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# Class Note for CHEM 111 at UMass(17)

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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Massachusetts taught by a professor in Fall. Since its upload, it has received 15 views.

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Date Created: 02/06/15

CHEM111 General Chemistry 1 QUANTUM NUMBERS The Schrodinger wave equation describes the energies of an electron in an atom Solutions to this equation are called wave functions and in addition to describing the energy of an electron they also describe the shape and orientation of the volume element in which the electron exists The solutions are restricted due to three quantum numbers Acceptable solutions are called orbitals An orbital is a region in space or a volume element where there is a high approximately 90 probability of locating an electron Each orbital is uniquely de ned by a set of three quantum numbers The quantum numbers describe restrictions that are needed to nd solutions to the Schrodinger equation they therefore limit the number of acceptable solutions The three quantum numbers are described below 1 Principal guantum number 1n n has whole number values from 1 to in nity 11 indicates the approximate distance of the orbital from the nucleus and therefore its approximate energy For example an electron in an orbital with n 3 is located at a further distance from the nucleus than an electron in an orbital with n 2 and therefore has a higher potential energy The principal quantum number is essentially the principal level postulated in the Bohr theory 2 Angular momentum quantum number I may have values from 0 to nl Therefore the number of values is equal to 11 de nes the three dimensional shape of the orbital For example when 0 the orbital is spherical and when I l the orbital is shaped like a dumbbell values are generally given letter designation as follows 0 s l p 2 d 3 f 3 Magnetic guantum number 1mg mmay have values ranging from 0 m describes the orientation of the orbital in space For example when l m 10l These three mvalues describe three p type orbitals all of which have different orientations in space along the three coordinate axes An orbital is designated by its principal quantum number followed by its angular momentum quantum number or nl For example the orbital with n l and l 0 is called a ls orbital and when n 3 and l 2 this is a 3d orbital Orbitals with the same values for n andl but different values of m are differentiated by using subscripts x y and z for the coordinate axes along which they are oriented For example the three 2p orbitals are oriented along the x y and z coordinate axes and are therefore called 2px Zpy and 2pz Each orbital is uniquely described by a set of three quantum numbers The ls orbital is de ned by the three quantum numbers of 100 where the rst is n the second 1 and the third ml The three 2p orbital are described by 2ll 210 and 21l Quantum Numbers Summary Principal Angular Magnetic Quantum Quantum Quantum Orbital Number n Number I Number m3 Orbitals Tvpe Electrons l 0 0 l ls 2 2 0 0 1 2s 2 l l01 3 2p 6 3 0 0 1 3s 2 l l01 3 3p 6 2 2l012 5 3d 10 4 0 0 1 4s 2 l l01 3 4p 6 2 2l012 5 4d 10 3 32l0l 23 7 4f 14 n 0 n1 0 n2 2n2 total n A level is a collection of orbitals with the same value of n Thus the third principal level has 9 orbitals and 18 electrons A sublevel is a collection of orbitals with the same values of n and 1 Thus the 2p sublevel is a collection of the three 2p orbitals 2px 2py and 2pz The third level is composed of three sublevels the 3s 3p and 3d The number of sublevels for any given level is equal to the level number 11 All s sublevels contain 1 orbital and a maximum of 2 electrons p sublevels contain three orbitals and a maximum of 6 electrons and d sublevels contain 5 orbitals and a maximum of 10 electrons DL Adams October 17 2008

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