PCh9 Lec 5 - Revision history

Bes: /* Sec 9.5 Radial Probability Distribution Function */

2020-04-20T14:35:04Z

Sec 9.5 Radial Probability Distribution Function

Bes: /* Sec 9.5 Radial Probability Distribution Function */

2020-04-20T14:32:56Z

Sec 9.5 Radial Probability Distribution Function

Bes: /* Sec 9.5 Radial Probability Distribution Function */

2020-04-20T14:12:19Z

Sec 9.5 Radial Probability Distribution Function

Bes: /* Comments/Corrections/Edits */

2020-04-20T13:47:18Z

Comments/Corrections/Edits

Bes: /* Comments/Corrections/Edits */

2020-04-20T13:41:49Z

Comments/Corrections/Edits

Bes: /* Comments/Corrections/Edits */

2020-04-20T13:39:51Z

Comments/Corrections/Edits

Bes: /* Comments/Corrections/Edits */

2020-04-20T13:37:51Z

Comments/Corrections/Edits

Bes: /* Corrections/edits */

2020-04-20T13:36:30Z

Corrections/edits

Bes at 13:28, 20 April 2020

2020-04-20T13:28:04Z

Bes at 13:27, 20 April 2020

2020-04-20T13:27:14Z

@@ Line 41: / Line 41: @@
 :5) keep studying this figure...it is one of the most important figures in all of chemistry-related QM!
-One last thing:
+====One last thing====
-:So when we talk about/draw orbitals we show a hard surface...i sphere or a dumbbell shape. What dictates the distance the hard surface is from the nucleus? The answer is choose the 90% probability surface...ie. 90% of the time, the electron will be inside of the hard surface. This is of course a "weak" representation of the orbital wavefunction, but when you are first taught about orbitals...'''''you can't handle the "wavefunction" truth!''''' <-- this phase is stolen from the movie...[https://youtu.be/9FnO3igOkOk A Few Good Man]
+:So when we talk about/draw orbitals we show a hard surface...a sphere or a dumbbell shape. Q: What dictates the distance the hard surface is from the nucleus? A: Choose the 90% probability surface...ie. 90% of the time, the electron will be inside of the hard surface. This is of course a "weak" representation of the highly complex (and very attractive) orbital wavefunction, but when you are first taught about orbitals...'''''you can't handle the "wavefunction" truth!''''' <-- this phase is stolen from the movie...[https://youtu.be/9FnO3igOkOk A Few Good Man]

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 In all of the previous QM model systems, there was an equal amount of "space" were the particle could exist...what i mean is...think about the particle-in-a-box...there is an equal amount of space on the left side of the box as there is in the middle or right side. Now with a spherical space, there is a lot more space available the further you move out from the center. If you look at the 1s wavefunction (Fig 9.6) or the 1s<sup>2</sup> wavefunction (Figure 9.9), you will see that the probability of being at the nucleus is very high...but...how much "space" is available to this electron...because the area available to the electron at the nucleus is very small, then we must modify the wavefunction to incorporate this issue.
-So, the radial function, R(r) is squared to become the "probability" radial function, R(r)<sup>2</sup>, which when you take into account the "space/distribution" problem...we now have the radial probability distribution function, r<sup>2</sup>R(r)<sup>2</sup>.
+So, the radial function, R(r) is squared to become the radial probability function, R(r)<sup>2</sup>, which when you take into account the "space/distribution" problem...we now have the radial probability distribution function, r<sup>2</sup> R(r)<sup>2</sup>.
-:::R(r) --> R(r)<sup>2</sup> --> r<sup>2</sup>R(r)<sup>2</sup>.
+:::R(r) --> R(r)<sup>2</sup> --> r<sup>2</sup> R(r)<sup>2</sup>.

← Older revision		Revision as of 14:12, 20 April 2020
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	==Sec 9.5 Radial Probability Distribution Function==		==Sec 9.5 Radial Probability Distribution Function==

−	At this point you should be fully aware of the mathematical form of the hydrogen atom wavefunctions (see pages 170-171). It has taken us some time to develop these wavefunctions/eignefunction/orbitals.	+	At this point you should be fully aware of the mathematical form of the hydrogen atom wavefunctions (see pages 170-171). It has taken us some time to develop these wavefunctions/eignefunction/orbitals, but we are not yet done. The following discussion is referred to as the "real estate" problem. I looked on YouTube for a video to help explain this concept, but i failed to find one that was satisfactory...i guess i might need to make one of these...later.
		+
		+	In all of the previous QM model systems, there was an equal amount of "space" were the particle could exist...what i mean is...think about the particle-in-a-box...there is an equal amount of space on the left side of the box as there is in the middle or right side. Now with a spherical space, there is a lot more space available the further you move out from the center. If you look at the 1s wavefunction (Fig 9.6) or the 1s<sup>2</sup> wavefunction (Figure 9.9), you will see that the probability of being at the nucleus is very high...but...how much "space" is available to this electron...because the area available to the electron at the nucleus is very small, then we must modify the wavefunction to incorporate this issue.
		+
		+	So, the radial function, R(r) is squared to become the "probability" radial function, R(r)<sup>2</sup>, which when you take into account the "space/distribution" problem...we now have the radial probability distribution function, r<sup>2</sup>R(r)<sup>2</sup>.
		+
		+	:::R(r) --> R(r)<sup>2</sup> --> r<sup>2</sup>R(r)<sup>2</sup>.

@@ Line 14: / Line 14: @@
 |}
 ====Comments/Corrections/Edits====
-:1) As you can see in the Hydrogen Atom Schrodinger Equation on the bottom-left, the typical eq has the mass of the electron (''m<sub>e</sub>'') as opposed to the reduced mass (''μ''). Technically this is not incorrect, if the reduced mass is for the mass of the nucleus and the electron...the reduced mass of nuc/e- = nuc...so this term would then be considering the kinetic energy of the moving proton...but this is a different problem. If this is the H-atom Sch eq. it needs to be ''m<sub>e</sub>'' not ''μ''. Please remember that we are working under the [https://en.wikipedia.org/wiki/Born%E2%80%93Oppenheimer_approximation Born-Oppenheimer_approximation].
+:1) As you can see in the Hydrogen Atom Schrodinger Equation on the bottom-left, the typical eq has the mass of the electron (''m<sub>e</sub>'') as opposed to the reduced mass (''μ''). Technically this is not incorrect, if the reduced mass is for the nucleus and the electron...the reduced mass of nuc/e- = m<sub>e</sub>. It is best to be written as ''m<sub>e</sub>'' not ''μ''.
-:2) It was a smart to use the [https://en.wikipedia.org/wiki/Del "del"] symbol (i cannot find this character- upside down Δ) to represent the 3D coordinates. As you can see in the middle, the ''del'' is shown in cartesian coordinates, but more useful form in QM for atoms are the spherical polar coordinates (right).
+:2) It was a smart to use the [https://en.wikipedia.org/wiki/Del "del"] symbol (i cannot find this character- upside down Δ) to represent the 3D coordinates. As you can see in the middle, the ''del'' is shown in cartesian coordinates, but more useful form in QM for atoms are the spherical polar coordinates (right). It would have been very easy to make a typo is writing out either out the del.
 :3) Now onto the potential energy term...they are missing the 4πε<sub>o</sub>.

@@ Line 21: / Line 21: @@
 :4) I would prefer if the wavefunction was written with all variable, ''R, Θ, Φ'' as opposed to just ''R''...
 ==Sec 9.5 Radial Probability Distribution Function==
 At this point you should be fully aware of the mathematical form of the hydrogen atom wavefunctions (see pages 170-171). It has taken us some time to develop these wavefunctions/eignefunction/orbitals.

@@ Line 16: / Line 16: @@
 :# As you can see in the Hydrogen Atom Schrodinger Equation on the bottom-left, the typical eq has the mass of the electron (''m<sub>e</sub>'') as opposed to the reduced mass (''μ''). Technically this is not incorrect, if the reduced mass is for the mass of the nucleus and the electron...the reduced mass of nuc/e- = nuc...so this term would then be considering the kinetic energy of the moving proton...but this is a different problem. If this is the H-atom Sch eq. it needs to be ''m<sub>e</sub>'' not ''μ''. Please remember that we are working under the [https://en.wikipedia.org/wiki/Born%E2%80%93Oppenheimer_approximation Born-Oppenheimer_approximation].
-:# It was a smart to use the [https://en.wikipedia.org/wiki/Del "del"] symbol (i cannot find this character- upside down Δ) to represent the 3D coordinates. As you can see in the middle, the ''del'' is shown in cartesian coordinates, but more useful form in QM for atoms are the spherical polar coordinates.
+:# It was a smart to use the [https://en.wikipedia.org/wiki/Del "del"] symbol (i cannot find this character- upside down Δ) to represent the 3D coordinates. As you can see in the middle, the ''del'' is shown in cartesian coordinates, but more useful form in QM for atoms are the spherical polar coordinates (right).
-:#
+:# Now onto the potential energy term...they are missing the 4πε<sub>o</sub>.
 ==Sec 9.5 Radial Probability Distribution Function==
 At this point you should be fully aware of the mathematical form of the hydrogen atom wavefunctions (see pages 170-171). It has taken us some time to develop these wavefunctions/eignefunction/orbitals.

@@ Line 13: / Line 13: @@
 |[[File:Screen Shot 2020-04-20 at 8.15.13 AM.png|300px]]||[[File:Screen Shot 2020-04-20 at 8.15.30 AM.png|300px]]||[[File:Screen Shot 2020-04-20 at 8.15.48 AM.png|300px]]
 |}
-:Corrections/edits
+====Corrections/edits====
-:# As you can see in the Hydrogen Atom Schrodinger Equation on the left, the typical eq has the mass of the electron (''m<sub>e</sub>'') as opposed to the reduced mass (''μ''). Technically this is not incorrect, if the reduced mass is for the mass of the nucleus and the electron...the reduced mass of nuc/e- = nuc...so this term would then be considering the kinetic energy of the moving proton...but this is a different problem. If this is the H-atom Sch eq. it needs to be ''m<sub>e</sub>'' not ''μ''. Please remember that we are working under the [https://en.wikipedia.org/wiki/Born%E2%80%93Oppenheimer_approximation Born-Oppenheimer_approximation].
+:# As you can see in the Hydrogen Atom Schrodinger Equation on the bottom-left, the typical eq has the mass of the electron (''m<sub>e</sub>'') as opposed to the reduced mass (''μ''). Technically this is not incorrect, if the reduced mass is for the mass of the nucleus and the electron...the reduced mass of nuc/e- = nuc...so this term would then be considering the kinetic energy of the moving proton...but this is a different problem. If this is the H-atom Sch eq. it needs to be ''m<sub>e</sub>'' not ''μ''. Please remember that we are working under the [https://en.wikipedia.org/wiki/Born%E2%80%93Oppenheimer_approximation Born-Oppenheimer_approximation].
 :#

@@ Line 6: / Line 6: @@
 Before we continue with the last lecture of the chapter, i wanted to discuss the White and Nerdy video shared in the last lecture...yes it is the hydrogen atom Schrodinger equation showing up in pop culture! First, Q: who is the person with Weird Al? ...A: it is [https://en.wikipedia.org/wiki/Donny_Osmond click here]...and if you wish to see him perform one of his ''Joseph and the Amazing Technicolor Dreamcoat'' tunes , click [https://youtu.be/CpK9dThD6qs here].
-Back to QM...is this equation correct?
+Back to QM...Q: is this equation correct? A: no.
 {|
 |[[File:Screen Shot 2020-04-20 at 7.45.47 AM.png|400px]]||[[File:Screen Shot 2020-04-20 at 7.43.32 AM.png|400px]]
@@ Line 14: / Line 13: @@
 |[[File:Screen Shot 2020-04-20 at 8.15.13 AM.png|300px]]||[[File:Screen Shot 2020-04-20 at 8.15.30 AM.png|300px]]||[[File:Screen Shot 2020-04-20 at 8.15.48 AM.png|300px]]
 |}
 ==Sec 9.5 Radial Probability Distribution Function==
 At this point you should be fully aware of the mathematical form of the hydrogen atom wavefunctions (see pages 170-171). It has taken us some time to develop these wavefunctions/eignefunction/orbitals.