Chemical Forums
Chemistry Forums for Students => Inorganic Chemistry Forum => Topic started by: kapital on May 29, 2013, 05:07:31 AM
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Is 1s orbital inside 2s orbital? Do they cover each other?
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They occupy the same space. I would not say one is inside the other, although 1s is definitely smaller, so the space it occupies fits into the space occupied by the 2s. But even that is a little bit clumsy way of looking at things, as technically orbitals don't "end" - they occupy whole space to the infinity. What we draw is the surface in which probability of finding electrons has some arbitrarily selected value, like 0.9.
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They occupy the same space. I would not say one is inside the other, although 1s is definitely smaller, so the space it occupies fits into the space occupied by the 2s. But even that is a little bit clumsy way of looking at things, as technically orbitals don't "end" - they occupy whole space to the infinity. What we draw is the surface in which probability of finding electrons has some arbitrarily selected value, like 0.9.
If "They occupy the same space" why then " would not say one is inside the other"?
If the s orbitals are spheres, with nucleus in the centere, thene I cannot se how the 1s orbital is not inside 2s orbital and so one? (exept if the 1s orbital is not part of 2s orbital and the 2s orbital is not real sphere but just part of it)
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"Inside" suggests one is part of another, which is not true - they are separate entities.
It can be only semantics.
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@OP
You are having difficulty because your conceptual understanding of an orbital is poor. s-orbitals are not simply "shells". They are probability distributions and if you look at the form of the radial wavefunction for an s orbital, you will see that there is probability of an electron being at all regions of space, not just as the maximum value as it is typically drawn. This is the primary distinction between the Bohr model of the atom and more sophisticated models informed by the Schrodinger equation. For example, higher order s orbitals (n > 1) have multiple nodes. Even an electron in the 6s orbital has decent probability of being located very close to the nucleus at any given time.
E.g., see the picture of the 6s orbital under the "Shapes of Orbitals" section here:
http://en.wikipedia.org/wiki/S-orbital
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All s orbitals have nonzero density at the nucleus, so they overlap at least there.
There is more. The distribution ψ of different orbitals are othogonal, and for s orbitals, ψ is a real (non-complex) function of distance only. To obtain a zero integral over space of the product of two ψ distributions, these must change their signs at different radius.
For instance, 1s and 2s being positive near the nucleus, the zero integral of product requires 2s to become negative before 1s has decreased too much. So significant overlapping is mandatory. Same for 1s 3s, for 2s 3s...
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""Inside" suggests one is part of another, which is not true - they are separate entities. "
"So significant overlapping is mandatory. "
So which one is it? To me this to statments look contadictive.
And if orbitals are "just" space with some probability of findig electron, how can they have such a meaning in chemistr(molecular orbitals in bonding, interactions, stability,..)
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""Inside" suggests one is part of another, which is not true - they are separate entities. "
"So significant overlapping is mandatory. "
So which one is it? To me this to statments look contadictive.
No contradiction here.
Lame analogy: in the air you have 79% of nitrogen and 21% of oxygen. Would you say that oxygen is inside nitrogen, or would you agree they are separate, but both occupy the same volume?
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So if the electrons are like molecules of gas from your analogy, can they interchange?
Can electron from 1s "go" into 2s orbital and one from 2s orbital in 1s orbital.
And in the wikipedia it says orbitals are mathematical functions. Is that mean classical mathematical functins( f(x)=(x,y,.)) or it si somthing diffrent?
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So if the electrons are like molecules of gas from your analogy, can they interchange?
Can electron from 1s "go" into 2s orbital and one from 2s orbital in 1s orbital.
Yes and no. If there is one electron on 1s it can get excited to 2s. But they can't just "interchange" as they are indistinguishable.
And in the wikipedia it says orbitals are mathematical functions. Is that mean classical mathematical functins( f(x)=(x,y,.)) or it si somthing diffrent?
Not sure what you mean by "classical functions", but I guess the answer is yes. See them here for example: http://panda.unm.edu/Courses/Finley/P262/Hydrogen/WaveFcns.html (rightmost column contains the final function, other columns are related to the way it is calculated).
Note that these functions describe orbitals, but not in a direct way. They are solutions to the Schroedinger equation. When squared, they give the probability density of finding the electron is space around nucleus.
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So if electrons are indistinguishable, for example if one ectron of 1s and one electron of 2s orbitals are in the 1s orbital space, how woud 2s orbital electron "know " that he will after from some point in time move moore in 2s orbital and the other wont.
And why have 2s electron higher energy? What kind of energy that is?
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Electrons don't have an infinitely localized volume element. You can't think of electrons being "here" or "there" at any one point in time. Essentially we can only measure averages. The average distance between the nucleus and a 1s electron is smaller than the average distance between the nucleus and a 2s electron - hence the average potential energy of the latter exceeds that of the former. This does not mean that at every point in time the 2s electron must be farther away than the 1s electron. It means that if you were able to take a snapshot of the electron position at a certain time, the probability you would see the 2s electron farther out would be pretty large.
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Electrons don't have an infinitely localized volume element. You can't think of electrons being "here" or "there" at any one point in time.
Why not? If we cannot measure precise electron location at thime, we could at least think he has one, or not?
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No, by Heisenberg principle it doesn't have an exact position.
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Ok, what abaut my previus question, if orbitals are "just" spaces with some possibility of electron finding, how can they have such apllications in bonds stability, interactions, reactions
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Think about an orbital as a "charge cloud" - it interacts with another similar "charge clouds". The way these charges interact depends on the cloud shape - different shapes mean different interaction and different properties of the bonds.
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Ok, what abaut my previus question, if orbitals are "just" spaces with some possibility of electron finding, how can they have such apllications in bonds stability, interactions, reactions
Because those properties you mention are also all based on probability and averages. In the macro-world, those probabilities are very predictable, and so we see deterministic behavior. Not so at the quantum world, where events are rolls of the dice and completely unpredictable. Physical rules (such as orbitals) just tell us how likely certain faces on the dice are likely to show up.
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A simple way to describe the distribution of electrons in 1s and 2s atomic orbitals would be as follows: Most of the time an electron in a 2s orbital will be found in a region further from the nucleus than an electron in a 1s orbital. This region is not normally occupied by an electron in 1s orbital. Occasionally; however, the electron in the 2s orbital will be near the nucleus, a region normally occupied by an electron in a 1s orbital. Similarly, occasionally an electron in the 1s orbital occupies a region far from the nucleus normally occupied by an electron in the 2s orbital.The same is true for an electron in a 2p, 3p, orbitals; that is, an electron in these orbitals is usually further away from the nucleus, but occasionally it occupies a region normally occupied by a 1s electron. Would you then say, a 1s orbital is inside a 3p orbital? As you see, the solid model of orbitals is misleading.