The nature and shape of atoms - Revision history

Apm: /* Notes */ added note on no exact solutions beyond hydrogen

2021-05-27T19:17:36Z

Notes: added note on no exact solutions beyond hydrogen

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	Exact solutions exist only for the hydrogen atom (and one electron ions).		Exact solutions exist only for the hydrogen atom (and one electron ions).
	As soon as there is more than one electron mutual electrostatic repulsion drastically changes the results.		As soon as there is more than one electron mutual electrostatic repulsion drastically changes the results.
	There are approximation methods. An important basic one among them is the "Gram–Schmidt process".		Exact solutions are no longer possible. There are iterative approximation methods.
			An important basic one among them is the "Gram–Schmidt process".

	Spherical harmonics are often depicted as surfaces where the magnitude value is misused as radius. These (tear shaped) plots can be easily confused with molecular orbitals (bean shaped). But molecular orbitals are constant value surfaces of the square of the absolute value of the spherical harmonic angular part of the wave function multiplied by the radial part of the wave function.		Spherical harmonics are often depicted as surfaces where the magnitude value is misused as radius. These (tear shaped) plots can be easily confused with molecular orbitals (bean shaped). But molecular orbitals are constant value surfaces of the square of the absolute value of the spherical harmonic angular part of the wave function multiplied by the radial part of the wave function.

Apm: /* d orbitals and their hybridization */

2021-05-27T19:15:33Z

d orbitals and their hybridization

← Older revision		Revision as of 21:15, 27 May 2021
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	This gas is of especial interest for advanced [[mechanosynthesis]] of diamond because a triple bond between two carbon atoms leaves just two bonds capped with hydrogen. When assembling something like a block of diamond instead of hydrocarbon chains there is very little surface area and all that excessive hydrogen would need to be reacted to water leading to a massive energy excess.		This gas is of especial interest for advanced [[mechanosynthesis]] of diamond because a triple bond between two carbon atoms leaves just two bonds capped with hydrogen. When assembling something like a block of diamond instead of hydrocarbon chains there is very little surface area and all that excessive hydrogen would need to be reacted to water leading to a massive energy excess.

	=== d orbitals and their hybridization ===		=== d and f orbitals and their hybridization ===

	* TODO ...		* TODO ...

Apm: /* Beside sphere shaped nodes there can be two other shapes of nodes */ formatting - fat

2021-05-27T19:14:19Z

Beside sphere shaped nodes there can be two other shapes of nodes: formatting - fat

← Older revision		Revision as of 21:14, 27 May 2021
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	In the 2D drum model imagine the left side of the drum going up-then-down and the right side going down-then-up.		In the 2D drum model imagine the left side of the drum going up-then-down and the right side going down-then-up.
	It's a bit more complicated in 3D atoms though.		It's a bit more complicated in 3D atoms though.
	* There are nodal surfaces that have the shape of nested double cones (and one plane in case of even node-surface numbers) dividing the wave function in one double lobe and some rings. (Rings only if there's more than one node-surface.)		* There are nodal surfaces that have the shape of '''nested double cones''' (and one plane in case of even node-surface numbers) dividing the wave function in one double lobe and some rings. (Rings only if there's more than one node-surface.)
	* There are nodal surfaces that are all flat planes which divide the wave function into orange slice shaped antinodes.		* There are nodal surfaces that are all '''flat planes''' which divide the wave function into '''orange slice shaped antinodes'''.
	The former is described by the "secondary quantum number" with symbol "l". Again numbers of l have associated letters (1=s 2=p 3=d 4=f). The latter is described by the "magnetic quantum number" with symbol "m"		The former is described by the "secondary quantum number" with symbol "l". Again numbers of l have associated letters (1=s 2=p 3=d 4=f). The latter is described by the "magnetic quantum number" with symbol "m"

Apm: /* Atoms are mostly electrons by volume. Soft electron density clouds. No empty space. */ improved on correctness - hopefully

2021-05-27T19:08:18Z

Atoms are mostly electrons by volume. Soft electron density clouds. No empty space.: improved on correctness - hopefully

← Older revision		Revision as of 21:08, 27 May 2021
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	Electrons density clouds in atoms can not be smaller than the innermost electron shell. <br>		Electrons density clouds in atoms can not be smaller than the innermost electron shell. <br>
	This is because of a see-saw effect that:		This is partly because of a see-saw effect that:
	* makes tightly constrained electrons move more vigorously and that		* makes tightly constrained electrons move more vigorously and that
	* makes electrons with a very precise temperature (very cold is easiest) very big		* makes electrons with a very precise temperature (very cold is easiest) very big
	This see-saw effect is called the "Heisenberg uncertainty relationship".		This see-saw effect is called the "Heisenberg uncertainty relationship". <br>
			Where it exactly equilibrates out is determined by the Schrödinger equation.

	Beside the electron density cloud interpretation there is also the probability density cloud interpretation. <br>		Beside the electron density cloud interpretation there is also the probability density cloud interpretation. <br>

Apm: /* How do atoms work? */ added notes on nulceus

2021-05-27T19:01:52Z

How do atoms work?: added notes on nulceus

← Older revision		Revision as of 21:01, 27 May 2021
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	A decent intuitive picture for atoms are soft/blurry clouds that are (in a certain mathematical sense) as smooth as possible and can exert soft forces on other of these clouds in case they come close. There are no hard surfaces and certainly no sharp planet like orbits.		A decent intuitive picture for atoms are soft/blurry clouds that are (in a certain mathematical sense) as smooth as possible and can exert soft forces on other of these clouds in case they come close. There are no hard surfaces and certainly no sharp planet like orbits.
	These clouds are made of so called "electron density". Atoms basically are electrons ~~(determining all volume an chemistry)~~.		These clouds are made of so called "electron density". Atoms basically ''are'' electrons.
	The electrons in atoms (especially the outermost ones) not just have the size of atoms they literally are the atoms.		The electrons in atoms (especially the outermost ones) not just have the size of atoms they literally are the atoms.
			The nucleus of an atom gives it basically just its mass (which is almost irrelevant at the nanoscale).
			<small>And sometimes weak magnetic properties that can in the context of [[mechanosynthesis]] be ignored. </small>

	Electrons in solids can occupy a space that is much bigger than an atom. As an example: Free electrons in metals are of such nature.<br>		Electrons in solids can occupy a space that is much bigger than an atom. As an example: Free electrons in metals are of such nature.<br>

Apm: /* Atoms are mostly electrons by volume. Soft electron density clouds. No empty space. */ factored out all of the mad stuff on a separate page

2021-05-27T18:54:28Z

Atoms are mostly electrons by volume. Soft electron density clouds. No empty space.: factored out all of the mad stuff on a separate page

← Older revision		Revision as of 20:54, 27 May 2021
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	The electrons in atoms (especially the outermost ones) not just have the size of atoms they literally are the atoms.		The electrons in atoms (especially the outermost ones) not just have the size of atoms they literally are the atoms.

	~~<small>~~		Electrons in solids can occupy a space that is much bigger than an atom. As an example: Free electrons in metals are of such nature.<br>
	~~'''Side note A:'''~~ Electrons in solids can occupy a space that is much bigger than an atom. As an example: Free electrons in metals are of such nature.<br>

	~~'''Side note B:'''~~ Electrons density clouds in atoms ~~(atomic orbitals – electrons in stable states belonging to the atom)~~ can not be smaller than the innermost electron shell. If electrons in atoms would be smaller than the innermost electron shell (in a non virtual sense - more on that later) then they would need to have so much impulse (and kinetic energy) that they would leave the atom promptly.		Electrons density clouds in atoms can not be smaller than the innermost electron shell. <br>
	~~Why? Because electrons clouds in atoms have the smallest possible product~~ of ~~blurriness in space and blurriness in mass~~-motion (proper term: impulse). Squeezing the cloud any further down in space blows up the electron cloud in an abstract but very useful mass-motion space (proper term: impulse space). A "space" which describes a distribution over motion directions and speeds. This smallest possible product of blurriness in space and blurriness in impulse is called the "plank constant".		This is because of a see-saw effect that:
	~~The seesaw~~ effect that:
	* makes tightly constrained electrons move more vigorously and that		* makes tightly constrained electrons move more vigorously and that
	* makes electrons with a very precise temperature (very cold is easiest) very big		* makes electrons with a very precise temperature (very cold is easiest) very big
	is called the "Heisenberg uncertainty relationship".		This see-saw effect is called the "Heisenberg uncertainty relationship".
	~~</small>~~

	~~There are~~ the earlier mentioned "virtual energy fluctuations" of electrons (not to confuse with the related virtual matter antimatter particle pairs arising from vacuum) which "exist" in the sense that they lead to measurable effects (forces). They do not "exist" though in the sense that they can be directly measured / observed. The electron cloud ~~size that would correspond to these fluctuations can be much smaller than atoms (how small open~~ is ~~an question - but infinitely small points are a sure sign of a model breakdown).~~		Beside the electron density cloud interpretation there is also the probability density cloud interpretation. <br>
			While useful mathematically the author of this wiki is not a fan. <br>
	~~Collision experiments can strongly mislead one to believe that one can catch a snapshot of the electron when it was orbiting~~ the ~~nucleus in a classical way, since with a collision one can force an atomic orbital electron~~ cloud ~~to "collapse" to a much smaller size than the atom. There are two reasons why this is problematic: "hidden variables" and "delayed choice". An elaboration follows~~.		See "[[on the probability interpretation of quantum mechanics]]" for details. Warning this gets a bit technical.

	~~Such a collision experiment could look roughly like so (largely simplified to be suitable as thought experiment):~~
	~~One shoots e.g. a second electron (a free electron) at a stable atomic orbital electron cloud in a hydrogen atom.~~
	~~This other "projectile" electron is best pictures as a wave package in~~ the ~~shape~~ of ~~cloudy disk much thinner than the atom.~~
	~~The diameter of the disk~~ is ~~of no particular importance it can be much bigger than the diameter of the atom.~~
	~~(Side-note: An actual experiment would have more of~~ a ~~fat disk / stream / dispersed wave front, with many electrons hitting many atoms~~.)

	In the probabilistic view (Copenhagen interpretation of QM) one gets some collision probabilities from the overlap of the two electron clouds that occurs when the disk shaped projectile electron cloud passes through the electron that constitutes the majority of hydrogen atoms volume. In case a collision is detected the location of this collision and thus the location of the electron of the atom can (theoretically) be resolved much finer than the size of the atom.

	~~Assuming the electron was already in this overly localized spot before~~ the ~~collision occurred is inconsistent with local hidden variables though. Well one still can ponder about global hidden variables (pilot wave~~ interpretation of ~~QM).~~

	~~Assuming the electron was in the measured freshly kicked out strongly localized state right after the collision is also inconsistent with~~ quantum mechanics. Actually its more like all possible collisions occur in parallel (superposition of many freshly kicked out states) and the wave collapse only happens when the scattered electrons hit the detector (multi world interpretation of QM) or even later when you feed the measurement results without detour into a quantum computer. (One could say that parallel worlds "exist" in the sense that they can do useful work in form of quantum-parallel-computation and have measurable effects. Parallel worlds don't "exist" in the sense that they can't provide as much power as actual parallel computation - not that it could be implemented, and they dont "exist" in the sense that they can't be checked one after another exhaustively.)

	=== Only because electrons are forced to "stack" on each other directed chemical bonds exist. ===		=== Only because electrons are forced to "stack" on each other directed chemical bonds exist. ===

Apm: /* Atoms are mostly electrons by volume. Soft electron density clouds. No empty space. */ completed Heisenberg see-saw analogy

2021-05-27T17:43:03Z

Atoms are mostly electrons by volume. Soft electron density clouds. No empty space.: completed Heisenberg see-saw analogy

← Older revision		Revision as of 19:43, 27 May 2021
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	'''Side note B:''' Electrons density clouds in atoms (atomic orbitals – electrons in stable states belonging to the atom) can not be smaller than the innermost electron shell. If electrons in atoms would be smaller than the innermost electron shell (in a non virtual sense - more on that later) then they would need to have so much impulse (and kinetic energy) that they would leave the atom promptly.		'''Side note B:''' Electrons density clouds in atoms (atomic orbitals – electrons in stable states belonging to the atom) can not be smaller than the innermost electron shell. If electrons in atoms would be smaller than the innermost electron shell (in a non virtual sense - more on that later) then they would need to have so much impulse (and kinetic energy) that they would leave the atom promptly.
	Why? Because electrons clouds in atoms have the smallest possible product of blurriness in space and blurriness in mass-motion (proper term: impulse). Squeezing the cloud any further down in space blows up the electron cloud in an abstract but very useful mass-motion space (proper term: impulse space). A "space" which describes a distribution over motion directions and speeds.		Why? Because electrons clouds in atoms have the smallest possible product of blurriness in space and blurriness in mass-motion (proper term: impulse). Squeezing the cloud any further down in space blows up the electron cloud in an abstract but very useful mass-motion space (proper term: impulse space). A "space" which describes a distribution over motion directions and speeds. This smallest possible product of blurriness in space and blurriness in impulse is called the "plank constant".
	This smallest possible product of blurriness in space and blurriness in impulse is called the "plank constant".		The seesaw effect that:
	The seesaw effect that makes tightly constrained electrons move more vigorously is called the "Heisenberg uncertainty relationship")		* makes tightly constrained electrons move more vigorously and that
			* makes electrons with a very precise temperature (very cold is easiest) very big
			is called the "Heisenberg uncertainty relationship".
	</small>		</small>

Apm: /* Atoms are mostly electrons by volume. Soft electron density clouds. No empty space. */ made the side-notes into small text

2021-05-27T17:35:56Z

Atoms are mostly electrons by volume. Soft electron density clouds. No empty space.: made the side-notes into small text

← Older revision		Revision as of 19:35, 27 May 2021
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	The electrons in atoms (especially the outermost ones) not just have the size of atoms they literally are the atoms.		The electrons in atoms (especially the outermost ones) not just have the size of atoms they literally are the atoms.

			<small>
	'''Side note A:''' Electrons in solids can occupy a space that is much bigger than an atom. As an example: Free electrons in metals are of such nature.<br>		'''Side note A:''' Electrons in solids can occupy a space that is much bigger than an atom. As an example: Free electrons in metals are of such nature.<br>

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	This smallest possible product of blurriness in space and blurriness in impulse is called the "plank constant".		This smallest possible product of blurriness in space and blurriness in impulse is called the "plank constant".
	The seesaw effect that makes tightly constrained electrons move more vigorously is called the "Heisenberg uncertainty relationship")		The seesaw effect that makes tightly constrained electrons move more vigorously is called the "Heisenberg uncertainty relationship")
			</small>

	There are the earlier mentioned "virtual energy fluctuations" of electrons (not to confuse with the related virtual matter antimatter particle pairs arising from vacuum) which "exist" in the sense that they lead to measurable effects (forces). They do not "exist" though in the sense that they can be directly measured / observed. The electron cloud size that would correspond to these fluctuations can be much smaller than atoms (how small open is an question - but infinitely small points are a sure sign of a model breakdown).		There are the earlier mentioned "virtual energy fluctuations" of electrons (not to confuse with the related virtual matter antimatter particle pairs arising from vacuum) which "exist" in the sense that they lead to measurable effects (forces). They do not "exist" though in the sense that they can be directly measured / observed. The electron cloud size that would correspond to these fluctuations can be much smaller than atoms (how small open is an question - but infinitely small points are a sure sign of a model breakdown).

Apm: /* Atoms are mostly electrons by volume. Soft electron density clouds. No empty space. */

2021-05-27T17:33:48Z

Atoms are mostly electrons by volume. Soft electron density clouds. No empty space.

← Older revision		Revision as of 19:33, 27 May 2021
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	A decent intuitive picture for atoms are soft/blurry clouds that are (in a certain mathematical sense) as smooth as possible and can exert soft forces on other of these clouds in case they come close. There are no hard surfaces and certainly no sharp planet like orbits.		A decent intuitive picture for atoms are soft/blurry clouds that are (in a certain mathematical sense) as smooth as possible and can exert soft forces on other of these clouds in case they come close. There are no hard surfaces and certainly no sharp planet like orbits.
	These clouds are made of so called "electron density". Atoms basically are electrons (determining all volume an ~~chemisty~~).		These clouds are made of so called "electron density". Atoms basically are electrons (determining all volume an chemistry).
	The electrons in atoms (especially the outermost ones) not just have the size of atoms they literally are the atoms.		The electrons in atoms (especially the outermost ones) not just have the size of atoms they literally are the atoms.

Apm: /* Atoms are mostly electrons by volume. Soft electron density clouds. No empty space. */

2021-05-27T17:33:36Z

Atoms are mostly electrons by volume. Soft electron density clouds. No empty space.

← Older revision		Revision as of 19:33, 27 May 2021
Line 6:		Line 6:

	A decent intuitive picture for atoms are soft/blurry clouds that are (in a certain mathematical sense) as smooth as possible and can exert soft forces on other of these clouds in case they come close. There are no hard surfaces and certainly no sharp planet like orbits.		A decent intuitive picture for atoms are soft/blurry clouds that are (in a certain mathematical sense) as smooth as possible and can exert soft forces on other of these clouds in case they come close. There are no hard surfaces and certainly no sharp planet like orbits.
	These clouds are made of so called "electron density". Atoms basically are electrons.		These clouds are made of so called "electron density". Atoms basically are electrons (determining all volume an chemisty).
	The electrons in atoms (especially the outermost ones) not just have the size of atoms they literally are the atoms.		The electrons in atoms (especially the outermost ones) not just have the size of atoms they literally are the atoms.