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Topic: Calculations based on electrons  (Read 4657 times)

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Offline enzzz

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Calculations based on electrons
« on: October 22, 2008, 01:14:57 PM »
Well okay, my second topic and I won't spam any more, I'll put all the questions here.
I'm not sure, but I wanted to ask, is it possible to calculate every property of an element with electrons? I'm asking this because thinking through formulas makes me understand everything very easily.

If it can, could anyone give me some basic formulas to do so (since I had troubles searching from google, all I got was some graphs about those values, but how did those values come... No idea!
The only formula I succeeded with was E=(-k(Z^2))/(n^2) which explains the potential energy of electron...
For example, how can I calculate:
1) Melting point
2) Boiling point
3) Atomic Radius ( I have tried to make a formula by myself, but I found out that also subshells affect so it got too complicated for me at the moment to create a precise formula...

Also, how do electrons affect the colour of an object? And taste?

If there are any other properties that you can calculate with electrons, please add them, and I would be so, so thankful : )


Offline cliverlong

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Re: Calculations based on electrons
« Reply #1 on: October 22, 2008, 01:40:46 PM »
OK.

I'm guessing this is an attempt to answer a question along the lines of

"What properties of a substance are affected by electrons? Can we make calculations from some elementary information about the atoms in a compound to deduce properties of a molecule or compound"

That's probably too big a question to answer in a systematic way but here is my contribution.

In a sense most (all?) properties we as humans can sense are affected by electrons. What is more important is the interaction between the electrons between atoms - that is chemistry my old chum. So you could describe every differerent type of chemical reaction as examples - might take some time .

My feeling is you want to tackle some of the concepts before you tried to chuck any maths at it.

Regarding physical properties such as melting and boiling point have a search on this forum about the bonding in molecules. I made a contribution to a thread that distinguished between inter-molecular and intra-molecular forces that may be relevant. There are other posts in that thread that are useful.

So where do the calculations come in? I would suggest that once you have identified the type of interactions (measuring energy and maybe entropy, not force) you might be able to do some kind of calculation. I suppose what you are doing is trying to build a mathematical model of the atom - or at least the interaction of electrons. I guess the calculation would be "quantum" in nature and involve complex numbers and probability. So I don't think you could end up with a "number" for the interaction - which is what I think you are looking for. Beyond that I don't really have an idea.

As far as colour is concerned, I would you suggest you look up three topics

What is light?
Why do different atoms have different spectra?
Why are transition metal compounds coloured and how can that colour be modified for "complex" transition metal compounds that have ligands (d-orbital splitting)?

I will stop now.

Clive

Offline Borek

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Re: Calculations based on electrons
« Reply #2 on: October 22, 2008, 01:46:27 PM »
There are no simple formulas like the ones you are looking for.

I found out that also subshells affect so it got too complicated for me at the moment to create a precise formula...

And subshells are one of the easiest parts.

In general - to calculate properties like the ones you are looking for you have to solve Schroedingers equation. This equation has exact solutions only for the simplest case - hydrogen atom. For many other cases we can find numerical solutions - but almost always they are only approximate. The more atoms - the more approximate solution.
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Offline enzzz

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Re: Calculations based on electrons
« Reply #3 on: October 22, 2008, 02:10:45 PM »
There are no simple formulas like the ones you are looking for.

I found out that also subshells affect so it got too complicated for me at the moment to create a precise formula...

And subshells are one of the easiest parts.

In general - to calculate properties like the ones you are looking for you have to solve Schroedingers equation. This equation has exact solutions only for the simplest case - hydrogen atom. For many other cases we can find numerical solutions - but almost always they are only approximate. The more atoms - the more approximate solution.

Yes well, they probably are, but even approximate could help me.
About the subshells, okay, they are easy yes, but constructing a formula is another thing : ). Anyway what I have thought so far of atomic radius:
I've used this one to try and clear things for me:
http://en.wikipedia.org/wiki/Atomic_radius#Calculated_atomic_radius

since it's calculated I thought it would be the easiest one to find logic in..
What I found was:
since H has 53 and He has 31, and only difference they have is that He has more electrons and protons in it. From that I was able to tell that each electron or proton makes atomic radius smaller.

Going on to the next line, I can see that each shell adds more to it ( since Li has 167 compared to H's 53. )

Okay.. Now I'll skip a little and start from K.
Difference between K and Ca is much much greater than the difference between rest of elements in this period. I explained that to myself that they are the ones who have only s orbital filled. And since K has two times less electrons it has a lot bigger atomic radius. (K has 1 while Ca has two, which means s orbital is filled). And by that logic I also found out that if an orbital fits more electrons the lesser the gap of atomic radius change goes... So all the elements from Sc to Zn have the difference quite low ( since they have d orbital ).
And from Ga to Kr the difference gets bigger, because their last orbital fits just 6 electrons.

Actually after writing this text, I think it should be fairly easy to calculate the formula ( I don't know why I thought it was way too difficult for me before ).

Anyway, I hope you understood my text, because I had hard times explaining it, because I'm not even slightly sure if I'm on the right track.
And if you see some logic errors then please tell me : )

Offline Astrokel

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Re: Calculations based on electrons
« Reply #4 on: October 22, 2008, 02:22:53 PM »
well you are pretty right on the idea and since you are aware of transition elements having d-orbitals, you should probably aware of proper terms like screening effect, effective nuclear charge, no? why do you want to come up with a formula? i would say it is not easy and as Borek mentioned, it involves wave functions and there are many factors to account for.
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Offline enzzz

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Re: Calculations based on electrons
« Reply #5 on: October 22, 2008, 02:36:46 PM »
well you are pretty right on the idea and since you are aware of transition elements having d-orbitals, you should probably aware of proper terms like screening effect, effective nuclear charge, no? why do you want to come up with a formula? i would say it is not easy and as Borek mentioned, it involves wave functions and there are many factors to account for.
I'm trying to build an excel sheet where it contains data about each element (and their properties) so I thought calculating out atomic radius would be little bit easier and would make a little bit more sense than writing them over from wikipedia. Also different formulas really help me to memorize different things and when I'm trying to explain the logic of these formulas to myself I understand everything much better. About the d-orbitals, yes I think I have learned about these at school, but I didn't really remember much about them, since the teacher didn't explain much, he just said that they transition metals are in the d-group (or something). Actually I discovered this from looking at their configuration.

About the screening effect.. There's a great language barrier for me in chemical terminology, since I have never learned it in English so it's quite new experience for me. I googled it and found out it was same as shielding effect, I don't think I knew that effect before, but well I understand this and I think my explanation of atomic radius included that. Same goes for "effective nuclear charge".

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