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Author: Subject: Quantum Mechanics/Wave Mechanics in Chemistry Beginners Thread
blogfast25
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[*] posted on 8-7-2015 at 17:15
Quantum Mechanics/Wave Mechanics in Chemistry Beginners Thread


I’m starting this thread in ‘interactive seminar form’ for the benefit of beginners and burgeoning chemists who haven’t had the benefit of a higher education in science and want to understand better what causes chemical bonds to form.

Being a normal thread anyone is welcome (and it’s FREE! ;)) to contribute, correct me or ask questions. Of more knowledgeable contributors I ask only to take one thing into account: this thread is not about cutting edge Quantum Physics, rather because of its stated intent shouldn’t really exceed A-level/1<sup>st</sup> year Uni levels of sophistication. If interest warrants it, we can always build up.

To the extent of the possible and practical I will only move on from one concept to the next if I feel most ‘students’ have reached sufficient understanding of each concept.

It’s a two part ‘course’:

Part I: Basic wave mechanics, up to atomic orbitals. I will use mainly HyperPhysics as an online textbook.

Part II: Applications of wave mechanics in Chemical Bond Theory, mainly from a VESPR perspective, but touching on most types of chemical bonds.

First instalment tomorrow.


[Edited on 9-7-2015 by blogfast25]

Quick Navigation (Updated):

Part I – Basic Wave Mechanics

Part II - Applications of Wave Mechanics in Chemical Bond Theory




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smaerd
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[*] posted on 8-7-2015 at 17:25


Cool idea blogfast25. Q&M was one of my favorite topics as an undergraduate. So I'll be really happy to read through this as it grows. I found the atkins physical chemstry book to be exceptional for teaching Q&M from a chemists perspective. At least the entry level models. Also the book, "physical chemistry a biochemists perspective" was really great at being simple.

Edit - I may even have a primer on some of the calculus involved. I was writing it for an applied mathematics book. Hmm...

[Edited on 9-7-2015 by smaerd]




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[*] posted on 8-7-2015 at 19:20


It's already a "Cliff Hanger". I have to put my popcorn up for tomorrow.

Thank you for doing this Blog. I'm pretty excited to see what I actually know, can grasp, and can learn.




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[*] posted on 9-7-2015 at 07:19


Thanks Zombie man.

Smaerd, there's not going to be a whole lot of calculus rocking here but add some if you please (within reason, of course)

And we're off!

Part I: Basic wave mechanics

The Particle/Wave Duality

At the level of the very small (atoms and smaller) things get decidedly strange because Classical Newtonian Laws governing moving objects no longer apply. A number of unexpected experimental results around the turn of the 19th Century showed that waves could behave like particles and vice versa (the list below is far from exclusive).

1. The photo electric effect:

http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html#c2

2. Compton Scattering:

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint....

3. Davisson-Germer Experiment:

http://hyperphysics.phy-astr.gsu.edu/hbase/davger.html#c1

While 1. and 2. show electromagnetic waves behaving like particles, 3. shows moving electrons behaving like waves!

The Davisson-Germer Experiment served as an experimental verification of the DeBroglie Hypothesis:

http://hyperphysics.phy-astr.gsu.edu/hbase/debrog.html#c1

A more formal treatment of the DeBroglie Hypothesis and Wavelength can be found here:

http://hyperphysics.phy-astr.gsu.edu/hbase/debrog.html#c3

Free-moving microscopic (atomic or smaller) particles, like electrons, with momentum p (= mv, m = mass in kg, v = speed in m/s) thus behave like waves with wavelength:

λ = h/p (with h = Planck’s Constant)

Food for thought: which objects we are familiar with in chemistry contain electrons?

This is the end of this particular 'lecture' and questions/comments will now be taken. Thank you, please!



[Edited on 9-7-2015 by blogfast25]




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[*] posted on 9-7-2015 at 09:28


Nice one !

Thanks for taking the time to put this together bloggers.

Can us eejits ask questions yet ?

Plancks Constant (https://en.wikipedia.org/wiki/Planck_constant) being the smallest amount by which a system must change ?




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[*] posted on 9-7-2015 at 10:06


Yes, questions/comments are now taken, before moving on to the next session.

Aga, for NOW it's best to look at h as nothing more than a proportionality constant, e.g. E = hf, with E the energy of a photon, and f its frequency.

But h is closely related to the minimum change in energy a Quantum System can undergo, in that sense you are correct.

To ALL 'students': bear in mind the profound differences between moving particles and classic waves, to appreciate just how momentous the discoveries described above really were. They were the start of description of the 'weirdness' of the QM world, known as Quantum Physics.

For fundamental differences between waves and moving objects, see:

http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html#c1 and SCROLL DOWN to:

Wave-Particle Duality: Light


[Edited on 9-7-2015 by blogfast25]




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[*] posted on 9-7-2015 at 11:14


@Aga- the photoelectric effect can be used to show how the value of plancks constant can be experimentally determined, and sort of what it means in at least that scenario. (http://physicsnet.co.uk/a-level-physics-as-a2/electromagneti...)

The DeBroglie wave idea is one of my favorite things that came at the dawn of Q&M :). I had a physics professor who posed a very fun question.

Question: Say a man who took first year physics ends up in court for shooting a man (who survived). He claims that he had no idea that his bullet would actually hit the stationary man. While a bystander took a video on his camera phone which shows he aimed right at the guy! He further claimed that the bullet can be considered as a wave and it's wave-like nature gave an uncertainty in his aim that was significant enough to state that he had reason to believe he would not hit the man.

The cops found that his gun fired a bullet at 1000m/s, and the average bullet mass was 3grams (0.003kg). Is what the shooter claims a valid defense? (Hint: use an equation from this page- http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/debrog2.h...). Assume the bullet traverses a 1-D path and ignore relativistic effects of the bullet (ex: just use the rest mass).

Answer here: The debroglie wavelength of the bullet can be calculated as follows. First we know that the 'particle' is not travelling at the speed of light, so substitute c(speed of light) for v(velocity), this is one of debroglies postulates iirc. λ = hv/pv => h/p => h/(m*v)
= 6.63*10^(-34)J*s/(3.0kg*m/S) = 2.21 *10^(-34) m
So no, the man cannot make the claim he did. The object is essentially newtonian! Another way to approach the problem would be the Hiesenberg Uncertainty principle. Hope I did this right,




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[*] posted on 9-7-2015 at 12:35


Whoosh ! Went right over my head by introducing too much too fast.

Wading through the question the best i can, am i to assume that if i could calculate the wavelength (got NaN a lot on the calculator linked to) of the bullet as if it were a wave then if the cycle length of that wave were such that it could not impart energy to the target then it'd all be OK ?

Bullet or Wave : it'd still hit the target if aimed correctly.




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[*] posted on 9-7-2015 at 13:01


Aga: I'm not sure where he's going with this either but try and calculate the DeBroglie wavelength of the bullet first. Then we'll see... (Hint: it's extremely small!)

λ = h/p, with p = mv

No calculator needed even: p = 0.003 kg x 1000 m/s = 3 kg m/s,

So λ = h/3 = 2.2 x 10<sup>-34</sup> m. 'Average' visible light is about 600 nm = 6 x 10<sup>-7</sup> m.


[Edited on 9-7-2015 by blogfast25]




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[*] posted on 9-7-2015 at 13:10


Hmm.

With this jobbie λ = h/p
we got h/(0.003 * 1000), so
6.62606957 x 10<sup>-34 </sup>/ 3
2.2086898 x 10<sup>-34</sup>

= 0.00000000000000000000022086898 pico metres

So very high energy indeed. Hang the man.

[Edited on 9-7-2015 by aga]




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[*] posted on 9-7-2015 at 13:22


Quote: Originally posted by aga  

So very high energy indeed. Hang the man.



No, not high energy. The energy is 'classical': E = 1/2 mv<sup>2</sup> = 150 kJ, enough to kill man of course.

But the bullet's DeBroglie wavelength is extremely small and shot accuracy isn't remotely affected by it. The bullet behaves 'Classically'.

[Edited on 9-7-2015 by blogfast25]




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[*] posted on 9-7-2015 at 13:31


I mean 'very high' in terms of affecting human tissues, not 'high' in comparison with the output of a Star.

Why would a longer wavelength affect the accuracy ?

I can see how the amplitude could be seern as a way for the wave to 'miss' the target but not the wavelength.




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[*] posted on 9-7-2015 at 13:42


Quote: Originally posted by aga  

Why would a longer wavelength affect the accuracy ?



It's to do with the Uncertainty Principle, which I will hit on a few sessions down the line. I'd rather not right now because I don't like mixing concepts in stuff like this (I know how confusing things can get). I will use this specific bullet example when I get to it.

Of course I can't stop smaerd from doing it anyway. ;)

+++++++++

Go back a bit to the Davisson-Germer experiment:

http://hyperphysics.phy-astr.gsu.edu/hbase/davger.html#c1

Here electrons are accelerated to an energy of 54 eV ("electron volt"). If you work out the DeBroglie wavelength associated with those electrons, it turns out to be in the same order of magnitude as the distance (1.65 Angstrom - an old unit of length) between crystal planes in the Ni crystal lattice. This caused diffraction of the electron waves to occur.

From the electrons' energy, the crystal structure and DeBroglie's calculation the latter's hypothesis could be confirmed experimentally. Clearer, quantitative proof of these electrons' 'wavy character' would be hard to find. Without the latter the electrons would simply bounce (be 'reflected') off the nickel.

[Edited on 10-7-2015 by blogfast25]




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[*] posted on 9-7-2015 at 13:52


Right oh. Did seem a bit of a leap from square 1.

I'll ignore all that then, and as a bonus, i'll not mention anything at all that undermines the entire paradigm until after the end-of-course exams.

[Edited on 9-7-2015 by aga]




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[*] posted on 9-7-2015 at 14:27


Quote: Originally posted by aga  

I'll ignore all that then, and as a bonus, i'll not mention anything at all that undermines the entire paradigm until after the end-of-course exams.



Now, THAT you see, I find hard to believe! ;)

Looks like it's going to be one-on-one tuition anyway. Offer 2 cans of beans for the price of one and they'll queue for miles. A free course on the finest scientific paradigm? Two brothers and their dog show up! P-R-I-O-R-I-T-I-E-S, people! :D




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[*] posted on 9-7-2015 at 14:41


Yea sorry if that was too much too fast. The idea is basically to show that "big" things do not behave like small particles. If the particle had a very tiny mass then the debroglie wavelength becomes relevant.

The question is kind of slanted. The idea is basically that if the bullets wavelength was say 2 meter in radius. Then maybe the shooter would not be accountable because if it behaved like a particle (to collide) it would be less likely to hit the man. Similarly the de broglie wavelength of semi-trucks/lorry can be calculated. I liked it because it shows that something 'small' and 'fast' on the human scale still isn't really relevant for quantum mechanics.

Type in the mass of an electron into that equation and it's pretty clear that electrons have wavelengths that are not negligable.




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[*] posted on 9-7-2015 at 14:43


Fair point, smaerd.

Zombie would be late for his own funeral, so I'll wait to call it a day on this modulette yet.

[Edited on 9-7-2015 by blogfast25]




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[*] posted on 9-7-2015 at 14:48


Quote: Originally posted by blogfast25  
Now, THAT you see, I find hard to believe!

Honest : i won't say anything at all about that until after the course.

More people will turn up later.

There's Timezones involved in this global classroom, so some are asleep right now - not cos they find it boring, just that it's 4am where they are.




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[*] posted on 9-7-2015 at 15:17


I'm very interested in this subject and will be following this thread as it progresses. I don't yet have any questions, and certainly don't posses anything of use to add, but I am very appreciative for blogfast's and smaerd 's time and contributions. Thank you, wizards. Threads like these bring needed balance to the "don't say duck" and "joke threads." Please, don't let a lack of posters deter you. I believe a great many people will read and learn from it, even if they don't post.



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[*] posted on 9-7-2015 at 15:35


Time zones: someone is going to have to do something about that, sooner or later!

Thanks Bot0nist. Your subscription fee of $0.00 will not be deducted from your charge card.




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[*] posted on 9-7-2015 at 18:17


This is fascinating material and a review for all I have forgotten.

I found the explanation for the shape of the black body radiation curve vs temperature to be the most astounding. This explains how the color of a heated metal indicates its temperature. Was it de Broglie or was it Planck that discovered this?





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[*] posted on 9-7-2015 at 18:28


Planck.
https://en.wikipedia.org/wiki/Planck%27s_law




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[*] posted on 9-7-2015 at 19:52


Ditto what Bot0nist said, no questions yet, nothing to add, but will certainly be reading this.
Thanks for doing this, Blogster.




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[*] posted on 9-7-2015 at 20:55


Great idea for a thread!

The bullet question somewhat confused me... It's hard to match these quantum mechanical effects to real-life macro analogies. What I guess would make sense is that if the bullet's de Broglie wavelength matched (or at least was on the same scale as), say, the width of the nozzle of the gun, diffractive effects would lead one to believe (on the macroscopic scale) that there is some uncertainty in whether or not the bullet actually hits the guy right in front of it. Not exactly sure how correct this is, but the way I usually think of it is that even though something big like a truck has some tiny de Broglie wavelength, it could never pass through a sufficiently small opening for diffractive effects to occur, and thus its wave character to be even noticeable, whist electrons and other subatomic particles are on a scale such that these wave-like effects do come into play.

Also, I was actually lucky enough to do some labs this year regarding the photoelectric effect, and using the stopping potential for various frequencies to calculate planck's constant :) Physics just blows my mind, and I can't wait to see where this thread goes!




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[*] posted on 10-7-2015 at 03:17


Re. matter waves of large objects, one way of looking at it is like this.

λ = h/mv

With mass m an indication of size of the object. Obviously in the limit of m to ∞, λ tends to 0 m. 0 m obviously means no waves. The larger the object, the less 'wavy' it behaves.

Since as Zombie's gone AWOL, I'll put up the next modulette now. Z. will get detention and extra tuition, if he needs it.




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