PCh10 lec 2 - Revision history

Bes: /* Atomic Orbital Approximation */

2020-04-27T15:19:11Z

Atomic Orbital Approximation

Bes: /* Atomic Orbital Approximation */

2020-04-27T15:14:08Z

Atomic Orbital Approximation

Bes: /* Atomic Orbital Approximation */

2020-04-27T15:11:57Z

Atomic Orbital Approximation

Bes at 15:07, 27 April 2020

2020-04-27T15:07:34Z

Bes: /* Atomic Orbital Approximation */

2020-04-27T15:06:53Z

Atomic Orbital Approximation

Bes: /* Atomic Orbital Approximation */

2020-04-27T15:06:33Z

Atomic Orbital Approximation

Bes: /* Atomic Orbital Approximation */

2020-04-27T15:06:18Z

Atomic Orbital Approximation

Bes: /* Atomic Orbital Approximation */

2020-04-27T14:56:11Z

Atomic Orbital Approximation

Bes: /* Atomic Orbital Approximation */

2020-04-27T14:50:50Z

Atomic Orbital Approximation

Bes: /* Atomic Orbital Approximation */

2020-04-27T14:50:28Z

Atomic Orbital Approximation

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-: where the additional wavefunctions will use the H-atom 2s orbitals with a ''ζ'' for each of these electrons.
+: where the additional wavefunctions will use the H-atom 2s orbitals with a ''ζ'' for each of these electrons...and the general form of the obrital approximation would look like this:
 END OF LECTURE.

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 So what might a 3-electron or a 4-electron system look like?
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-[[File:Screen Shot 2020-04-27 at 10.11.11 AM.png|500px]]
+[[File:Screen Shot 2020-04-27 at 10.11.11 AM.png|550px]]
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 [[File:Screen Shot 2020-04-27 at 10.05.38 AM.png|700px]]
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 :1) You should have received your exam 2 score along with a link to an exam 2 summary page. Like with all exams, you should review the exam...in this case by looking over your exam and the summary page to figure out what material you did not fully understand. In a best case scenario, i would "hand back" your exams...the notes i wrote on your exam will assist you in identifying your errors...but since i am working at home and do not have a commercial, multi-document scanner i did not plan to return graded exams until you juniors returned to campus (sorry seniors). '''''[NOTE on grading...as a professional educator, i allocate my time to maximize learning...so, when grading an exam that will not be returned, i do not allocate the time to writing correct answers/notes on exams since you will not see them. This is often done with final exams that are not returned. So, when or if you get your exams back you might be disappointed that i did not make notes (did not fully identify your errors).]''''' Let me also remind you that since the last exam covers only Chapter 9, 10, 15...you will not need to review the exam 2 material for a comprehensive final.
-:2) ''Allocation of my time''...under normal curcumstances, it takes me very little time to prepare for Gen Chem lectures; Gen Chem labs have been refined and Steve does nearly all of the setup required. PChem (and research) students benefit from this since i normally have more time to allocate to them. Under these online conditions, i am having to allocate a large portion of my time to generating online content for lecture and lab, hence less time for you...and pchem in general. I look forward to returning to campus and returning to "normal"...i hope you do too. Although this statement of ''allocation of time'' seems unrelated to quantum mechanics...it is truly a key aspect that i will now share...
+:2) ''Allocation of my time''...under normal curcumstances, it takes me very little time to prepare for Gen Chem lectures; Gen Chem labs have been refined and Steve does nearly all of the setup required. PChem (and research) students benefit from this since i normally have more time to allocate to them. Under these online conditions, i am having to allocate a large portion of my time to generating online content for lecture and lab, hence less time for you...and pchem in general. I look forward to returning to campus and returning to "normal"...i hope you do too. Although this statement of ''allocation of time'' seems unrelated to quantum mechanics...it is truly a key aspect that i will share at a later time...
 ==Many-Electron Wavefunctions==

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 Back to the 2 electron system...so due to electron spin we find that there are 2 electrons per orbital each with their own set of quantum numbers (''n, l, m<sub>l</sub>, m<sub>s</sub>'') and '''''due to the electron-electron repulsion, this has an end result of each electron not "feeling" the entire nuclear charge of 2'''''...Z = 2, but ''ζ'' < 2. The 1s orbital in a 2-electron system is slightly "expanded" due to the nuclear charge acting on 2 electrons as opposed to just one in the H-atom...this is not a bad initial approximation.
 <div align="center">
-[[File:Screen Shot 2020-04-27 at 10.05.38 AM.png|600px]]
+[[File:Screen Shot 2020-04-27 at 10.05.38 AM.png|700px]]
 </div>

← Older revision		Revision as of 15:06, 27 April 2020
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	</div>		</div>

−	Back to the 2 electron system...so due to electron spin we find that there are 2 electrons per orbital each with their own set of quantum numbers (''n, l, m<sub>l</sub>, m<sub>s</sub>'') and '''''due to the electron-electron repulsion, this has an end result of each electron not "feeling" the entire nuclear charge of 2'''''...Z = 2, but ''ζ'' < 2.	+	Back to the 2 electron system...so due to electron spin we find that there are 2 electrons per orbital each with their own set of quantum numbers (''n, l, m<sub>l</sub>, m<sub>s</sub>'') and '''''due to the electron-electron repulsion, this has an end result of each electron not "feeling" the entire nuclear charge of 2'''''...Z = 2, but ''ζ'' < 2. The 1s orbital in a 2-electron system is slightly "expanded" due to the nuclear charge acting on 2 electrons as opposed to just one in the H-atom...this is not a bad initial approximation.
		+	<div align="center">
		+	[[File:Screen Shot 2020-04-27 at 10.05.38 AM.png\|400px]]
		+	</div>

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-The way that we adjust this H-atom atomic orbital wavefunction is first to change the ''Z'' into a ''ξ'' (a zeta)...sorry the "zeta" fonts are not the same...
+The way that we adjust this H-atom atomic orbital wavefunction is first to change the ''Z'' into a ''ζ'' (a zeta)...
 <div align="center">
 [[File:Screen Shot 2020-04-27 at 9.48.37 AM.png|450px]]
 </div>

@@ Line 38: / Line 38: @@
 The way that we adjust this H-atom atomic orbital wavefunction is first to change the ''Z'' into a ''ξ'' (a zeta)...sorry the "zeta" fonts are not the same...
 <div align="center">
-[[File:Screen Shot 2020-04-27 at 9.48.37 AM.png|600px]]
+[[File:Screen Shot 2020-04-27 at 9.48.37 AM.png|500px]]
 </div>