Forces and Poten al Energy in atoms Bohr Rutherford Model From Monday Allotropes di erent arrangements of atoms An allotrope is a variant of a substance consis ng of only one type of atom It is a new molecular con gura on with new physical proper es Substances that have allotropes include carbon oxygen sulfur and phosphorous Forces Force is nega ve if charges are di erent sign Force is posi ve if charge have same sign where is the permiIvity 0 of free space Poten al energy V r Poten al energy is the capacity to do work By conven on V r 0 as r in nity Consider an electron and nucleus of charge Z q1 is e and q2 is Ze Poten al energy of a proton and electron at r 1 Energy is very small indeed The electron volt as energy unit Energy Q V where V is the poten al and Q the charge Accelerate an electron by a poten al of 1V Energy e V 1 60217 10 19 J Poten al Energy Diagrams Fig 3 5 p 75 Mo on and Forces the poten al energy func on can predict the mo ons of the par cles The direc on of the force exerted by the par cle at the origin on the second par cle is determined by the slope the deriva ve of the poten al energy func on Mo on and Forces F dV dr i e the nega ve of the slope For a electron and proton note d dx 1 x 1 x2 F slope Example Li3 e 2 5 Angstrom Rutherford and es ma ng the size of a Au nucleus no electrons 200 eV par cle He2 with Au 79 nucleus Red line total KE of par cle Par cle losses energy as it increases poten al energy KE 200 V r in eV At turning point par cle does a turn around and is repelled 12 angstroms KE 0 Turning point p 76 Rutherford and es ma ng the size of a Au nucleus no electrons 2 MeV par cle He2 with Au 79 nucleus calculate the turning point Turning point is where kineJc energy E of parJcle V r V r q1 q2 4 0 r so set V r E r q1 q2 4 0 E p 76 Rutherford and es ma ng the size of a Au nucleus no electrons 2 MeV par cle He2 with Au 79 nucleus calculate the turning point rtp 11 4 10 14 m p 76 Mid term 20 pts Mul ple choice One 3pts one 2 pts rest 1 point 15 x1 3 2 20 Name and bring student ID card with Covers everything up to Wednesday lecture TRAJECTORY I Total E KE PE 10 eV The total energy kineJc and potenJal of the electron in the atom is posi ve E corresponds to unbound mo on in which the electron approaches the proton but passes by without becoming trapped or akached Kine c Energy Electron with KE 10 eV TRAJECTORY II Total E KE PE 13 6eV Electron is trapped by the nuclear eld nega ve total energy describes bound mo on in which the electron is said to be trapped within a poten al well centered on the proton Electron with KE 10 eV The ionizaJon energy IE 1 of an atom also referred to as the rst ionizaJon energy or in some textbooks the ionizaJon potenJal is the minimum energy necessary to remove an electron from a neutral atom in the gas phase and form a posiJvely charged ion in the gas phase It is the change in energy E for the process X g X g e E IE1 IE1 energy to remove the rst electron Its always posi ve p 79 Ioniza on Energy Consider Ioniza on as the simplest chemical reac on X g X g e E IE1 Is a measure of the stability of the free atom Higher IE1 means electron is more strongly bound to the nucleus E required to escape the poten al well holding it to the atom X g X g e E Energy of reactants Energy of products E Posi ve Periodic trends in the rst Ioniza on Poten al Noble gas and alkali metals Fig 3 7 p 80 Second Ioniza on Energy IE2 X g X2 g e E IE1 Measured in eV per atom 1eV 96 48 kJ mol 1 Trends in in IEn show characterisJc pa erns of behavior repeat in successive periods 1st period have stable shell with 2 e s 2nd period He core with 1 8 less bound e s 3rd period stable Ne core with 1 8 less bound electrons 4th period stable Ar structure 2nd 3rd 4th Table 3 1 p 81 General observa ons of IEn n 1 2 3 IP shows large discon nuity at He Ne Ar Suggests stable shells Values jump up for IE1 IE2 IE3 IE4 IE5 IE6 IE7 IE8 IE9 IE10 He Li Be B C N O F Ne Na Suggest shell structure of atom Shell 1 2 electrons shell 2 8 electrons shell 3 8 electrons Sodium Na shows evidence of a shell model 2 8 Ist IE creates a Ne like core IE 9 10 a He like con gura on is opened up NOTE LOG scale Number of electrons removed Fig 3 8 p 81 Shell model for atomic structure Shells correspond to periods First shell has 2 electrons Second and third shells contain 8 electrons Assume they are spherical Sulfur 2 in innermost 8 next shell 6 outermost Bohr Rutherford Model 1920 Fig 3 6b p 78 The Shell model of the atom V Ze2 4 0 1 r1 1 r2 1 r3 1 r12 1 r13 1 r23 No simple way to relate the bound mo on of all electrons Use e ec ve poten al energy Ze Z S S is the screening energy p 82 Ze Z S S is the screening energy 2 V V Z e 4 r e e 0 If an atom has Z electrons we select electron of interest and the e ec ve charge it sees is determined by the Z nucleus and the N 1 electrons that together determine Ze Shells the magnitude of Ze is important p 83 Outer intermediate and inner shell e ec ve nuclear charge poten als Fig 3 9 p 83 The shell model is a re nement of Rutherford s planetary model because it describes the Z electrons as being organized into a series of concentric shells based on their ioniza on energies The shell model is inspired by pakerns in experimental measurements of successive ioniza on energies Our one electron approxima on based on Z e and simple classical electrosta cs provides a qualita ve physical interpreta on of the shell model p 84 Core and Valence electrons Electrons in the inner shells called core electrons do not par cipate signi cantly in chemical reac ons because they are quite di cult to remove from the atom The outermost par ally lled shell called the valence …