[RGraham9]

Hi , i am curious as to why the density of alkali metals increase down the group on the Periodic Table ?
Is it because , upon going down the ground , the number of electrons for each atom increases , thus the number of protons and neutrons increases too , resulting in a much heavier atom (because the mass of an atom is dependent on the neutrons and protons that an atom has.) ?
Thanks ! Sorry for the trouble !

[thetada]

Density is concerned with mass and volume. You're right that the increasing number of protons and neutrons causes mass to increase down the group, but the increasing number of electrons also causes the volume to increase down the group. Volume is a function of atomic radius, which is affected by the number of electrons, the number of electron shells and the strength of attraction between the nucleus and the electrons. Since, as we know, density increases, it must mean that the rate at which mass increases down the group exceeds the rate at which volume increases. One way to think about it is like this: most of the volume of an atom is empty space so there is a lot of room to add extra protons and neutrons. However, doing so will affect the strength of attraction between the nucleus and the electrons, which in turn will affect the atomic radius. It's a case of competing factors. Basically, while mass and atomic radius both increase down the group, mass does just a bit more increasing than volume such that the ratio of mass to volume also increases.

[RGraham9]

Ah i get it now ! Thank you for the explanation. Appreciate the help a lot !

[Enthalpy]

[...] most of the volume of an atom is empty space [...]

I disagree with that detail. The electrons take all the volume of the atom.

[thetada]

That's interesting. Certainly I agree that electrons make use of all the space but surely at no time do they occupy all of the space? That is, there is always a lot of space between the electrons. Otherwise how could atoms be compressed into so much smaller of a volume in celestial bodies like neutron stars and black holes?

[Corribus]

That's interesting. Certainly I agree that electrons make use of all the space but surely at no time do they occupy all of the space? That is, there is always a lot of space between the electrons. Otherwise how could atoms be compressed into so much smaller of a volume in celestial bodies like neutron stars and black holes?

Yours is a very classical, particle-centric interpretation of atomic structure. In the quantum view, electrons do not have precisely defined locations, which is why we speak in terms of probability densities. Remember, they are waves as well. In a manner of speaking, there is no empty space between electrons because this implies that electrons are located at specific points in space - in reality electrons are located at varying degrees of everywhere at the same time. This doesn't change the fact that your explanation is basically right, and I think for the most part it's fine for a high school level understanding - but rather than speaking of "atoms being mostly empty space with a few electrons scattered here and there", it would be more appropriate to speak of most of the atomic volume having very low average mass density, because only a small electronic mass is averaged over a comparatively enormous (and, if we're being honest, not particularly well-defined) volume.

(In the case of exotic matter like that found in neutron stars, the gravity is so large that it overwhelms the "pressure" created by electrostatic interactions. Neutron stars have no electrons, though - the gravity is so great it causes protons and electrons to combine and form neutrons. So, I don't think extreme situations like this are particularly relevant to a discussion about atomic structure.)

[thetada]

Thanks that's very helpful.

[Enthalpy]

[...] at no time do they occupy all of the space?

Electrons are (or occupy, I don't care) orbitals almost always, and orbitals are stationary. So "at no time" isn't the proper approach. Stationary is almost a synonym of static and of immobile, the essential difference begin that the phase of the wavefunction varies over the position, and this gives some orbitals an orbital momentum and a magnetic momentum. Though, the amplitude of the wavefunction is independent of time.

Also, interactions are computed by the contribution of all the locations where the wavefunction is nonzero (or non-negligible). Or better, the locationS of the wavefunctionS. In this sense, since each particle acts from all the possible positions, it is everywhere at the same time.

Some reasons to keep the idea of particle are that its charge for instance doesn't split. But "particle" shouldn't be interpreted as "concentrated".

[thetada]

Thanks Enthalpy,

It seems as if you're saying that the orbital is the electron and that any movement of the electron can be interpreted in terms of the movement of the orbital, by its angular momentum. How does this sit with Heisenberg's principle that one cannot simultaneously record the position and the momentum of the electron? Clearly I'm conceiving of electrons as little dots that zing around their capacious orbitals, which I wholly accept does not take sufficient account of their wave properties.

I often analogize electrons as moths buzzing around a light bulb. I like that it gives a familiar example of how the attraction between two bodies need not dictate that the distance between them always decreases until they are touching. Also I like the fact that the path each moth follows is effectively unpredictable. Based on this discussion, I begin to worry that the analogy is unacceptably misleading even at the senior high school level. Does anyone have any thoughts on this?

[Corribus]

I often analogize electrons as moths buzzing around a light bulb. I like that it gives a familiar example of how the attraction between two bodies need not dictate that the distance between them always decreases until they are touching. Also I like the fact that the path each moth follows is effectively unpredictable. Based on this discussion, I begin to worry that the analogy is unacceptably misleading even at the senior high school level. Does anyone have any thoughts on this?

The emphasized phrase is the problem. Electrons don't follow paths. They don't have defined locations and they don't have defined trajectories. It's important to abandon words and phrases that imply that they do.  I understand this is difficult to do because we are drawn to classical analogies to help us understand exotic concepts. At the high school level, honestly, it's probably fine: those of us who have moved beyond the high school level have a tendency to be overzealous in correcting technical shortcomings of the most elementary conceptual models, which can be counterproductive because there's a fine line between being technically accurate and being inscrutable to students. My approach has always been to use whatever conceptual models can help students understand the material, but at the same time be careful to knowledge that all conceptual models have their weaknesses.

This might just be a matter of misinterpreting what Enthalpy was trying to write, but I don't agree that electrons are orbitals. Orbitals are mathematical constructs to help explain the behavior and properties of electrons (and the bonding of atoms). Orbitals don't really exist. Electrons do.

[Enthalpy]

I know only two difficulties with saying that electrons are orbitals (when stable in a atom):
- The Landé factor hints at a point particle
- The electron doesn't repel itself between the varied locations the wave spans.
There may be more.

For the second difficulty, maybe (I don't know enough to assess that) we could say that only interactions exist, not "auto"-action. That would at the same time solve the finite electron mass without needing dressed particles.

Orbitals are observable and observed, so I have no difficulty to call them "real". Here is an example:
https://www.zurich.ibm.com/st/atomic_manipulation/pentacene.html
https://www.zurich.ibm.com/st/atomic_manipulation/images_pentacene_fig2.html
one nice aspect of electron force microscopes is that they observe all the time the same pair of electrons. Their image is not a statistical mean value over many electrons like with a tunnel effect microscope. The picture is really the highest occupied molecular orbital there. Also interesting: observing the pair at one position of the needle does not force it to be only there. AFM are useful to debunk usual misinterpretations of the double slit.

Heisenberg in an atom: the indetermination of the electron's position is the size of the orbital and the indetermination of its momentum is the spectrum of momenta that make the orbital. A 3D Fourier transform of the orbital writes the orbital as a linear combination of plane waves, which extend to some mean momentum (there is no limit) in ±x ±y ±z which is the indetermination. The product of both obeys Heisenberg's limit.

Up to now I feel very comfortable with electrons being waves, with some attributes unsplittable. By the way, I'm not alone in this: Schrieffer (from the BCS superconductor theory) used the same wording. It gets less comfortable with several electrons, for instance in a helium atom as its two electrons must be described by a single wavefunction. If in the future I meet something incompatible I'll change my mind.

[thetada]

Thanks guys, this has been very useful. I think I need to do some intense reading to develop my understanding. I don't suppose either of you could recommend a good book?

[Enthalpy]

In English? Feynman I'd say. His book might even be on the Web, and for sure it exists on paper. But the title may differ from "quantum mechanics", possibly "electrodynamics", I don't quite remember.

For QM you must be easy with linear algebra and waves to the very least, or you'll miss the math approach.

One advantage of discovering QM through its math is that this part is rather well established and consensual. Look, Corribus and I have suggested slightly different wording here, but as we'd compute the same way, it's detail.

Unfortunately, I know no explanation nor book without maths. The ones who attempt it fail, as they just try to bring comparisons that obfuscate the topic instead of enlighting it, and such misconceptions are hard to get rid of once learned.

Also, don't read texts too old. QM was very difficult and abstract for its founders, it has been misunderstood by many books, and many interpretations that were scientifically valid in the past have been disproven meanwhile. So, recent texts are both simpler thanks to new observations, and (should) avoid useless abandoned interpretations.

And be aware that most newspaper articles, most second-rang books tell or suggest concepts that are grossly wrong, so pick only the best sources.

[Corribus]

Orbitals are observable and observed, so I have no difficulty to call them "real". Here is an example:
https://www.zurich.ibm.com/st/atomic_manipulation/pentacene.html
https://www.zurich.ibm.com/st/atomic_manipulation/images_pentacene_fig2.html

This is getting into semantics, I guess, but: it's a good thing the microscope images resemble orbital diagrams, because it reveals that the models are doing a good job. But that doesn't mean you are actually viewing orbitals. The AFM responds to positions of particles. Orbitals and other electronic structure theories help us predict and understand why particles are arranged they way they are. You don't observe an orbital - you observe the behavior of electrons, and orbitals are a bonding theory to explain that behavior. To wit, not all bonding theories use orbitals. You might as well equally say the microscope images observe density functionals. Orbitals are just mathematical functions that describe electron position, derived from first principles considerations with a whole heap of a lot of approximations - and there are many possible functions you can use. They aren't even perfect (or necessarily even good) quantitative description of electron behavior in many circumstances.

@thetada

A general chemistry book will have a very elemental treatment. For a deeper exploration, you'll have to start looking at physical chemistry books, but be prepared for some math.

[Enthalpy]

[...] The atomic force microscope responds to positions of particles[...]

What I feel interesting is that the electrons (mostly the Homo pair) of the sensing CO molecule interact with the electrons (mostly that Homo pair too) of the sensed molecule (pentacene on the picture) over all the volumes of both orbitals, not just over one pair of possible positions, so the electrons act as diffuse entities. The wavefuntion is much more than a mathematical means to evaluate a probability.

I also feel important that this interaction doesn't reduce the position uncertainty of the sensed electrons. Useful to debunk wrong interpretations that the double slit often brings.

The rest is wording detail.  It shall guide us towards the proper computation. I don't put more importance in it.