How Quantum Physics Predicts the Size of an Atom (Bohr Radius) by Parth G

Atoms are tiny particles that make up everything. But exactly how big (or rather how small) are they?
In this video, we'll start by defining the "size" of an atom as the distance between the center of the nucleus, and the furthest (outermost) electron. This can also be known as the radius of the atom. If we study a simple hydrogen atom, then this radius simply becomes the distance between the proton forming the nucleus, and the electron in the lowest energy level.
According to quantum mechanics, it is not necessary that these two particles will be found exactly the same distance apart. Instead, the wave function of the system tells us the probability of finding the electron a certain distance away from the proton. And from the wave function we can see that the electron is most likely to be found a certain distance away from the proton.
This most likely distance is known as the "Bohr Radius" after Niels Bohr. It can be calculated in terms of some important physical constants (such as the permittivity of free space, Planck's constant, mass of the electron, and charge of the electron). It can also be rewritten as a simpler expression in terms of the reduced Planck constant, electron rest mass, speed of light in a vacuum, and the fine structure constant.
Ultimately though, the numerical value of the Bohr Radius in meters is about 5.29 x 10^(-11) m. This is roughly 0.0529 nm, or about 100 million times smaller than the width of an average pencil. In other words, atoms are extremely tiny, and the hydrogen atom is (of course) the tiniest of them all.
It's also worth noting that the Bohr Radius is calculated using an assumption about the proton, which is that it is completely stationary at the center of the atom. This is equivalent to assuming the proton has infinite mass. This assumption is necessary to make the math easier, and is reasonable since the mass of the proton is much larger than the mass of the electron. So the result we get using this assumption is quite close to the actual most likely size of the atom.
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Timestamps:
0:00 - Exactly How Big is a Hydrogen Atom?
0:22 - What Do We Mean by the "Size of an Atom"? Radius of Atom
1:48 - The Quantum Wave Function and the Position of the Electron
3:36 - The Most Likely Size of a Hydrogen Atom - the Bohr Radius
4:32 - Electrostatics, and the Permittivity of Free Space
5:53 - The Reduced Planck Constant and the Electron Rest Mass
6:37 - Another Way to Write the Bohr Radius
7:20 - The Actual (Numerical) Size of the Hydrogen Atom
7:59 - The Proton Has Infinite Mass?!
8:56 - Quantum Dice Merch Linked Below!

[@ParthGChannel]

Thanks for watching everyone! Let me know what else you'd like me to cover in future videos :)

[@varunrmallya5369]

Hey Parth! How about a video on Noether's theorem? You can continue your series on quantum mech by explaining its relation to the uncertainty principle. BTW love your videos.

[@Chiudahiphale]

Happy raksha Bandhan bhaiya 😊

[@kingklr1]

Cool video, thank you.

[@filthyfilter2798]

where are u from dude? nice video!

Is it possible to calculate the vacuum permittivity or is that assumed to be fundamental? I'm thinking that it could be related to virtual particles.

[@ljbdoa]

7:51 just a very minor correction: although hydrogen is the lightest atom, helium is the one that's the smallest

[@achyuththouta6957]

Oh

[@lokeswary15]

Yeah you're right. Helium atom is the smallest atom. If we compare hydrogen and helium,helium is the smallest one because it has 2 protons that attracts the valence shell electrons strongly subsequently it's radius also gets reduced. The radius of hydrogen > the radius of helium

[@ParthGChannel]

Completely slipped my mind!

[@Chiudahiphale]

@@ParthGChannel Happy raksha Bandhan bhaiya

[@thedarkknight1865]

If we look at Vanderwall radius then He>H

[@gato_omega]

And, wouldn't the "size" of the atom be more like 2 x a0 (i.e. diameter instead of the radius?) - anyway, excellent video! :)

[@CMDRunematti]

no, because that electron is always on one side. i think... on the other hand you could argue that the electron is a shell around the nucleus, so it is a sphere anyway...

[@tand9854]

I think he forgot to x2. Average diameter of atom is about 10^-10 m.

[@YourLocalCafe]

The size of an atom would indeed be of a spherical sort and its diameter would have to be considered but the electrons revolve in random yet not so random trajectory about yhe nucleus so really an atom is just the nucleus which is very small compared to the atom's alleged size with the electrons. To give perspective if an atom is the size of a cricket stadium a nucleus would be a cricket ball. -NCERT (11th, atomic structure.)

[@tand9854]

@@YourLocalCafe Rutherford alpha scattering experiment

[@AntoniGawlikowski]

Great video as always!

[@kashu7691]

i think at that point you just solve the time independent schrödinger eq numerically

[@anshumantripathi3977]

Hey Parth, can you plz make a video on the STRUCTURE Of ATOM.

[@tristanphipps6987]

Thanks for the video. I really appreciate the work you put into making physics assessable to those of us without a deep knowledge of maths. I find your videos inspire me to keep learning.

[@robertschlesinger1342]

Interesting and worthwhile video.

[@drrajeshps]

He explains without just pushing too much names and terms . He kept it small and simple 👍👍

[@girindrasinghrathore8418]

So, How big is an atom? Ans- very small 😅

[@deepinside8408]

*please answer* Which *SOFTWARE* You use to make such vedio??????????

[@snakez1747]

I understood more in this video than my uni lecture. Also, the format is very nice. Good job

[@rafaeldenuzzidias2523]

Amazing channel, and it is going better and better.

[@tdhanasekaran3536]

An easy way to remember the radius of H atom is approximately half angstrom. This is a good example of the use of angstrom units (and some hard core physicists love this unit) instead of meters or nanometers. 0.0529 nm ican be represented as 0.529 Angstrom. Bohrs model although incomplete in terms of describing atoms heavier than hydrogen, is still highly useful for H atom and describing many phenomena related to H atom, atomic spectra etc.

[@rustycobalt5072]

Wouldn't a better description be the angular compton wavelength of an electron over the fine structure constant?

[@josh9224]

Why do we want to take square modulus for the probability of wave function

[@azielmelo7756]

Short answer: The negative distances become positive numbers to sum. Example: the electron can be at -1m or 1m, simple average: (-1+1)/2= 0/2 = 0; taking the square distances: √ { [(-1)^2 + 1^2] /2} = 1. Justification: When you have numbers it's ok to take the module, but when you deal with equations the module it a lot warder do deal with than just squaring it an then taking the square root.

[@electronicsacademy2D2E29]

Awesome presentation. Just curious. Which software are you using for animating your diagrams?

[@prashantlale4976]

This was really helpful in revising th lost concept of atomic structure in my mind. Thanks Parth♥️

[@lowkey_entertaining9723]

Why does that heart emoji look slightly different

[@prashantlale4976]

What? I couldn't understand it

[@lowkey_entertaining9723]

@@prashantlale4976 my one looks like this ❤️

[@petermuller7079]

Very cool video! Thank you. Two questions (maybe for a part2 video ;-) ): 1.) Has anyone an 'explaination' (better: Can make plausible) of why the Bohr radius is anti proportional to the mass and the charge? Roughly speaking: Why would (Hydrogen)Atoms with more mass and/or more charge be smaller? 2.) With what approach would one determine the size of other atoms (Helium or "bigger")? Are there completely different aspects to consider or can one take a similar approach ("Bohr radius 2.0") ?

[@jeminkukadiya13]

Because it will require more electrostatic force to change direction of electron while revolving. So greater the mass the nearer it should be for all other parameters being constant. What is the second question. Brief me.

[@petermuller7079]

@@jeminkukadiya13 Thanks for your answer.If i understood you right, your approach is classical orbital - like planetary systems - with mass and revolution speed (both anti proportional to the orbital radius). Right? Interesting approach. The second question was: "...2.) With what approach would one determine the size of other atoms (Helium or "bigger")? Are there completely different aspects to consider or can one take a similar approach ("Bohr radius 2.0") ?..."

[@jeminkukadiya13]

@@petermuller7079 Hey, I think it depends on what you mean by similar. For best outcome, we have quantum theory with its complex equation and we have to solve them. But at this level, approximation is a very good model to understand nature. That is why classical approach is good until it don’t explain some phenomena. Second, I think there is no need for proving radius of Helium or any other by equations. Of course we can prove it but Who will do such Messy work. Just measure experimentally and use wherever possible. But if one still want to prove, then I think radius get changed over time due to quantum effects and complex interaction.

[@dcoded5217]

@@jeminkukadiya13 are we In a simulation or virtual reality in your opinion.

[@petermuller7079]

@@jeminkukadiya13 Hi Jemin, I think, you misunderstood my approach: I didn't want do question the math nor calculate it by myself. The exciting thing of those equations is, what they "MEAN". E.g. the Eigenvalues of Schroedinger Equation is often explained by "Energy levels", a wave function often as "probabilty to measure a particle", ... ... also the equations EXPRESS correlations between PHYSICAL (= maesurable) entities (e.g. Parth shows connections between the Bohr radius and the mass and charge of the electron; or to the speed of light). They are not only "cooking receipes" for determining a certain value. So the "orbital speed equation" (R * v^2 = G * M) shows that - a bigger (central) mass leads to a bigger radius and/or higher velocity of the orbiting mass or - if one increases the speed, one must also decrease the radius (by square factor) to stay in an orbit pr - ... That can be made plausible with a equilibrium of forces (gravitation vs centripetal). In this sense my question was: Why is the Bohr radius linked to the charge and the mass in that particular way? @Question2: Since the Bohr Radius is explicitly defined only for Hydrogen atom - isn't it logical to ask "what about the other elements?"? Is a "Helium Radius"-Equation somewhat similar? Has it other variables? Is it smaller oder bigger than H? Maybe it's not spherical symmetric anymore?... Nobady HAS to be curious - but i wonder what a non-curious person would want on this channel? ;-) ;-)

[@potawatomi100]

Outstanding explanation!

[@vedantxa573]

Love ur videos parth

[@KaliFissure]

Does anyone consider that when a neutron star inverts into a black hole that the neutrons have to go somewhere, and they are moving at c from the gravitational acceleration. If suggest they re emerge in deep space (eliminating information paradox) and then decay into amorphous hydrogen. The volume of neutron, tiny, volume of atom, as big as space allows (if you include electron cloud) so the sudden increase of size plus the repulsion between the atoms of H (since all have outer electron this negative charge) is the expansive dark energy. It's a neutron for neutron exchange in terms of energy. Gravity is the gathering back together, the endless falling into itself, of the universe. The manifold is lopsided temporally. The next moment locally is always more dense than the previous moment. Gravity is one way street

[@DuckStorms]

Did @ParthG just confuse average (mean) with most-likely (mode)?

[@mrichards]

? Average isn’t the mean. It can refer to mean median or mode depending on context

[@wellusee]

If you could strip the electrons off the protons , would a big bunch of protons be any good for something?

[@MrGlacierNova]

So is the radius of the atom defined using the most likely distance to the electron (aka location corresponding to max value of the squared wave function)? Or is it defined using the average radius of the electron ( aka the average or expectation value of the squared wave function).

[@lynsmith3154]

Hi Path, good work. My comments: You take a lot of the video to explain that the positions of the electron and the proton wobble or vary somewhat in position, which to me seems a bit superfluous; (Path, I'd like to see a bit more time on the actual maths calculations. ) Wouldn't every orbiting system wobble a little? The earth wobbles around the sun, (e.g. the Milankovitch cycles, hence climate change). I wonder what is the cause of the wobbling in the atom; internal (factors due to the atom and electron) or external (other nearby atoms) ?

[@markxxx21]

I would like you to do a video on color. Specifically, the press usually colors the coronavirus as red, but it's really too small to have color. So my question is, what is color and when does color come into play, sizewise.

[@amithabhay7326]

Hey parth please do a video on the quantum mechanical model please please

[@zenwarfare70]

Great video !

[@soumajitdas2044]

Hi Parth, a good video as always. Just wanted to rectify/add a small detail. The hydrogen atom is a two particle system as u said consisting of a proton and an electron and the internal motion of two particle about their center of mass is equivalent to the motion of single particle with a reduced mass. This reduced particle is located at r where r is a vector specifying the position of electron relative to the proton. So the mass is actually the reduced mass for any hydrogen like atoms. However for hydrogen atom this reduced mass turns out to be almost equal to the mass of the electron (𝝁 = (m_e× m_p)/(m_e+m_p)) and we know m_p ≈ 1836 times m_e so 𝝁= (m_e×m_p/m_p)≈m_e. Often we get questions regarding the ground state energy of positronium atom or muonic atoms where the only factor that will make difference with that of the energy for hydrogen atom is the factor of the reduced mass.

[@misterschifano]

Thank you for this! I now understand why k(e) continues to exist when studying quantum mechanics, while so many other constants go away. I really appreciate being able to visualize a new relationship like this. Quantum fuzziness and thermal jiggling are the reasons chemists resort to a sort of roundabout definition for atomic radius: half the distance between nuclei of atoms in a pure crystal at absolute zero. The third law stuff is of theoretical importance, but practically it means we can measure radius with Bragg's equation. It's a fun, clever workaround since any net deviation from "zero" position is limited by repulsion from nearby atoms. Unfortunately we can't do calculations for metal atoms and we can't observe metallic hydrogen yet so.... yeah :D

[@saqibbaba4474]

Please make a video on density

[@ruhnke]

Parth, why do we take the sqrt of the module of the wave function, since just squaring we already get a positive value? Is there complex numbers in the equations?

[@ruhnke]

Actually it will only make sense if the module were outside of the square... I'm lost

[@gabrielpetre3569]

Yeah, some functions have complex numbers

[@thewaytruthandlife]

a0 =5,29E-11m is its radius but the size of an atom is double that size so 10,58E-11 or 1,058E-10 m. or approx 0,1 nm

[@studiomattew]

Bonjour from France 👋🥖 Thanks for this great video !

[@abhamidbhat8844]

Plz sir make vedios on physics constants. And physical implications.

[@bk-sl8ee]

Shouldn't the size be of 2 x a, which will give us the diameter. Now i want to hear more on this. Seems like interesting topic

[@mr.winter538]

Does the reduced Planck constant have some uncertainty to it or is my knowledge out of date? If there is uncertainty to is, would that effect the distance or is the uncertainty too small to have a meaningful impact?

[@Abhi-mu2cy]

I think yes but it depends on temperature as temperature decreases electrons position becomes uncertain so it may be found anywhere in universe. Non Zero probability so by considering in that way distance can't be measured. but in room temperature or when measured electrons shows particle nature (uncertainty in position is soo less) then distance can measured

[@AdrianBoyko]

The reduced Planck constant is… constant.

[@md.al-aminsardar6096]

Outstanding ❤️❤️❤️.

[@DrDeuteron]

3:48 when you state thousands of _identical_ H atoms have _different_ configurations is going to cause confusion.

[@dmitrynuzhdin]

The trick is that they have the same configuration :) But every time you measure it you will get a different result - that's what QM is all about. He could say that "if we measure this distance for one atom 1000 times" but it will not be correct in terms of QM, because when you try to measure some values of a quantum state - you destroy the state. In other words, you can only measure one atom once, that's why he is talking about thousands of atoms.

[@DrDeuteron]

@@dmitrynuzhdin that's nice in theory. Of course you can't measure the position of the electron in the lab.

[@xtrailz]

I took my car to a quantum mechanic but he couldn't fix it

[@Chiudahiphale]

Can you make video on optics Please reply

[@odranreb000]

What about the size of an atom in a solid or a crystal. With a lattice structure?

[@danilorochacampanha5159]

You just helped me to finish my quantum chemistry homework!! I was doing a giant mess trying to find the a_0 value kkkkk

[@seethemadness9241]

Plz make a vdo on relativistic quantum mechanics

[@paulfrancis8836]

It's said that there are No two things identical in the Universe, so are Electrons or Protons all identical, or are they actually different, but we can't yet measure them accurately enough.

[@AdrianBoyko]

The funny thing about figuring out this value is that there is a 0% probability that a hydrogen atom will actually have that size.

[@steverdooley]

So gravitational attraction between the electron and proton can be ignored?

[@AdrianBoyko]

The electrostatic force between the electron and proton is about 2,000,000,000,000,000,000,000,000,000,000,000,000,000 times stronger than the gravitational force between them. So gravity plays a very, very, very small role.

[@capitaopacoca8454]

Gravitation in Quantum Physics? We don't do that here!

[@PurnamadaPurnamidam]

Thanks Parth u r great.

[@TheDavidlloydjones]

In one of his Lectures, something like tape 17 of the pre-editing audio tapes, he says (roughly, from memory), "Thus we can understand the hydrogen atom completely, but these methods haven't been able to go any further yet. Now the chemists do things differently and they can make stuff all the way up to organic molecules of sometimes unlimited lengths. You've got to understand that's just chemistry, though. That's just a bunch of approximations."

[@syedinayat3548]

can you make a video on how you can become a physicist from cambridge i want study there but i dont know what to choose in natural sciences like i dont know the procedure and i cannot understand can you help me with this.can you reply me or maybe make a video on it(if you have already made a video on such so please can you give me a link to that, and i searched whole youtube for such issue i didnt find any solution) and if there is someone in comment section who knows about such please,help me to clear this doubt of mine this will be very helpful to me thank you😊

[@syedinayat3548]

@Skippy yeah i have seen cambridge prospectus but i dont know how i am gonna get undergrad in pure physics from cambridge because there isn't such thing as pure physics for undergrads there is natural sciences dont know the process after taking natural science,so if anyone can help me, i would be very thankful to them

[@SirPhysics]

This is not a critique of the content of the video, but the title is a bit misleading. You don't talk at all about *how* quantum physics predicts the size of an atom, only what the size of an atom is according to quantum physics.

[@penumbraman99]

When I saw the title of this video, I thought it might be a trick question. I remember seeing a lecture on quantum mechanics by Dr Ben Schumacher where he tells the story of getting a question of how big is the photon on his Physics PHD oral exams. That is a very complicated question! I am sure calculating the size of large atoms are impossible without shortcut tricks.

[@jlpsinde]

Cool as always

[@enzbenzz]

I am a bit disappointed that you did not showed how to obtain the Bohr radius from the equations but still very good content

[@JohnDlugosz]

All the models assumed... You forgot about the "Plum Pudding Model".

[@arielnavarroeilas]

If a single atom size is defined by the wave function, in other words having different sizes at different times, why we can't perceive macroscopic objects wobbling in size/shape? Like a Brownian motion for solids affecting their shape.

[@ThatCrazyKid0007]

Because atoms are incredibly tiny and the scale difference is too large to notice a difference. It's like asking why can't you see the sea levels rise with the tide during the day from the Moon.

[@arielnavarroeilas]

@@ThatCrazyKid0007 Yes, I thought about that, the difference is small, but it could add up for each atom present. To put an example, if the size of a single atom can vary around 1%, every 100 atoms could signify one extra/less atom. In an object, if the differences add up at a certain point, it would still mean that the pencil size would oscillate 1%? Your example would fit better while observing a single atom (earth) from afar, but if you put 100,000,000 earths one on top of the other, the wouldn't the effect add up bringing the whole effect to the larger scale? One explanation I can think of is that on average those chances cancel each other, but still... not sure

[@gabrielpetre3569]

Yeah, but the chance that all the atoms aligns their movement to one side so it becomes macroscopic is.basically zero

[@dimension-ji7xk]

I've seen atoms while meditating.

[@whisper3493]

Pauli exclusion principle states that you cannot pinpoint the exact location of an atom at any given time. But the fact that the atom is moving constantly with almost the speed of light we can can say that we can actually easily point to it at any given time since it's all over around the atom. This seemed a contradiction to the principle. Is the property of electrons the same when it's inside the shell of an atom and when it is outside? Same with other sub atomic particles we don't know about it.

[@gabrielpetre3569]

Pauli says you cannot get position and speed at the same time,.in this case since you dint measure speed, you can calculate average positions

[@whisper3493]

@@gabrielpetre3569 that's what he said but you can sample a tiny quadrant of the sphere where the electron/s should be. Then the question is how many time the election/s would be in this particular area per tiny unit of time? Considering the size of the atom and the area traversed by a tiny particle/s like electron/s at the speed of light then we are certain it is present everywhere most of the time!

[@whisper3493]

@@gabrielpetre3569 then if you set a trap where an electron after moving in you can catch it almost 100% If you put a sensor to that sampled area then it would indicate the presence of electron all the time unless otherwise repelled by some forces. It it the same when scientists once said atom is a tiny "indestructible" particle of matter proved to be wrong with the advent of nuclear physics!

[@gabrielpetre3569]

Mm, not quite following, but its all a statistical analisis, you can calculate the volume of the orbital, and then calculate the probability that the electron is in a square, or in this case the shell in which.you will have a higher chance of finding electrons

[@whisper3493]

@@gabrielpetre3569 yah you are right and that is really the idea. Then came the superposition. The idea of particle-wave in nature. So this model will remain as is untill the time they have a better understanding of what is not been understood at the moment. Entanglement also exist that defy explanation.

[@deepsahay1080]

❤️👏 great video

[@GamerGuild]

Simple as always

[@TheHumanHades]

Please make a video on why the square of a wave function is actually what we can directly measure.

[@Ni999]

Imagine that you are standing on a checkerboard. Label one direction x and the other y. I come along and place some gold on a square neither directly on your row or column. You can go pick it up if you only move using one pair of moves. Method 1 - go so far in the x direction, make a right turn, and go in the y direction until you reach the gold. Note how far in x and how far in y you had to go. Method 2 - turn until you are directly facing the gold, walk directly to it. You can no longer count in squares so can you explain how far you went in terms of square marks on the board? Yes. Yes, you can. And you probably already know the equation. r = √( x² + y² ) A wave function expresses a thing in time as being made up of constituent parts in frequency. Any signal can be represented that way and all it takes is some complex trigonometry. If you want to find *the magnitude of any one frequency component* then you are asking about the Method 2 path, *_by definition of how you got the values for the wave function._* Repeat it until you have hit all of the frequencies, one by one. Unless you're far into science, math, or engineering, every frequency chart you have seen was built that way - your speakers' frequency response, for example. They looked for something in time in the quantum world and couldn't make sense of it. So they broke it down into frequencies (of how often something happened or where or by how much) using the simple math you know applied to complex math that maps time to frequency. I hope that helps, it's the easiest explanation I could give and still be accurate. See 3Blue1Brown for Fourier videos to get introduced into the full power of the underlying math involved.

[@TheHumanHades]

@@Ni999 Thank you so much man you really have me a very good intuition. Yes I have watched 3b1b's video on Fourier but it was a little over me 😅 as I am just in 12th standard. Still I appreciate you effort. 😀

[@Ni999]

PS - You asked about the square, he said that it was about the square. And then he immediately said in a lower voice and I quote - _actually the square of the modulus._ And he never explained what that detail was about, did he? No, he did not. He simplified it. (If he hadn't muttered those additional magic words he would have oversimplified it.) You're right, that's the subject for another video and lots of others have made those videos. But I promise I understand what he meant, I understood your question, and if you followed my answer then you know enough to get your arms around what they're talking about until you can learn about more details (a lot more, trust me, they almost all oversimplify things).

[@TheHumanHades]

@@Ni999 😅

[@Ni999]

@@TheHumanHades Haha, I didn't see your reply when I thought to add on the PS. 😛 Use the intuition you have from the explanation and you're going to be far ahead of the curve as you learn more. 😉😊👍

[@fukpoeslaw3613]

how do you measure that? it's far to small I would think

[@fukpoeslaw3613]

or did you just explain that?

[@fouadudh2110]

And as for the proton, it must be having a cloud too, which is surely small for the hydrogen atom but is of a size quite noticeable when it comes to the muonic hydrogen atom.

[@Vagabond-Cosmique]

What's a muonic hydrogen atom?

[@myothersoul1953]

I don't buy the assertion that atoms are mostly empty space. That space is filled with fields and fields are at least as real as protons and electrons. :-)

[@klassemyra]

How do we actually know that helium and hydrogen are the smallest atoms? Can it not be the other way around, that hydrogen is the biggest? And how do we know it’s vacuum ”inside” the atom? This doesn’t sems logic!

[@pranjaljagtap8398]

why did you say that proton has infinite mass instead of assuming the nucleus having infinite mass

[@schmetterling4477]

It doesn't have infinite mass, but a proton is approx. 2000 times more massive than an electron. To a physicist 2000 is basically as good as infinity.

[@pappa6085]

i think you've calculated the radius of an atom

[@SeanCMonahan]

I'm stuck on the fact that a pencil eraser is only 100,000,000 hydrogen atom radii across!

[@SeanCMonahan]

It's also wild that the smallest transistors we can make currently are only a few hundred atoms across.

[@hossainboard86]

Physics:This is a topic of quantum mechanics Parth: let me throw the big daddy(schrodinger equation) of quantum physics 😏

[@RocketsNRovers]

parth G kaise ho

[@TheNosarajr]

You could have just said so many side by side equal the width of a pencil.

[@fukpoeslaw3613]

so 200x = about infinite that's precise enough??

[@etme1572]

I guess the important part here is that the proton is much heavier, and therefore its motion in the system is less significant compared to that of the electron. I don't know much about quantum mecanics but I know that those approximation based on the weight of each part in the numerical result are quite common in physics. Just a guess though

[@jfrjr7964]

So, if the size of an atom is that. Then the vast majority of the atom volume is made of NOTHING! As electrons are mostly like light, some times matter and sometimes energy, then if you have the correct frequency you can virtually puncture through anything without any effort. As if it was an image, like a shadow. But you need the right frequency for that single material. For complex materials you will need more complex solution, which is to find the frequency that makes that substance to be held together.

[@MuzixMaker]

Yep, any object is mostly empty space.

[@yili3339]

how big is an atom? infinity!

[@MirlitronOne]

If you stood in front of a hydrogen atom that had been expanded to one metre diameter, you would see - nothing. The electron is too small and moving too fast, and the proton would not be visible to the naked eye from 50 cm distance.

[@DrDeuteron]

or not. The electron is a point, or a Planck length: invisible, but it occupies a Compton wavelength, and that would be 1/2 x 1/137th of a meter = 3mm. The proton would be 16 microns, but it's orbital would be a 1/2 a millimeter.

[@soloperformer5598]

So only predicts, doesn't verify.

[@Waterfront975]

This was not bohring. Hahahahahaha!

[@MAHESH-qe8cv]

Its small.

[@michaelmelling9333]

While I don't believe it, I've heard that there are more legal moves in a game of chess than there are atoms in the known universe.

[@alecplano9563]

#1

[@HD-dz4uk]

Bigger than Bidens brain 🧠that's for sure. Sorry couldn't resist.

[@IdeasOfAjit]

Can we have clubhouse conversation?

[@achannelfornoreason6550]

1st to comment 😄

[@anshumanchoudhary4732]

Great video!