Alexis C Einstein's facial reaction at the end went well with it.

8:10

Stop

Beast Master 😂😂😂

One of the best comments I ever found on the internet omg thank you. xD

Ahahaha what a genuine laugh you have provoked in me :D

Thanks for a beautiful comment!

I'm glad it was helpful!

My understanding of pilot wave theory is that it is basically the same as my video, just with lots more math-- people, especially David Bohm (1950s) attempting to bring electron behavior back to de Broglie's original interpretation. The "pilot wave" is the same as what is being called a "standing wave" in this video, with the addition of "hidden variables:" variables that are not yet known but that exist and bring the electron back from the precipice of probability and thus eliminating all "quantum weirdness." Pilot Wave Theory is an unpopular interpretation among today's physicists, but it was an essential step in creating the quantized world of quantum mechanics, and a remarkable leap forward in understanding nature, setting the stage for quantum mechanics, even though de Broglie's interpretation of his own math was not accepted by most.

agreed

Thanks! Glad to help!

You're welcome!

Thanks!

I'm glad it was helpful!

You're Welcome!

Yes! That is what established the existence of quantized energy, despite Planck himself not quite believing it to be correct at the time.

Interesting!

My student asked if she could help make a video, so I made a script and had her read it...

The animations were done entirely with powerpoint.

@@CrashChemistryAcademy for real??? I must know more!

Good question! One of the driving forces of nature is the tendency of a system toward lower energy. A system, however defined, will release energy if it can get to a path that will allow it to do so. If we call the atom the system, when an electron absorbs energy then the system has more energy. A path to getting rid of energy is now possible, which is the release of light energy by the energized electron. We can just as legitimately call the electron itself the system, and the same applies: it can get to a lower energy by emitting light energy. Chemical reactions are driven by this process, where atoms will rearrange into compounds that have less total energy than the reactants, requiring a release of energy. This very often involves electrons going to lower energy states, and sometimes releasing light in the process, which is probably most evident in fire.

Great questions! The visualization was purely pedagogical. Although de Broglie did apparently picture the electrons oscillating, his math was quite sophisticated and beyond my expertise. One thing you should keep in mind is that de Broglie is adhering to electrons with specific allowed energies, and it is those energies that are being interpreted here as electron paths of different sizes. So your idea of decreasing wavelength would not fit the visualization since wavelength for the electron would correspond to a specific energy. Changing the wavelength is changing the energy. So electrons can change energy, as specified in the video, but only to allowed energies, not just any energy corresponding to changing wavelength.

@@CrashChemistryAcademy Aren't this 'allowed energies' are harmonics of the basic wavelength?

@@moonshine7374 Yes, it is a great analogy-- given a particular length of a vibrating string or spring or air, the allowed standing waves, with their corresponding nodes/anti-nodes, are dictated by the energies being put into the string or the air, which are the harmonics. This is only an analogy, however, because the electron harmonics correspond specifically to the probabilities of existence: the anti-nodes give the area where electron is most likely to be found, the nodes give areas where the electron has zero probability of being found. This is quite different than de Broglie's vision of an electron moving as a wave, and was proposed in 1924 by Max Born (for which he won the Nobel Prize), after seeing de Broglie's idea of electron-as-standing wave published in 1924.

​@@CrashChemistryAcademy , sorry for the late response (youtube notifications are not very reliable it seems). Yes I understand that De Broglie explanation of electrons' discrete "orbitals" is simplification and as such is incorrect (or at least very imprecise). This is easy to guess even the first time one hears it - it assumes specific shape of the electrons' wave (ie in what direction they oscillate for example) that somehow electrons have some basic wavelength and in order to fit additional one they jump into higher energy orbital ... But De Broglie attempted to explain what was stated by Niels Bohr years earlier. And I personally love the attempts for such explanations (and their shortcomings usually because of simplification). That's why De Broglie is among my favorite scientists, because of his struggle for Realism. Niels Bohr had no explanation for the electrons discreetness (in an atom), just very precise description. We know that De Broglie explanation isn't correct, but we actually don't know what the correct (and precise) explanation is. Today we have the electron orbitals described by QM which are basically solutions of electrons Schrodinger wave equations for Hydrogen! Not for every element!! Because the equations quickly become way too complex to solve. (I'm curious to what element have these equations actually been solved?) And from what I find I see that some electron's orbitals have been observed for real ... but only in Hydrogen again. I don't like how QM "explains" everything with solution of given equations. I mean I don't doubt that they're correct in most cases at least. But it's very misleading by having a very successful and precise theory to start thinking that Reality MUST OBEY exactly your theory and not be interested in experimental proofs or explanations. Also I think that real understanding is what is needed in order to jump to the next level in physics (or any science really). Many phenomenon are unintuitive, which is easy to see, as our intuition is built and evolved in rather narrow scope of things we can observe (see, hear ...) around us. Most sciences have pushed way ahead of what we're used to observe, and thus we need to train our brains to comprehend these new concepts even if unintuitive (as many of them are). In any case the quantum (ie discreet) behavior of electrons (in an atom) seem to be caused by simple** geometry and interactions of the main forces (mostly the EM force in this case) ** simple not in the sense that you can draw it on a napkin, but that it's simple in principle, just complex to describe precisely. But even in that geometric aspect we're no clear on many things - like do electrons move in an atom, how, the shape of their waves, the total*** length of their waves etc... And I'm quite annoyed when QM simply sweeps all these questions under the carpet by calling the wave a probability wave. Sure I can easily see that probabilistic, statistical approach can be used with things that are inherently difficult (or even impossible) to observe directly, but that doesn't necessarily mean that probabilistic wave is actually a real thing, just that it's our best current description. In my opinion until these and more such questions aren't asked and tested we won't be able to progress QM beyond current state (in which it has been stuck for decades now). *** the TOTAL wave of a particle is what I've been searching for lately, and it's practically impossible to find anything (at least with google) it always in 100% of the cases matches topics about wavelength (which is a different thing). But a total wave's length but be a thing, because we know that for example photon's wave has a front, and that its total energy is very important for some interactions, ie it must have an end too. But we don't know how long a photon is. You can describe a wavelength with a small fraction of the curve, but you need the whole wave in order to deliver its whole energy. It's sad that this is not discussed anywhere even in principle (ie from philosophical point of view). That's not critique to the video - not at all! :) I understand that especially difficult and unintuitive concepts have to be simplified and be processed in chunks. But I've been trying to build up my understanding of the quantum world for years now, and every time I try to push a bit further I hit a brick wall. It's either - no explanation beyond the too simplified one, or it's a ton of QM equations (which in many case QM haven't even solved!!!). Also as I mentioned above just because our current Math works wonderfully well, it doesn't mean that Reality has to somehow obey our Math. No matter how precise our theories are it's always the other way around - our Math & theories is just description of Reality. And trying to explain things with pure Math is inherently wrong imho. And there are many key things in QM that only come from math without any explanation. Out best is that they match our limited observations but that's it - zero explanation. Some of these things are for example: Pauli exclusion principle; QM electron orbitals (beyond the observed orbitals of Hydrogen, which also were observed long after the QM model); Born rule (of squaring the wave function to find the probability); the entangled particles stronger-than-classical correlation etc.. Actually it seems QM has way more inconsistent (ie potentially wrong) interpretations than good explanations.

Great question! The video is concerned with how de Broglie envisioned the electron, which was as a particle moving around the nucleus in the pattern of a standing wave. That was immediately countered by Max Born (1924) who said the standing wave represents the probability of where the electron could exist within the atom, and not a representation of how it moves (which got him a Nobel Prize). Born's idea was taken further by Schrodinger and Heisenberg (1926) to create the quantum mechanical model, in which the electron's energy dictates the size of the standing wave, as well as the number of nodes & antinodes, based in the wave being a wave of probability-- the electron's path is unknown, but the electron exists in "clouds" of negative charge, and within those clouds we can know the probability of where the electron (as a particle) might be based on its standing wave: within the cloud the antinodes show where the electron is most likely to exist, and the nodes show where the electron cannot exist (zero probability). But, additionally, the electron's existence is also the standing wave itself, as you stated, but still a wave of probabilities as stated in the previous sentence. This dual existence (particle & wave) is only manifested through the nature of the devices used to measure the electron's behavior, and not considered to be how the electron actually exists. The electron seems to be a wave if you measure it one way, and it seems to be a particle if you measure it another way. However the way we measure the electron does not change the electron itself, it only changes how its behavior is manifested. All of this came out of Schrodinger's and Heisenberg's math describing electron behavior, which includes a correction by Paul Dirac in 1928 in order to account for the electron travelling at relativistic speeds. Additionally, Heisenberg's Uncertainty Principle (1927) tells us that we cannot know the specific location of the electron at any given moment, and so that means that de Broglie's idea of electron behavior is incorrect-- not being able to know the location of an electron means we cannot know of any particular path it is taking. de Broglie's electron traveling as a standing wave violates the Uncertainty Principle. Tens of thousands of experiments during the past 95+ years have confirmed the predictions of the mathematics, with not one experiment to date being able to show that the math is flawed. An impressive bit of work by those scientists in the 1920s.

@Crash Chemistry Academy wow! honestly, I didn't expect to receive such a detailed and well written answer on KZfaq. Thank you so much. So, if i understood this correctly based on the device we use to look at the electron, sometimes we observe it as: 1) a particle. We can't know the exact position of that particle, but the probability of its position is a standing wave. Other times, we observe it as 2) a standing wave, the same standing wave that describes the probability of the position when we view electron as particle Also, why do we say that de Broglie thought of the electron as being both a particle and a wave? He just thought of a particle moving in a wave orbit

Yes! An excellent summary. de Broglie introduced the electron as having wave properties in order to justify the quantized nature of the electron's energy states. If the electron could only exist at energies that allowed it to be a standing wave, then Bohr's model of the atom (1913) is vindicated. Bohr proposed quantized electron states in his atomic model but could not provide any theoretical basis for this quantization other than that it explained experimental data. de Broglie provided the needed basis with his electron-as-wave hypothesis (1924). I should add that de Broglie's hypothesis was his entire doctoral thesis, with a sound mathematical footing that no one was able to dispute. More specifically regarding de Broglie regarding the electron as both particle and wave, I can only think that he did not view the electron as having this dual existence. I believe for him, the electron was a particle that travelled in a specific sinusoidal path needed to be a standing wave in order for the electron to exist. The duality came very soon afterword with Max Born and the rest of the cabal that came up with quantum mechanics, as well as those many experiments showing the electron as either a particle or a wave.

@Crash Chemistry Academy thank you once again, it's perfectly clear to me now. If it wasn't for your answer, I'd be really stuck . THANK YOU

@@captainamericawhyso5917 You're welcome, I'm glad it helped.

The wave path I showed was in the plane of the screen, when in fact the path is considered to be perpendicular to the screen, that is, the waves are "waving" above and below the plane of the screen as it orbits the nucleus, for which I did not have the software to animate. If you're view of the atom is perpendicular to this path, it will appear as a circle. This idea of a wavy path was very short lived. The year de Broglie published the electron-as-wave mathematics, 1924, Max Born stated de Broglie's standing wave must be representing a probability function, where the nodes and anti-nodes occurring in the standing wave represent areas of zero and maximum probability of finding the electron at some specified radius. This became the basis for Schrodinger's equation of 1926 describing the wave mechanical model of the atom. This is shown briefly at the end of the video.

@@CrashChemistryAcademy thank you so much I got a really good mark on my test after watching your explanation. Forever grateful!

yes but the electron can only absorb light that has the exact energy needed to get to a higher allowed energy.

Strangely enough, all matter has properties of both waves and particles simultaneously. There is an inverse relationship between the wavelength and the mass, and only very tiny masses (electrons, etc) have wavelengths large enough to measure. The wave and particle nature of matter is built in-- it is an inherent part of what a particle is, of what matter is. Further, via Einsteins special relativity, we know that matter is only a form of energy, and so to make analogies between what matter really is and how we experience matter is very difficult because in our large-scale macro world the way we as biological beings experience matter is very different than how we experience energy.

Yes, de Broglie interpreted his math (1924) to mean that the electrons move in a wave pattern. However, the wave pattern drawn in the video is just a trace of the path of a single electron. So when the electron meets up with its path (in phase), it is not coming in contact with itself, so there is no interference. It is simply continuing along its sinusoidal path. A single piece of matter cannot cause either constructive or destructive interference unless it interacts with another piece of matter. My guess is your confusion comes from Schrodinger's quantum mechanics that came along two years later, and more importantly, the double slit experiments using electrons that came along later (1950's?)(double slit experiments had been done with light previous to Schrodinger, but not electrons). In those double slit experiments with electrons, a single electron was shown to cause interference, but that is attributed (from Schrodinger's math) to the ability of an electron to exist in more than one place simultaneously, and so the interference can be thought of as a single electron existing in two different places (as a wave if you'd like) that then come in contact and result in interference, either constructively or destructively, depending on how the interaction goes. That may not make any sense to you, but it comes out of Schrodinger's equation, which, after tens of thousands of experiments over the last 90+ years, has never been shown to be incorrect. The data from all those experiments have only strengthened the nutty mathematical interpretations people have come up with, such as what I described above. By the way, de Broglie hated those interpretations, and insisted there are other explanations for the electron's behavior, but neither he nor anyone else has been able to came up with any empirical support for de Broglie's objections, although many have tried.

The elctrons will only go to a higher energy if they absorb that energy from an outside source, such as light (electromagetic radiation), or heat or electricity. but they will not stay at the higher energy, they will immediately emit that energy as light and so will go back down to a lower energy.

Crash Chemistry Academy thanks

It is just a matter of what the allowed energies are. The example in the video is showing that the energy of a red photon is the enrgy needed for the electron to jump to the next higher energy level. It can absorb several other energies, the energies needed to get it to two energies levels higher, or three, or four, etc. So depending on the atom and the starting energy (ground state) of the electron, there are several specific energies any electron can absorb to get to higher allowed energies. So yes, let's say this electron can also absorb a green photon (two energy levels up) or a violet photon (a jump of three energy levels), etc. Electrons can also absorb IR and UV, so in the scenario I just gave you, we can assume the electron can absorb a UV photon of a specific energy to get it to jump 4 energy levels (etc.).

Oh right .. didn't think about that thanks for the detailed answer!!! So it is not possible that a blue photon which is in the middle of two energy ranges kicks up the electron to the lower of those two and the rest of the energy goes somewhere else?

Good question-- for photons the answer is no, the photon has to have the exact energy. For heat (kinetic energy transfer), I don't know but I would imagine it could be possible, although kinetic energy, and thus heat, is quantized. Everything in the universe seems to be quantized-- time, space, gravity, etc. Nothing is continuous. We live in a weird place.

Ok perfect thank you for your answers, you won a new subscriber with them :D

Born isn't very new. He died a very old man about 50 years ago. De Broglie and Born were the bridge between Bohr's quantized electron (1913) and Schrodinger's quantum mechanics (1926). De Broglie established HOW an electron could exist as a quantized particle via having a wave quality, and Born re-interpreted the wave as a probability in the space surrounding the nucleus. So the electron can seem like a particle if measured in a way that makes it appear to be a particle, and it can seem like a wave if measured in a way that makes it appear to be a wave. The electron is an electron-- it is its own fundamental particle, and it is the way it is measured that makes it seem to be both a wave and a particle. It is not an EM wave, which is quite different.

@@CrashChemistryAcademy yes i know the guy and his theory was around long ago but im juts learning about him now,i guess they never went into deep quantum mech in school beyond bohr's model and yet despite my years online with science and physics i never heard of this guy or his theroy till yesterday when i was talking to a laser enthusiast named zendilion but he told me that electrons are not matter or particle ,im sure he is wrong on that ,its photons that are not actual particles (ie mass) even though they may look like particles or waves they are massless unlike the atomic structure

Yes, electrons are considered to be matter simply because they have mass. They certainly behave very oddly though. While there are many good books on the history of quantum mechanics, I think the best introduction is by one of the physicists who was actually there with Schrodinger and Heisenberg and de Broglie and Born (etc., etc.), named George Gamow: "Thirty Years that Shook Physics, The story of Quantum Theory" (1966). The book covers the development of QM from 1900-1930 and is quite fascinating, and introduces all the players and their contributions, of which there are many. Photons behave in a similar fashion to electrons in that they can appear to have both wave and particle properties, but they have no mass. Einstein's photoelectric effect (1905), for which he won the Nobel Prize, proved light's particle nature. All matter is considered to have this "dual" "wave/particle" behavior. We do not see the wave nature of larger objects because the wavelength is inversely proportional to mass, so once you get to larger masses, the wavelength becomes too tiny to measure.

@@CrashChemistryAcademy "We do not see the wave nature of larger objects because the wavelength is inversely proportional to mass, so once you get to larger masses, the wavelength becomes too tiny to measure." that is alot to wrap your mind around and visualise, i figured a photon is juts the energy fields of a particle and are invisible till it interacts with something at which point it can appear like a bullet or a wave ,another model i thought of would be that each photon is an expanding sphere of energy kinda like radio waves

I love that you said (paraphrasing) "energy fields of a photon are invisible until it interacts with something." That is exactly the case for how we experience light. However the fields of a photon are a disturbance of electric and magnetic fields that are already out there, so the photon always seems to be interacting with those fields. The disturbance itself is the photon. Regarding radio, is the radio photons that are expanding out in different directions from the source, not the electric or magnetic fields of the radio photon. This is pretty weird stuff and your laser friend might give you a better explanation. Anyway, the disturbance is contained (does not spread) along the path of the photon. The photon itself is the disturbance. That disturbance over time creates what we can map out mathematically as a periodic function, a sin wave, with a specific wavelength and frequency, and so that is often how light is shown, as a sin wave, even though the disturbance is a moving (speed o' light) localized disturbance, with a maximal amplitude at the center and rapidly decreasing amplitudes on either side of the maximum occurring along the path of the photon. The distance between each amplitude is the wavelength. The frequency is how fast the fields are created along the photon's path, in other words, how fast the photon is able to oscillate the electric/magnetic fields it is disturbing. It is weird stuff.

de Broglie’s 1924 model was a description of electron behavior justifying Bohr’s quantum electron (1913). The mathematics of Schrodinger’s 1926 equation was modified by Pauli (1926) to include his exclusion principle, which creates degenerate orbitals to account for the existence of multi-electron atoms. These mathematical expressions I believe do not specifically address de Broglie’s idea of wave interference beyond the separation of degenerate orbitals. The flaw here is that all occupied orbitals overlap at some point since all orbitals converge at the nucleus. So while I have not really answered your question (sorry) I do think the answer lies in Pauli’s modification of the Schrodinger equation.

Interesting! Thanks for the comment.

Crash Chemistry Academy lol I thought kinetic energy was a vector

The Bohr model quantizes the electron energy which removes the problem of falling into the nucleus. The model was later modified to remove the orbiting electrons with probability 'clouds': the electrons existing with some probability within a defined volume per Schrodinger's equation. I just use powerpoint (microsoft).

@@CrashChemistryAcademy yes i agree with all but bohr also concluded this em wave problem and told that in his model the electron are not moving the are stationary in its orbit but he has no reason for that so then debroglie shows up with his standing wave model

@@fathomless5414 Bohr new that stationary electrons would be very unstable in the presence of the large attractive force of the nucleus. In his model the electrons orbit the nucleus. The electrons' orbit radii were determined by their energy. A specific energy equated to a specific orbit radius. This was his quantization of electron energy-- the electrons could only exist at allowed orbits = allowed energies. de Broglie supported this quantization mathematically by providing the electrons with a wave property.

@@CrashChemistryAcademy but that's the problem the moving electron will produce a lot of electro magnetic radiation and finally electron losses all its energy and falls in the nucleus and this thing was known at the time of rutherford also that's why bohr came up with the new postulate to make electron stationary meanwhile he does not know give the reason for it

@@fathomless5414 Not sure where you're getting your information. Bohr never said the electrons are stationary, unless you are referring to stationary orbits. He said that EM radiation could not be emitted from orbiting electrons because electron energy is quantized, in other words they could only lose specific amounts of energy, and that would only happen if they had previously absorbed enough energy to go to a higher energy orbit (the excited state), otherwise they would remain at their lowest possible energy (ground state) as determined by prinicple energy level, n, derived from atomic emission data of the previous few decades. In a stable atom electrons would not go to energies below their ground state. I would suggest watching my video on the Bohr model at kzfaq.info/get/bejne/l9alisyQq8jYqac.html

It has been shown, mathematically and experimentally, that your scenario would not (cannot) happen, due to quantization. The electron can only exist at allowed energies dictated by the math (experimentally shown to be correct), so it would never reach any other energy.

Perturbation Theory is only an approximation-that-works... So-if an electron goes flying into a neutral atom (degenerate state aka ground state) it can't interact with any orbital electrons unless it has exactly the quantum needed to pump one to an energized orbital (and the others adjusting for that) and escape itself...

I do not see how that is different from my reply. You stated the electron needs the exact quantum....

[that is-a consequence of-your reply]

Little Orphan Annie

The electron is considered a point particle so it can only trace a 2-D wave. I have seen models where the waves oscillate above and below the plane of the screen, but to my knowledge that is not what de Broglie had in mind.

A student asked to do it, so we had some fun. I should ask my daughter to do one. She was in my chem class!

@@CrashChemistryAcademy I am stealing some of your thunder! Saw a comment about how you do everything in ppt. see my latest video on orbital hybridization if you have a sec. and yes your daughter should totally do a video!

@@chemistrymattersgetit4161 What a great video! Did you do it in powerpoint? I ask because some of the graphics (for example at 0:20 and 15:00) look a little beyond the capabilities of ppt (or beyond my capabilities). I'll have to investigate. My junior-in-college daughter seems to not be interested in narrating a youtube vid. Maybe when she gets a bit older! Thanks for sharing.

The video is attempting to show de Broglie's interpretation of his own math, which is the sinusoidal path. I address this issue at the end of the video. There are currently a small amount of physicists who think the sinusoidal path (or something similar) is the correct interpretation, and they call it a pilot wave.

For de Broglie it was mechanical, but two years later (1926) this was reinterpreted by Max Born to be probability waves, and that is the accepted model: the wave nodes and anti-nodes represent the probability of where an electron might be-- high probability (anti-nodes), or zero probability (nodes).

ok ty for the response because it was an confusion in many sites...other said mechanical other probability...also when we say shell (i.e. n=1,2,3) we mean the space where electron can be?and how we are sure for the electron configuration if its only the probability to be in a specific space?

The word shell is unfortunate for two reasons: 1) it implies the electron exists on a 2-dimensional surface, which it does not, and 2) it is sometimes used indiscriminately to mean either n (principle energy level) or n and l (the orbital). So in the majority of contexts people use it to mean n, which is NOT directly the space where an electron is likely to be, except in hydrogen. To clarify, when we say where an electron is likely to be, that refers to the energy of the electron, because it is the energy of the electron that dictates where it is likely to be found, which takes the shape of the orbitals we see from Schrodinger's equation, designated by n + l. When n (the shell) is greater than 1, it can have multiple energies, and thus multiple orbitals. However with hydrogen, due to it having only 1 electron and therefore free of electron repulsion, electron energy becomes = n, and so only in hydrogen does n (the shell) equal both the electron energy as well as the orbital. The electron configuration is itself a probability in terms of where you will find the electron spatially: keep in mind that even if the electron momentarily leaves the space defined as the orbital, it still has the energy of that orbital.

ty 1 more time for your response...so for the configuration the electrons are always in the same shell but in a different space for a given time? am i wrong?i mean if we could name the electrons ,(i.e. electron A,electron B) we "could" see them only in the same shell but in different position?

Since shells are n, then n = 1 has 1 orbital (1s) for a maximum of 2 electrons, n= 2 has 2 orbitals (2s, 2p) for a maximum of 8 e-, n=3 has 3 orbitals (3s, 3p, 3d) for a maximum of 18 e-, etcetera.

Yes, but Heisenberg's (1926) model was the same as Schrodinger's (1926), based on the electron's energy manifesting as a wave. A mathematician (forgot who) in 1926 pointed out the the two mathematical expressions were describing the exact same atom, the same electron behavior, and in 1930 Paul Dirac combined the two into a single formalism.

The electron always maintains its mass. It does not lose or gain mass. de Broglie (1924) thought the electron, with its mass intact, would travel in a wave pattern. That was supplanted by the wave representing the probability of where the electron could be in the atom (Max Born, 1924), rather than actually travelling in a wave-like pattern. The mass, however, does not vary.

You sort of answered your question, being that the behavior of large aggregates of atoms (the macro level of our everyday world) cannot be compared with the quantum behavior of particles in the world of the very small. While de Broglie was known to believe the electron travelled as a wave, as shown in the video, I use it more as a pedagogical device. Max Born immediately re-interpreted de Broglie's wave path as a probability wave, a wave that portrays the probability of where an electron might be within an orbital, but the wave can only exist as a standing wave, which requires specific energies. Any energy between standing wave energies are not energies where the electron can exist. The standing wave energy allows for "nodes" of zero probability of existence and "anti-nodes" of maximum probability of existence within an orbital, but only a standing wave can have nodes and anti-nodes. So any other energy "disrupts" the node - anti-node structure, and so the electron cannot exist at those energies.

شكرا

Lo sentimos, este video no tiene subtítulos (cc). Para cualquiera de mis videos que tienen cc, puede ir a configuración -> subtítulos -> traducción automática -> español. El video tendrá subtítulos en español. Lamentablemente, el video de Broglie no es cc y, por lo tanto, no tiene esta característica.

My student was 16 when she made this video!