shape for s orbitals Figure 1213 Three repre er ala li ne Ellquot 39il lef i iy k lr gel i is 2 5 ard orbitals 3an Thr ecglmrr cat the TaraIre kineticin lbl Slices of the threecilrrenelienel eleztrcn density ici The surfaces that earlain 95 of the lutell eleulrun probability tlhe quotagesquot of the erbifelsl lquotch latter areas 2 5F 25 I in is o of nodes increases as n increases 2 types of representation for the 2p orbitals there are no 1p orbitals are shown in the image below 0 Note p orbitals are not spherical like the s orbitals but have 2 lobes separated by a node at the nucleus 0 an area of an orbital having zero electron probability p orbitals are labeled according to the axis of the Cartesian coordinate system along which the lobes lie A simple wave oscillates from to H and repeats this pattern Atomic orbital functions also have signs Functions for s orbitals are positive everywhere in 3D space 0 When the s orbital function is evaluated at any point in space t is number In contrast p orbital functions have different signs depending on which of the regions of space is being evaluated Glance at the image below For example pzorbital has a sign in all regions of space in which 2 is and has a H sign when 2 is negative lmportant to understand that these are mathematical signs not charges 0 Just as a sine wave has alternating and H phases p orbitals have and H phases as well Ept upbeat 39 tall 33 Figure 7121 Represent etien ei the Be emitele e The eleetree ereeetiility dietrihutieh ter e 2e erbitet Generetee trem e eregrem by Hebert ellendeerier en Prejth SEHePHIM diet PIG 24132 reprinted with permieeient h The heueeery eurfeee repreeentetiene et all three 2e erbitele Nete that the eighe ineide the eurfeee indicate the pheeee eigne til the ereitel in that regieri ei epeee 3p orbitals have a more complex probability distribution than that of the 2p orbitals Figure 1220 but they can still be represented by the same boundary surface shapes 0 Surfaces grow larger as the value of n increases Figure 1220 It ereee eeetien ef the eleetren prebe billity distribution tier e 3e erbitel o D orbitals 2 rst occur when n3 the ve 3d orbitals have the shapes illustrated in the image below Figure 1221 0 D orbitals have 2 different fundamental shapes four of the orbitals dxz dyz dxy and dX2y2 have 4 lobes centered in the plane indicated in the orbital label nyand dX2y2 are both centered in the xy plane 0 5th orbital dzz has a unique shape w 2 lobes along the z axis and a belt centered in the xy plane 0 Signs phases of d orbital functions are indicate inside boundary surfaces 0 D orbitals for levels ngt3 look like 3d orbitals but have larger lobes F orbitals rst occur in level n4 Figure 1222 represents 4f orbitals 3 along w their designations o F orbitals are not involved in the bonding in any of the compounds 0 Because of their complexity the phases of the f orbital functions aren t represented in the diagram 0 all orbitals with the same value of n have the same energy 0 aacaymtpmm 39 meg mun 3mquot 11mm a Eh Figure WEE Heereeemetinn Eff The Ed erbitele E EJeetren density plate ef selected 3d erbiiele Generatee frem e pmgrem by Hubert Mieneeerf er en Preieet EER F HIM disk 2402 reprinted with permieeien la The ten ndery eur feeee 31 all five erbit eJe with the eigr le phaeeej indicated Figu re Fieereeentetien et the 4f erhitele in terrrie e f their itieurreiergr eurieeee Jae 0 Figure 1223 demonstrates the energies for the orbitals in the rst 3 quantum levels for hydrogen llnerggir Figure Qrbitel energy letrele fer the hydregen Hydrogen s 39 mm39 electron can occupy any of its atomic orbitals however in the lowest energy state the ground state the electron resides in the ls orbital Energy put into atom l electron transferring to a higher energy orbital l excited state Th a Hydrogen A tam In the quantum mechanical meldelj the electrnny is described as a water This repl resezntatinn leadis tn a series pf wave functinns inrhitals that describe the pnssible energies and spatial distr ihutinns available tn the electrnn i In agreement with the Heisenberg ll C rlial t ff principle the model cannnt specify the detaile electrnn mntinns instead3 the square leif the wave functicun represents the prnbabilit distributinn Di the electrnn in that nrhital This apprnach allnws us tel picture nrbitals in terms at prnbability clistributinhisr nr electrnn density maps The size at an nrhital is arbitrarily tiefined as the surface that cnntains 9390 tie at the total electrnn prnhahility The hytlregen atetn has many types nit nrbitals ln the grinan state the single electan resides in the 1s Orbital The electrnn can be excited tn higherenergy erhitals if the stem abstithe energy 1210 Electron pin andthe Pauli Principle 0 Developed by Samuel Goudsmit and George Uhlenbeck in 1925 found that a fourth quantum number was necessary to account for the details of the emission spectra of atoms New quantum number is called the and can only have the values of 12 or 12 0 developed by physicist Wolfgang Pauli and he claimed that in a given atom no 2 electrons can have the same set of four quantum numbers n I m and ms 0 Rephrase since ms can only have 2 different values An orbital can hold only 2 electrons and they must have opposite spins o This principle will have important consequence when you use the atomic model to relate the electron arrangement of an atom to its position in the periodic table 1211 Polyeleci mic Amms Quantum mechanical model provides a description of the hydrogen atom that agree with experimental data however this model wouldn t be useful if it didn t account the properties of other atoms as well atoms with more than one electron such as helium He 3 energy contributions of the He atom that must be considered 0 KE of electrons as they move around the nucleus 0 Potential energy PE of attraction between the nucleus and electrons 0 PE of repulsion between the 2 electrons Dif culty arises in dealing with repulsion between electrons Electron correlation problem refers to the fact that we cant rigorously account for the effect a given electron has on the motions of the other electrons in an atom occurs w polyelectronic atoms 0 In order to treat the system you must take approximations Simplest approximation involves treating each electron as if it were moving in a eld of charge that is the net result of the nuclear attraction and average repulsions of all the other electrons 2372 k of energy is required to remove 1 electron from all atoms in a mole of He for He it require 5248 kl it takes twice as much energy to remove an electron from He than from He 0 In both cases the nucleus has a 2 charge however there are 2 electrons that repel each other in He but in He there is only 1 electron thus no electron repulsion Energies required to remove one electron must arise from electron repulsions in neutral atom Effect of the electron repulsions can be thought of as reducing the nuclear charge Actual HE Hypothetical atom He atom the apparent nuclear exerted on a particular electron and mathematically expressed as Zactual Z which is the atomic number of protons This simpli cation allows you to treat each electron individually and each electron is viewed as moving under the in uence of a positive nuclear charge Ze Large nuclear charge draws electrons closer to the nucleus l binding each electron more tightly a given electron is assumed to be moving in a PE eld that is a result of both the nucleus and the average electron density of all other electrons in the atom o This approximation allows manyelectron Schrodinger equation to separate into a set of oneelectron equations 0 Orbitals oneelectron functions that result out of this have angular properties