Difference between revisions of "PCh9 Lec 3"
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:- Okay, so write down the modified Schrodinger Equation (eq. 9.5) in your notes... | :- Okay, so write down the modified Schrodinger Equation (eq. 9.5) in your notes... | ||
::*Acknowledge that this modified Schrodinger equation originated from the more complex Schrodinger equation (eq. 9.2)...ie. we solved the angular (θ, Φ) portion (3D rotation), plugged the energy "answer" into the Schrodinger equation, regrouped the terms to form an effective potential (V<sub>eff</sub>)...resulting in eq 9.5 having only a radial part, R(r), ie the radial wavefunction. <--''consider re-reading this statement multiple times and even reviewing the notes from last week.'' | ::*Acknowledge that this modified Schrodinger equation originated from the more complex Schrodinger equation (eq. 9.2)...ie. we solved the angular (θ, Φ) portion (3D rotation), plugged the energy "answer" into the Schrodinger equation, regrouped the terms to form an effective potential (V<sub>eff</sub>)...resulting in eq 9.5 having only a radial part, R(r), ie the radial wavefunction. <--''consider re-reading this statement multiple times and even reviewing the notes from last week.'' | ||
| − | :- On page 168, the radial wavefunctions R(r) are now written as R<sub>n,l</sub>(r) | + | :- On page 168, the radial wavefunctions R(r) are now written as R<sub>n,l</sub>(r) are plotted in Figure 9.2. Study the 1s, 2s, and 3s wavefunction and compare these to the ~same plots in Fig 9.6 <-- don't pay attention to the p-orbitals just yet. |
:- So we cannot just disregard the angular portion of the wavefunction...flip back to the spherical harmonics (solution to 3D rotation), ''Y<sub>ml,l</sub>(θ, Φ)'' (eq. 7.33) and acknowledge that the hydrogen atom wavefunction is: | :- So we cannot just disregard the angular portion of the wavefunction...flip back to the spherical harmonics (solution to 3D rotation), ''Y<sub>ml,l</sub>(θ, Φ)'' (eq. 7.33) and acknowledge that the hydrogen atom wavefunction is: | ||
::::''R<sub>n,l</sub>(r) * Y<sub>ml,l</sub>(θ, Φ) = ψ<sub>n,l,ml</sub> (r, θ, Φ) | ::::''R<sub>n,l</sub>(r) * Y<sub>ml,l</sub>(θ, Φ) = ψ<sub>n,l,ml</sub> (r, θ, Φ) | ||
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:- Show in your notes how the following wavefunctions are formed: | :- Show in your notes how the following wavefunctions are formed: | ||
| − | ::* ψ<sub>2,1,-1</sub> ( | + | ::* ψ<sub>2,1,-1</sub> (r, θ, Φ) |
| − | ::* ψ<sub>2,1,0</sub> ( | + | ::* ψ<sub>2,1,0</sub> (r, θ, Φ) |
| − | ::* ψ<sub>2,1,+1</sub> ( | + | ::* ψ<sub>2,1,+1</sub> (r, θ, Φ) |
| − | There is more...X2, but i will stop for now. If you are confused, then re-read, re-read | + | There is more...X2 more related to wavefunctions, but i will stop for now. If you are confused, then re-read, then re-read again...aka study, study study these concepts. At this point you should have written down at least one page of notes... |
'''END Chem 9, Lec 3''' | '''END Chem 9, Lec 3''' | ||
| + | |||
| + | [https://www.goalcast.com/2017/03/29/top-30-most-inspiring-albert-einstein-quotes/?jwsource=cl ...another interesting article/quote/video about Einstain - optional, but good!] | ||
Latest revision as of 14:34, 15 April 2020
(4/15/20, bes)
Greetings,
- - If you have not checked your email, please read the note i sent yesterday...do it now.
- - and about those exams...i am finding it hard to grade exams...i know it is something i should do, but i would much rather generate content like the notes below. I will get these done by the end of the week.
We will continue with our Ch 9 discussion of the hydrogen atom and specifically the wavefunctions. Although i am hesitant to give away the punchline, i will do so, the hydrogen atom is the first and last element that can be completely solved by quantum mechanics...WHAT???...yes, although we can solve the Schrodinger Equation for the hydrogen atom, when we add a second electron (Ch 10) to the atom, we can no longer solve the Schrodinger equation. So why did we do all of this? It turns out that QM provides a foundation in which approximations can be made to solve many of the chemistry related problems. The "approximations" are pulled into QM within the computational chemistry models (Ch 15). I will get to wavefunctions soon, but i have opened a small can of worms that i feel we must purse in order to clarify the above mentioned issue...in keeping with my ability to move tangentially within a lecture...ie. going off-track!
- - Did you know that although Einstein (and the photoelectric effect) was one of the foundational experiments that lead to QM, he did not "like" QM...the following video is quite interesting. If you don't know who Alan Alda is, he was the main character in a the 1972 TV series M*A*S*H who has become very interested in promoting science within the public arena. Brian Greene is a theoretical physicist and similar to the more popular Niel deGrasse Tyson who has done a lot to educate the public about complex science topics. Have a look at this interview...
Brian Greene and Alan Alda Discuss Why Einstein Hated Quantum Mechanics
- ... and now you know a bit more about gravity as well!
Hydrogen Atom Wavefunctions
- - Okay, so write down the modified Schrodinger Equation (eq. 9.5) in your notes...
- Acknowledge that this modified Schrodinger equation originated from the more complex Schrodinger equation (eq. 9.2)...ie. we solved the angular (θ, Φ) portion (3D rotation), plugged the energy "answer" into the Schrodinger equation, regrouped the terms to form an effective potential (Veff)...resulting in eq 9.5 having only a radial part, R(r), ie the radial wavefunction. <--consider re-reading this statement multiple times and even reviewing the notes from last week.
- - On page 168, the radial wavefunctions R(r) are now written as Rn,l(r) are plotted in Figure 9.2. Study the 1s, 2s, and 3s wavefunction and compare these to the ~same plots in Fig 9.6 <-- don't pay attention to the p-orbitals just yet.
- - So we cannot just disregard the angular portion of the wavefunction...flip back to the spherical harmonics (solution to 3D rotation), Yml,l(θ, Φ) (eq. 7.33) and acknowledge that the hydrogen atom wavefunction is:
- Rn,l(r) * Yml,l(θ, Φ) = ψn,l,ml (r, θ, Φ)
- these wavefunctions, ψn,l,ml (R, θ, Φ) are shown on pages 168-169.
- - Show in your notes how the following wavefunctions are formed:
- ψ2,1,-1 (r, θ, Φ)
- ψ2,1,0 (r, θ, Φ)
- ψ2,1,+1 (r, θ, Φ)
There is more...X2 more related to wavefunctions, but i will stop for now. If you are confused, then re-read, then re-read again...aka study, study study these concepts. At this point you should have written down at least one page of notes...
END Chem 9, Lec 3
...another interesting article/quote/video about Einstain - optional, but good!