what is the radius of the hydrogen atom?

What is the radius of the hydrogen atom? How has this answer changed over time? Quantum mechanics is fun and cool. Tablet math is tedious.
If anyone is trying to solve a homework problem and just googled this, a_0= 0.53e-10 m
Does anybody actually read these things?
The textbook is Principles of Quantum Mechanics by Professor R. Shankar.
Here is a link to his YaleOpenCourse course: • 1. Course Introduction...
You can join my Patreon if you like. I post a new, patron-only video each month. / acollierastro

[@stevenklinden]

Shankar was the chair of our physics department when I was in grad school. He was a funny guy. For some reason, one thing that sticks in my mind is when he was introducing a seminar speaker who was going to talk about hot, compact stars, and Shankar goes, "Like Danny DeVito".

[@Kavukamari]

this guy sounds like a riot, i kind of miss university

[@Telonious_Terp]

😂

[@ChumbisDilliams]

What a king

[@DoctyrEvil]

He was a legend among the undergrads as well when I was there. He taught freshman physics to the advanced students for a number of years and was much loved by his pupils.

[@pmurderhoboexpo]

I mean, his greatest discovery, according to Shankar, is "a small parameter that justifies most calculations performed in physics: 1/ego, where ego is the author’s ego." I want to email him a love note.

[@Chris_winthers]

Pretty small probably

[@valjean76]

yeah that's probably close enough for physics.

[@lbgstzockt8493]

Big if true

[@Nylspider]

True

[@drorbedrack8720]

Less than 2

[@HarryNicNicholas]

well, fairly small. it depends on if you're looking.

[@cyborg555]

When I took undergrad physics back in the 70s we didn't have fancy CMOS spectrometers. We shine those hydrogen and neon tubes (which look just like the ones you showed) through a small slit, refracted them off a piece of diffraction grating, and measured it with a ruler. Uphill both ways

[@AlanCanon2222]

I assisted Dr Kielkopf in spectroscopy at U of Louisville in 1987, and we made good use of exactly that kind of kit augmented with a pretty fancy laser. I saw Helium ionized enough to form He2, and then watched as Dr. K. tuned the laser until the molecular bond of the He2 itself became an excimer laser (the gaussian hump on the PC turned into a razor sharp peak). I was just a Freshman but being the only undergrad physics major in the entire University but one, I was snapped up as the department's favorite pet. Working in a real life physics lab is one of the most memorable experiences I ever had, even though I didn't go all the way. Channels like these help me catch up, now that I'm in my 50s, and ready to go back and learn PDEs and tensors, etc., just for the pure intellectual enjoyment of it.

[@thomasfahey8763]

I remember sitting down for a midterm when my lab partner asks me "What's the square root of four?" I immediately pulled out my slide rule and told him, "Looks like about 1.98."

[@joseapar]

When i an astronomy undergrad 23 years ago, we also made the measurement by hand not because there weren't new digitally assisted ways to do it, but in order to teach us that it could be done by hand and the problem solving it took to figure it out. It was kind of fun since it was a one time lab and mostly we were doing the measuring.

[@stevegredell1123]

@@joseapar Same in my astronomy undergrad we looked at the hydrogen alpha absorption line with a prism (or a slit, IDK it was 15 years ago). Just needed a good sunny day

[@0Coeus]

I absolutely love the quote "the thing about differential equations, is.. if its possible to answer it, you just know the answer."

[@stuartdryer1352]

My quantum mechanic said I was having a little problem with my wave function but he replaced it and now everything is working fine. Only cost about 900 bucks.

[@kentix417]

He can tell you exactly how much it will cost to fix or exactly when it will be ready, but not both at the same time.

[@thear1s]

Replace mechanic with doctor and this conversation definitively happened. Quantum mechanic is a quack magnet, and not in the electromagnetic way

[@cubandarknez]

I am here for the developing character dynamics/conflict between past Angela, future Angela, and editor Angela. Oh and the science communication is also nice!

[@Takyodor2]

You can just sense the tension. I bet there's gonna be some backstabbing in season 2.

[@turnerburger]

Currently taking PDEs as an engineering student, and hearing you mention the eigenvalue problem made the separation of variables method jump out at me, glad to see that was on the right track! We have a project in which we lecture on a topic not covered in class, and I might just make it over solving the schrodinger equation for a hydrogen atom. Thank you!

[@Rabcup]

Lol if I was an engineering student I’d need to take PEDs not PDEs

[@TIO540S1]

As near as I can tell, any time you’re solving PDEs, it’s “let’s use separation of variables.”

[@m.f.3347]

​@@TIO540S1it's either that or *shudder* Green's functions

[@primenumberbuster404]

As a math major I swear, Engineers be getting all the nicest looking functions to deal with. 😔

[@mastershooter64]

@@primenumberbuster404 Bro Lmfao ikr! All we get is an insane function that's continuous "almost everywhere" and then they ask you to integrate it! then I have to learn measure theory

[@traywor]

I actually found the 1/137 thing really intresting, and wondered, why the hell would it be such a simple fraction. However it all gladly went away, once you told us, that it isn't exactly 1/137. It's like finishing a bag of chips: You first feel sad, that it was the last one, but then you realize that there are still some crumbs to eat.

[@slawless9665]

"Does anybody actually read these things?" yes Also I love that you pumped up that "joke" like it was the cleverest, funniest joke ever told in the context of physics and it was just the word "anyway" and what we can infer from it. Comedy is fascinating!

[@Crescent_Audio]

I learned how small an attosecond was the other day, along with how high the temperature of a particle can be before it rips itself apart, both numbers are so far outside the realm of human comprehension and intuition it’s fascinating. Glad to be early for another banger of a video!

[@oliviapg]

My favorite thing is when numbers completely beyond comprehension cancel out and leave something bizarrely comprehensible. My favorite example is the Hubble-barn. The Hubble length is the radius of the visible universe, and the barn is a unit of area used in nuclear physics that's equal to about the cross-sectional area of a uranium nucleus. If you multiply these two absurd numbers together you get the Hubble-barn, a unit of volume which is equivalent to the volume of a cylinder with a cross section the size of a uranium nucleus and a height the size of the visible universe, and you get.. about 13 liters or 3.5 gallons, a volume which sounds like you're describing the amount of gas left in your car.

[@dah_bard1160]

​@@oliviapgwow never heard of that, kind of hilarious 😂, just imagining a near infintely tall miniscule pole whose volume is 13 liters lol

[@lbgstzockt8493]

Thats a great fun fact, thanks for sharing@@oliviapg

[@wernerviehhauser94]

Usually, when I teach the hydrogen atom, I rephrase Bohr's postulate this way: Electrons are only allowed to have orbits where the length of the orbit is a multiple of the deBroglie wavelength of the electron on this orbit. This way, I skip the angular momentum, which is something the students usually have never heard before. I got this from an article where they imagined the electron not radiating energy because it is in resonance with itself, like an oscillating ring, as a way of looking at why there is not radiation from the accellerated electron.

[@andrewfleenor7459]

Where are you finding students that have heard of electrons but not angular momentum. Not trying to diss anyone, it's just wild to me because I've had the ice-skater/angular momentum thing in my head for as long as I can remember. :D

[@Robert_McGarry_Poems]

Nice. Yeah, the electron orbit stuff always made me think too much... wait why doesn't it just fall in? (empty looks and whispers) he knows...

[@wernerviehhauser94]

@@andrewfleenor7459 curriculum. Not much to be done about that..... The students usually know about the ice skater piroutte effect, but there's not math, derivation or formula going with it.

[@AndDiracisHisProphet]

I heard this too and the idea was even in my 13th grade textbook, but it cannot really be historically accurate, can it? DeBroglie formulated his idea of matter wave quite some time after Bohr.

[@wernerviehhauser94]

@@AndDiracisHisProphet Afaik this idea came up much later, even much later than deBroglie thesis in 1924; and I do tell my students that this is not what actually happened. I like the approach, and you could have discovered and constructed it this way.

[@orterves]

I'm ten minutes in and I feel like the video has already covered an hour's worth of material - but I feel like I'm actually still following on; great work!

[@vibesplaneoverflow-bz1xy]

As someone who majored in Physics and works as an engineer now, this was weirdly comforting and nostalgic. Like I remember deriving this on the final exam. I may have gotten a C+ in Quantum 2, but it was still a good time, and expanded my mathematical and scientific horizons. Thanks, Dr. Collier.

[@FollowSmoke]

Hang on, I'll grab my ruler

[@rakino4418]

Matt Parker, is that you?

[@djmcheme]

First of all anyone can watch Shankar teach intro to physics on KZbin. I have and I highly recommend the videos. Second…these videos are such a treasure. I have taken 4 semesters of math for engineering school at the university of Pittsburgh but that was 25 years ago. I didn’t completely follow but I did enjoy going through the exercise with this wonderful young physicist. Thank you so much for this great content.

[@chrisglosser7318]

The analogy about the getting the joke is absolutely spot on

[@ironbutterfly3701]

44:18 it is spherically symmetrical. I have a blog post on it “p orbitals are not dumbbells”. The point is these are harmonics the actual wave function is a combination of px py and pz and the combination is spherically symmetrical. This is similar to say Fourier transform but in three dimensions.

[@m.f.3347]

i remember trying to Google this during my 1st year of undergrad and being so confused at all the seemingly conflicting information

[@ekuude]

War flashbacks

[@douglasrank-im1gp]

I went to Rice Univ in 1976 with a burning desire to be a physicist. But though I won the math award in HS (400 in class), I was so lacking in math understanding that in the end I became a psychiatrist. I loved your video, reliving a long lost, beautiful dream.

[@choosetolivefree]

Had this video up on my phone for like two weeks before finally pressing play. Surprised to find, you're a rare person who can make such a dry and boring topic actually interesting to watch. I feel like you'd make a good teacher, as, aside from the maths, which I am not educated on, you made complicated things make sense (as much as they can with quantum physics). I was engaged throughout this hour long video, learned some cool things. Well done.

[@RooockGamer]

It must've been nice to have fun while reading a quantum mechanics textbook. In my quantum mechanics classes, I used the Cohen-Tannoudji one (with some sprinkles from the Sakurai one), and I only ended up with tears, lots of tears. The silver lining is that this sentiment was shared by my friends who also took those classes.

[@RooockGamer]

btw, It is a fun exercise to do the whole calculation step-by-step; however, it quickly ceases to be enjoyable when you start working with the polynomials and normalization 😩

[@rbr1170]

My biggest gripe with my teachers is that they made mathematics sound and feel like you need to be born with the ability to be able to do it. We should be telling kids that mathematics is also a language. No one is born with the ability to speak just any language, you learn it. And although some people can learn faster and learn more, we all have the prerequisite to learn it and speak it to a degree that will allow us to converse and make progress on some ideas. At first look (first listen), everything can sound nonsensical but once you learn the languange, it starts to make sense. But just like other languanges, we should learn to speak it to talk about things in it. This is why I have a gripe with my teachers, it is as if you can have a deeper conversation on something which does not even have the "right words" for something. It will be close to impossible to contribute without knowing the mathematics behind quantum mechanics and most of physics, in fact, it often misleads you because you have to rely on intuition alone. Unfortunately, intuition can only take you just far enough but not anywhere near the truth of things.

[@volbla]

Your teachers sound very weird. Their job is to help people learn. If they assume some people have the capacity to learn and some don't, then they may as well not even be there. You could just hand out textbooks instead and wait for some students to learn and some to not.

[@marymegrant1130]

​@@volblaI completed a mathematics undergraduate degree in the USA. I assure you, this is not an unusual attitude. The graduate mathematics students are selected for their potential to be mathematicians.They teach math to be paid a stipend by the school and to have their tuition fees waived. Their priority is their own math classes, not teaching. Below the university level, teaching is poorly paid compared to technical jobs. This means talented people often choose more lucrative professions over teaching. The better students will receive better teachers. I was fortunate that I was placed in advanced classes in my lower grades with the better teachers. Even with this advantage, I had many bad teachers. These issues reinforce the idea that math requires a natural talent. Also, since math builds so quickly upon itself and much of the early subjects are a linear path, a student falling behind often cannot catch up. There are also issues with classroom discipline, uninvolved parents, violence in the schools which cause talented people to leave the profession. Every year I went to a public high school, I would miss school because of a teacher's strike during contract negotiations. The teacher's union made it difficult to fire incompetent teachers. This was in the 1970's. I don't think anything has improved.

[@todhagan2966]

Yes, I read those things! I always appreciate videos with links/citations in the description.

[@cruxofthecookie]

I have (what is probably a dumb) question: why use 0.014 x 10⁻¹³ rather than 1.4 x 10⁻¹⁵? Is it to indicate the precision/significant digits?

[@FordFourD-aka-Ford4D]

I love that your channel is blowing up

[@wkgmathguy218]

'Does anybody actually read these things? ' Yes 🙂 Very nice video Dr. C, more please!

[@TIO540S1]

32:46: “Deal with it!” “Like and subscribe” with eye roll. How can you not love it?

[@mybuddyphil8719]

Ångström has the a with the cute little circle on it, which in Swedish makes it not an a, but something pronounced half way between A and O. I checked through his Wikipedia a bit and saw he grew up in the Ångermanland province, and that that province gets Ånger from the old Norse term for "deep fjord". So his name might mean something closer to "Stream of a Deep Fjord". Though just ång in modern Swedish means steam, so it could be "Steam Stream"

[@Takyodor2]

Fun tangential fact: "ånger" also translates to "regret".

[@scottmclaughlin1410]

I tried to think of how Terry Pratchett and Douglas Adams would describe the smallness and I realized that I can't do it justice so just imagine a really funny analogy was here but it was so small you didn't notice it.

[@billysoup9483]

Babe wake up new acollierastro video

[@sanderscamper]

Instead of giving us a spectrograph for determining the wavelength, my physics unit had us build one with prisms and mirrors in a dark room. One of my favourite experiments.

[@volbla]

Cool! Big, physical examples are always welcome in class.

[@GingerWithEnvy]

I love how this video serves as both a lovely informative video on the history of how we use quantum mechanics in application to the Hydrogen atom as well as a cheat sheet to the derviation worksheets (though tbf, for this particular problem there are plenty of other cheat sheets out there and a lot of the nitty gritty like converting to spherical polar coordinates from cartesian that would be in the worksheet is moved quickly through)

[@RealMenWorshipZeus]

Another banger video. So good. If anyone is looking for another very funny and good QM text: check out How to Be a Quantum Mechanic by Charles Wohl. He taught QM at Cal for 40 years and has a really dry humor that permeates the book. 10/10

[@mayna2083]

Thanks for the new video Angela. I was fiending and you're going to make the rest of my work day great.

[@zach.hanford]

I just thought you should know that on my homepage I saw an hour long video about the hydrogen atom and thought "nope, absolutely not" and then I saw that it was one of your videos and well... here we are.

[@jacoblojewski8729]

Ah yes, the spherical Laplacian - the bane of every undergrad math and physics student. When I did this in undergrad, our book used a lower-case rho (ρ) for the radius, so my professor would make a joke after expanding it out - he'd flip the equation upside down (overhead projector) and say "look! it's the same equation!".

[@F.W.Goodsell]

Cool. Now do the simplest quantum biology example. What even is that? Is there a wave function for chlorophyl?

[@hunterlouscher9245]

I have a bug up my butt about how diffyQ is taught. Please I want that video.

[@rainbowkrampus]

"...and then she wandered over to another campfire and they were discussing whether or not the universe is a simulation. And at yet another, Tom Bombadil."

[@davidangeliglesiastinoco3598]

Comment on video around 10:20: You can treat it classically, the model is in chapter 10 of "Advanced Classical Electromagnetism" by R.M. Wald (2022). See also "On a Classical Theory of Charged Particles with Spin and the Classical Limit of the Dirac Equation" by Dixon (1964) [Dixon ignores self-force effects while Wald's model includes them].

[@BobAxiom]

I love the comments that are all “that’s not physics! It’s computer science or something engineering or something something other-ology…” My doctorate is in computer science. Nothing that Angela noted as a physics achievement in the last 70 years was computer science. It enabled a lot of computer science research later (like mine). We can’t do any of the things we do today without the physics that they did then!

[@marcuselliott9219]

Quoting lyrics from "Louisiana Saturday Night" elevates you to Shankar's level. Nicely done.

[@caspermcgonagle1532]

Putting this video in my watch later for when I learn linear algebra next year

[@JB-ky5qg]

I thought the math was going to be the hardest part of this to understand, but that comment montage was the real mind blower.

[@rjlesch]

Now I want to see an episode where you interview Dr. Shankar.

[@horrorhotel1999]

There are actually pretty decent instructions online for making DIY spectrographs from webcams. You can kinda calibrate them with LEDs. Definitely not perfect, but maybe a fun extension of the project if you want the full STEM package

[@thylacoleonkennedy7]

4:41 "Oh cool, this probably won't take too long -" **glances at progress bar** ah.

[@aurthurwillis6889]

Absolutely devastated that nobody got the Louisiana Saturday Night reference. Seriously though, I'm getting ready to work through a second QM course. I did Zwiebach's book and bought Sakurai for a more advanced text. How much am I missing by not doing Shankar? Thanks, I've been enjoying the series!

[@MrBigKahuna-e9n]

i disabled my ad blocker just to watch this. i liked the old navy ad.

[@HighKingTurgon]

Cool Argonath, Dr. Collier. Who drew it? (I literally have not been able to find it.) Thank you for taking this classicist through the world of quantum quantum quantum.

[@icepick117]

Engineering on its own is a fine field, it's the engineers that I can't stand!!

[@ClunkyChemE]

"Suck it nerds" made me laugh out loud. Us nerds are still waiting on your broader board game video. The Stratego video was fantastic and helped me realize how much my parents helped foster this passion, even if inadvertently.

[@MinMax-kc8uj]

"It has to be true." Nope, there is another type of angle that doesn't use pi. We can do arctan angles, which is most likely what this universe uses. Any element or compound could probably be represented with arctan in its particular phase state. When you say something is quantized, it's probably arctan. Which would lead to rational slopes as well as irrational. But I could be wrong. I'm just saying that there are other options. Also, the Smith Chart seems like a major indicator of arctan.

[@Carl_Ellis]

I love the math. I'm one of those did=it-30-yrs-ago, don't remember too much, but haven't not seen it before.

[@eerikay5367]

Ångström, more closely pronounced as O-ngström (Å is like AU or somewhere between O and A) , is probably derived from 'Ånga' which means steam, vapor or fumes. So it can mean something like "Steam-stream". Of course I can only speculate where the name comes from, but I doubt his name comes from Ångsta. Great video as always!

[@emanuellandeholm5657]

Swede here: Ångström = ånga (steam) + ström (stream). Stream of steam. Ström is also the Swedish word for current, as in Amperes. Edit: Also, it's pronounced something like Aung Struem. The dots and circles over the vowels matter. "ång" rhymes with "long", and the vowel in "ström" is like the "ea" in Amber Heard. :D

[@allenaxp6259]

Yes be careful don't touch.... Excellent video.

[@tehW1ckerMan]

"has anyone ever been so wrong, but also so inspiring to the people around him, that he made other people figure out the correct answer? " yes, Sigmund Freud

[@hntrofdmads]

this is a great video to listen to in the background while writing about lobsters and sea urchins and bathymetry. thank you acollierastro

[@danmacarro]

I love your channel and how you communicate with the hard details of equations. My step-daughter wants to be an astronomer ever since the Webb telescope was launched. I want to show her your videos, but she's in 10th grade and, while I love it, I can barely follow everything! Do you have astronomy-physics KZbinrs you would recommend or particular videos of yours that are more HS in level?

[@salihalbayrak-es8ky]

a 1 hour video about the radius of the most basic element? yes please

[@scraps7624]

Holy crap, this video really brought me back to my atomic physics clases in undergrad lmao

[@sanalone9492]

"sorry" she says as if i haven't hunkered down with a hot cocoa and a brownie for this very video

[@killua_dev]

I'd love to see the Mathematicians DNI Differential Equations video

[@profbrento]

My man Shankar out here getting slammed by billions of photons but just takin it like a man.

[@CysteicAcid]

Ånga means in swedish, vapour/steam. Så you could translate it from swedish into vapour/steam stream. Ångst means anxiety (angst, german), but then it would be Ångstström, and

[@FrancisFjordCupola]

From Angstrom, the town and the river, I'd guess you'd think it's a shame Albert's last name wasn't Reinstein.

[@Mj323_bb]

A couple weeks ago I had this dream. I was in it and you were in it and lots of other people were in it -- we were at some talk or lecture, and Dr. Shankar was the professor/speaker. Everything he explained seem so incredibly true and profound to me. But you kept making like that patented acollierastro frowny face like he was making mistakes, little mistakes. Finally, the lecture came to and end, and I felt like I was some kind of mythical sponge, completely filled with the wisdom of the ages. But then Dr. Shankar fixed his gaze on me and slowly pointed his finger right at me and said "Vujade". And I woke up and couldn't remember any of that mystical knowledge. But my morning coffee did taste unusually good that day, so there was that

[@jonathandurbin5534]

I just had a quiz over all of this in my modern physics course!

[@vulpes82]

I find it fascinating that Bohr seems to be really getting it from all sides these days. Or at least that's how it seems based on this video and Sean Carroll's two-books-ago and some other books I've read in the past few years. Funnily, the books all kind of shit on him for being mean to Everett, while Angela has no truck with multiverses. But after a period around the time that play "Copenhagen" about his relationship with Heisenberg and the German atomic bomb program came out where he was really lauded, it's just funny to see the "other side." Of course, his actions during WWII aside, I think despite being wrong about everything, his greatest contribution is undoubtedly that he seems to have been an incredible mentor and colleague. Oh, and finally, apropos of nothing: Riemann Zeta-Jones, I salute you and your Patreon name!

[@tariq3erwa]

33:45 we had the same course titled differently "Special Functions in mathematics", one of my colleagues was studying so hard he swore that Legendre with this picture came calling on him in his dreams.

[@jeremybuckets]

I clicked on this video trusting the question was much more interesting than it sounded on its face, and I was not disappointed.

[@AlijahWright]

this is the greatest channel on the website. peak fucking youtube.

[@petevenuti7355]

Before my comment gets buried, I just want to say I love your videos, point of view, humor and knowledge. Off to work, I'll actually watch this one later and might have more comments and questions. Unrelated question, how is a black hole singularity not like Gabriel's horn? It seems the same in concept as I understand both. (Not a joke, but feel free to add a punchline if you want)

[@JT-rg7kl]

A tiny bit above my pay grade, but riveting explanations that really increased my understanding, so thanks for that. Also, love framed Gates of Argonath laying atop the trick or treat tablecloth(?)....a thousand and one jokes right there!

[@EmpyreanLightASMR]

5:41 i only just discovered your channel but i'm guessing you've looked up Snell's Law... Snell's name is right out of the Harry Potter universe (sorry if that's a touchy subject): Willebrord Snellius, born Willebrord Snel van Royen. In my research, the van Royens were Ravenclaws until, in his time, he chose (talking back to the hat) to be in Slytherin, becoming a Snellius. He was an evil genius, discovering that the angle from which any spell is fired in one medium will always equate to the angle at which the spell enters another medium, usually the body of an enemy, times the index of magical penetration. The modern day physicist was able to boil down index of magical penetration (a complex equation) by removing irrelevant constants (e.g., the magnitude of the velocity of magic in waveless aether, represented by a rune that no longer exists in writing) and properties of magical physics like diffusion of enchantment over time, shimmer particles as derivatives of glimmer with respect to gleam, the Fairy Dust Postulate, and a myriad other untold factors long forgotten by muggles - along with angles (angles are angles, no matter who you are) into the standard law we use today.

[@WouldbeSage]

Thank God for the calculation skip time stamp, because everytime Angela writes a greek letter my eyes instantly glaze over and my mind is suddenly a million miles away.

[@TheWayfaringFox]

48:30 I've done these integrals enough times that you can make a variable substitution of like u = 2r/a0, and then, with some algebra, the integral will reduce to the gamma function.

[@stephanieparker1250]

Is that a framed photo of the towers of Argonath behind you? Sweet 🤗

[@dexterrity]

*acollierastro on parasocial relationships:* "I feel like he gets me, and we would be friends... and that's weird" *Me watching acollierastro videos:* 👀

[@m802001]

Chipmunk Angela was the best thing I’ve heard all evening.

[@rajkobizjak1]

Thank you, you helped me solve some questions i have regarding spectra! Well done!

[@rudyj8948]

that mu at 38:56 is the most perfect mu ive ever seen in my life

[@allanjmcpherson]

I studied engineering physics, so I find those comments about all that experimental physics research being engineering hilarious (and slightly insulting) on both fronts.

[@Jesayou]

Yes people read the little thing bellow the video probably not a ton but most likely a lot more since you have a good link in there. Also love the content don't understand most of it but Im here for It

[@catStone92]

honestly, those "that's not physics, that's engineering" comments have some real "actually physics is what advances math" energy

[@jamesjohn2537]

i love the mathematical equations without seeing inside and why!, but later find out to be that, they describe physical phenomenon. dear thanks keep up💫

[@testostyrannical]

Gonna tell my homie Shankar "I know this person with a science channel on youtube and she is, like, _so obsessed_ with you..."

[@Takyodor2]

I wonder if in a 100 years, physicists will be like "haha, those silly people in the early 2000s though this special case in describes atoms, when it's just a tiny part of the whole picture!", or if we're actually close to the "truth" with quantum mechanics.

[@kennethkatz6782]

1980,81 was a very interesting advance. The same day the Mandelbrot shape was fractal proven was the same day the 1st computer program advance occurred. He worked at IBM and that shape vs. Pi is hard but true. The main.

[@DamienPalmer]

@6:00 The thing is the emotional state of "angst" is named after that town. It's not a fun town.

[@vlogerhood]

I have taken DiffEq, and Linear Algebra, both for my engineering degree. I have used both of them exactly never in the about 20 years since then. So I recognize the words you said, but have no clue beyond that.

[@son0of0the0beast]

I knew that calc 4 would come in handy so i could watch a KZbin video and be like "yeah i can kind of follow that"

[@Andrewlohbihler]

According to the Bohr model, the radius of a hydrogen atom in its ground state (the lowest energy state) is approximately 0.53 Ångströms (or 0.53 x 10^-10 meters).

[@uploadJ]

Does anybody have a good explanation for why when two Hydrogen atoms meet to combine, in order to 'combine' they require a third body to transfer energy to? The two atoms don't just give off a photon like most reactions when they react (H + H -> H2), the two must come into contact with and transfer the energy via contact with like a metal or whatever, they do not just emit an EM wave/photon via emission.

[@gabrielsantiago7318]

As a chemistry major who will eventually need to take pchem in a year or so, thank you for this video

[@realfunnyman]

When I was studying physics, my quantum professor cut the hydrogen atom section because we had covered it well enough in our modern physics class. Unfortunately I was a terrible student when we took modern physics, and didn't remember much from it.

[@NVM_SMH]

I like it when I have an exciting day at my desk.

[@milahokelpling3631]

This whole 1 hour long video isn't about the radius of the hydrogen atom, but about how people should admit they're wrong, when they're proven wrong.

[@flinxsl]

Engineers and physicists can be good friends. I'm sure you enjoy technologies like iPhones and youtube, and we are happy to build whatever practical tools the scientists need to learn more about the universe and will be your biggest fans when you tell us about it.