What is the Bohr model of the atom?
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- เผยแพร่เมื่อ 19 มิ.ย. 2024
- This video looks at the pioneering work of Niels Bohr who proposed a novel model of the atom in 1913 which would lay the foundations for a quantum mechanical treatment ten years later. After discussing the limitations of Thomson's Plum Pudding model and Rutherford's Nuclear model, Bohr's quantum model is discussed as a union between classical ideas of electrostatics and angular momentum quantisation. The radii and energies of the allowed electron orbits for the Hydrogen atom are calculated, along with the visible emission spectrum. The video ends with a brief discussion of Bohr's influence on the development of quantum physics.
References:
Quantum physics of atoms, molecules, solids, nuclei and particles - Eisberg and Resnick
Introduction to Quantum Mechanics - Griffiths and Schroeter
Introduction to Quantum Mechanics - Phillips
The Quantum Story - Jim Baggot
Quantum Physics for Dummies - Steven Holzner
Thirty Years that Shook Physics - Gamow
Inward Bound - Abraham Pais
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I am calling it right now. You are the 3Blue1Brown of Physics! This channel is going to get big. I am loving going through your videos to get a a better understanding of physics in this universe. This is fantastic source material of the future when I do decided to start studying physics seriously. Getting to conceptually understand the struggles that past scientists had to deal with when confronted observational data is turly eye-opening. We are standing on the shoulders of giants, and most individuals in our species are unware of their existance. Our modern society exists because of them, and their contributions to the field of phyiscs.
KEEP UP THE GREAT WORK!
Although 3B1B has some beautiful animatons and sourceful content, this channel is way better in terms of quality and approach to viewers, at least for now. Hoping to see much more from this amazing guy. :-)
@@oumuamua12 Agreed.
@@oumuamua12 I've got a feeling that your opinion on this may change when this channel gets older. Stuff is going to ramp up in complexity, and some people will get lost along the way. Zach Star (formerly 3Blue1Brown) is doing an _incredible_ job with the stuff he is dealing with at this point.
If Physics Explained can match him when he gets as far into things, everyone is in for a treat. This video is definitely fantastic but there's still a long way to go until all of physics is covered. I just hope that he keeps the level of detail as high as this one throughout. Equations is what I''m missing more of on TH-cam - there is plenty of the handwavy stuff.
@Physics Explained: Thanks for sharing, I really appreciate your work. 👍
@ I have some understanding of linear algebra, calculus and integrals from university + using it on many projects. Plus having taken physics in highshcool and once in unviersity. I don't feel like I am completely lost. However, I see what you mean about when the completexity ramps up. It certainly could become off putting for some.
@ That being said, you should definetly check out Michel van Beizen's channel.
Dude you're pumping out quality stuff
100% agree
Yes. 100%
InstaBlaster...
I am very engrossed in the minimalist style that you present these concepts. The quotes from the scientists are well appreciated. I want to see this channel to grow in to something great.
That is not how things work, sadly
Outstanding video and very well narrated.
from one physicist to another, amazing work! this is so very useful to both the laymen and professional scientists themselves!
please do keep up the good work
Thank you very much for the kind words, very much appreciated
From content to presentation this was an absolutely outstanding production. Very well done!
Much appreciated!
At high school I never learnt the derivation of the Bohr model. Physics curriculum should be less about exercise and worksheet, more about derivation and a little bit of history.
Couldn't agree more. The history makes it real.
In the UK at A level physics, your school chooses a module for you, and by far the best one to choose is Turning Points in Physics, as it gives a nice overview of the differences and similarities between theories before and after some great discovery (obviously not in as much detail as this video - high school physics isn't really like proper physics, as it needs to be accessible to someone who isn't doing A level maths)
I just wish theyd have like a problem solving lab in a derivation based class like they do for expirimental labs
@@stpirate89 I'm a wee bit confused. Is it true that A level physics doesn't rely on knowing A level maths? Asking for an American friend.🤔
@BeachesRuS that is true yes. Its one of the reasons I hated teaching A level physics. It ruins the physics syllabus because of it, and realistically, nearly all students take A level maths anyway if they're going to take physics. In my 6th form, we had a lot of people take physics in year 12, around 60 to 70 people, and only 3 of them didn't also do maths. I don't think any of them carried physics on to year 13 either.
First time I encountered this was 14 years back in school and today is when I can say I kind of have a grasp of it,thanks to you .
I am an art director at a small agency but people like you online keep feeding my thirst for curiosity. Thank you for doing what you do.
i really enjoy the way you go into the nuts and bolts of how the concepts you explain actually work. i've seen this subject matter addressed on various other channels, but the actual math is often glossed over or said to be "too hard", etc. i'm glad that you're willing to go into detail, and the clear, concise way in which you go through the details step-by-step make them easy to follow. please keep doing what you do! it's really great!
Thanks for the detailed feedback. My philosophy is to try and convey the thought process behind the ideas, so I am glad you have picked up on this and find it helpful
Amazing how you’re able to breakdown the monumental achievements of Niels Bohr in such an eloquent yet easy to understand manner. I’ve always loved physics since learning about it in high school, but I never understood why it bewildered so many of my peers. I guess it all depends on the way you view and breakdown information and I was blessed with an exceptional teacher whom guided me through tackling everything that is elementary physics. It would be wonderful if all teachers had the language to make learning fun instead of what they are for the most part information dumps that tend to overwhelm most students.
Thank you for the very kind feedback, much appreciated
I’m very glad I found your channel when I did. I’m a physics major in university and just started taking modern physics. Watching your videos in Compton scattering, the ultraviolet catastrophe, and now the Bohr model have helped me immensely. I’m so glad you don’t skip the deep and thorough math either, it only serves to drive home the conceptual explanation you put together.
Anyway, just wanted to thanks very much, keep doing what you’re doing!
I love TH-cam science videos, but they usually either remind me of things I already knew, or leave me somewhat baffled. This time I learned something new and understood what I was learning - nice one.
Glad to hear it, thanks for the feedback
As a young aspiring Physicist, I must say, finding your channel is amazing! Watching these videos and then trying to work them out on my own again later and trying my own stuff is always helpful. Thanks for this!
Glad you are enjoying the videos, keep up the hard work!
thats amazing little buddy
Is this my new favorite science channel? I think it is
same
Man this is an awsome video! I was always baffeled on why we can see what stars and planets are made off so many lightyears away because of the spectral lines. I never knew how the spectral lines worked for each kind of atom, but now I do. Thanks for this amazingly simple explanation!
I am at a very local university in kenya but i am learning physics like as if i am in world class university because of this youtube channel. Thank you so much❤❤❤🇰🇪🇰🇪😘
Thank you again for a clear account of the Bohr model. You also made it clear to me that higher energy level electrons gain more potential energy than they lose kinetic energy. I never thought of higher energy electrons moving more slowly. Also that the radius of an orbital increases as the square of n suggests that higher orbitals should be more further apart.
I'm glad to hear that you learnt something, thanks for the comment
The best explanation of the Bohr model I've ever seen, thank you
Thanks for the kind words, much appreciated
This is really great content, it is clean, well explained and very usefull.
I hope you keep work on this type of video
I must say this is the best explanation I have seen on TH-cam or for that matter any other documentary/educational service of the atomic model as conceived by Bohr. Outstanding and kudos to you, Keep up the awesome work.
These really are some of the best physics videos out there. Love how you don't shy away from the math. You can't fully understand physics without the math!
Thank you for this (and your other) masterpieces. The contributions and vision of these earliest quantum pioneers cannot be overemphasized (or overappreciated!)
Thanks for the comment, I really appreciate it
This is amazing, please make more of these in depth explanations on these interesting topics!
I'm really pleased to watch great content in this channel. Keep recording videos about the beauty of physics.
I SO admire your regard for the young students who thought about these things a hundred years ago. Yes they were students, unknowns. They spent decades cogitating. And we are spoon fed this stuff in minutes. And back then, to engage in this endeavor had no promise of economic success. No VCs, no patreon, no kickstarter. No promise of applicability or consideration of market. I wonder what motivated people like Maxwell, Bohr, Thomson, Rutherford,etc.. Your presentation is so engaging. Someday, perhaps an AI will weave these you tube videos into threads and tapestries so we can understand the human dimension as well as the abstract. But until then we only have a few people like you.
Thanks for the kind words, much appreciated
Keep them coming! Another incredible video. Great work.
I really, really enjoy your videos. I am a post-doctoral researcher in atomic and molecular physics. I work with quantum mechanics, molecular simulations and all sorts of things related to the atomic structure of materials and stuff. These things that you have been teaching are the bedrock upon which my entire field of research rests (apart from that one where you compute the distance between the Sun and the Moon) and you still managed to make me look at those things with fresh eyes. You have a good educational method, keep up the good work, we need communicators like you.
I really appreciate your feedback. Thanks for taking the time to leave such a positive and encouraging message. Best of luck with your post doc!
@@PhysicsExplainedVideos Thanks a lot. I mean it. It is hard making things sound as clear and easy as you do. The work you put on making everything obvious shows, I bet that takes A LOT of research and banging your head on the wall. I found myself binging the videos as if my life depended on it. Not only they have good, clear content, they are also a treat to watch. I agree with "The One" on this one, you have the potential to become the 3Blue1Brown of physics. I really want to see that happening.
Just discovered your channel. I am loving it. Just wow! Really good stuff, man! Congratulations!
Wow , I subbed after watching the first five mins of the vid , you are clear, concise and you articulate well, i can’t wait to catch up on your previous vids and learn something.
Thanks for the upload . R .
Thanks Dr. Rod for making us watch this, very cool!
Well done! Well written! Wonderful seeing the photos. Thank you.
First of all, Thank you very very much for these videos. This type of videos are the reasons for me to get motivated to understand the majestic beauty of nature/physics rather than running behind marks/degree.
At 9:50 I think angular momentum vector would be equal to m(r vector crossed with v), not the other way around.
Excellent video. The straightforward calculations and succinct explanations are much appreciated. Keep up the good work.
Thanks for the feedback!
a well-made explanation
P.S: 13:16 I think you made a typo in the expression of the speed. We must replace pi by the planck constant
These physics videos are among the best I've seen. I admit the maths gets a bit beyond me, but I remember enough High School maths to at least understand what is going on. It is the explanatory diagrams and the helpful narration that I like; I feel I understand and gain insights into the big questions being asked. Thank You!
Like the other people said, I hope this channel never loses its quality in the subject of the videos and its production. This channel is a rarity in so many ways that I really hope you continue this. Its really good. Outstanding, I would say.
I really love these videos because you don't explain the topic and call it a day, but also you do it just like the physicists form then developed their theories. This way it's so much more logical and understandable to arrive at those concepts and formulas. Thanks!
I am really glad you like the approach taken in these videos. When I was a student, I used to like understanding the historical context of the ideas.
The most clear, concise, and joined up explanation of this topic I have encountered. This is the first time I have understood this clearly, and I have a Physics degree.
Glad to hear it! Thanks for the feedback
this is lowkey my favorite physics channel now
I am learning all over again! This channel is going to be big. Make more videos and keep us awestruck!😀😀🤘
Best presentation on this subject on youtube so far
I love how are you going smoothly into quantum mechanics
Yes, that is the aim! Glad you are enjoying the videos
Subscribed. Beautifully articulated and factually correct. Rare in a world dominated by disinformation. Bravo.
I always wanted to learn more physics, then they teach you at high school. But it is a dry an intimidating read alone, i'm so glad that you take your time to explain it! Keep up the good work!
Glad to hear that you enjoyed the video, thanks for the comment
Brilliant for its clarity. So lucidly explained .
I believe I lucked out big time when your video on the ultraviolet catastrophe showed up on my homepage. Your presentations are very well -polished and have a great balance of not shying away from the math but also not getting too crazy with it. The history lessons remind me of Feynman's lectures - nobody else has really pulled off the "explain the history, stopping for a few minutes in each era to explain the minimal amount of information you'll need to understand the whole story, and make it captivating" sort of thing as far as I've been able to find. I'm hoping you keep it up!
Thanks for your detailed feedback and kind words. I absolutely loved reading (and listening to) the Feynman lectures, and they certainly have had a big influence over my approach to teaching. My hope is to produce a whole range of videos that combine the historical narrative with the ideas.
Excellent video. Well done!
This channel is excellent thank you! Cannot wait to see more!
Your work has been a stepping stone forward in my life literally. Thank you++.What seemed intimidating to my thinking you have made it all logical and rational with background to the problems and their eventual path to solutions.Each piece in the work made sense and the explanations were timely. Just wish you had more videos.
Absolutely fantastic content. For a layperson like myself, it's great to see the equations because it gives an real insight into the elegant beauty of the mathmatics behind the universe.
This channel is amazing. The concepts are explained very well. Thanks for making these videos.
After 20+ years I finally understand how spectral analysis works. Thank you!
You've been having a massive high-quality output this month. Keep up the great work!
Thanks, will do!
Your enthusiasm and passion for physics are clearly seen in these videos of yours. Thanks for reigniting the spark in an otherwise disengaged undergrad.
My pleasure, it really makes me happy to think that this helped reignite the spark. Don't give up! The hard work will pay off when you begin to see the world differently through the eyes of a physicist
What an awesome video man. Sincerely thank you.
I love your videos SOOO MUCH! You are a great explainer, and tbh I've never before seen someone explain the struggles that past physicists had to go through for us to be able to stand on their shoulders. Your explanations of how certain equations were derived are some of the best I've ever seen, only topped by some derivations of purely mathematical stuff (for example 3blue1brown, but he's extremely hard to top lmao). I feel that your channel is gonna blow up soon, and I can't wait for your next videos!
That last minute lierally gave me chills! Wow I cant be more thankful to you, I thought I would never understand this concepts but now i can say I do. You are a true educator. Thanks again!
Excellent video! I really appreciate your work. Can't wait for the next one!
Thanks for the feedback, hopefully should have another in the next couple of weeks
I honestly can't wait for the next one.
I need more.
Awesome work. Simplistic, but not simplifying. Marvellous.
Thanks for the encouragement, I really appreciate it. Hopefully should have another video in the next few weeks
We need more videos like this. Please continue to. make! Big thanks for your efforts.
One of your best yet!!! Thank you.
Thanks!
Just mind bunglingly dense accurate presentation. So beautifully put together. Absolutely a public service.
I’m impressed by the fact that when a question pops up in our mind by watching your vid, a bit of a second later the answer appears magically. It is as if you could predict our thoughts 💭😝.
A very good and complete work that make us realize a part of the beauty behind those subject and the answers given by the passing time and those who follow it. 🖤📐
Brilliant video! I only got a brief intro in school, and this explains much more. Very interesting.
Dude, your videos are awesome! You made me understand with them some concepts i was struggling for quite some time. Please, make more videos! And I totally agree with The One: you have the same gift to expain hard stuff as the guys over 3B1B have. Thanks a lot!
thank you - such an informative and entertaining at the same time upload. Much appreciated.
This is perfection. I will be watching this many times.
Thank you so much for making this
I have been waiting for this clear explanation so long.
Glad it was helpful!
Excellent, explains things that Ive always wondered about.
Oh please please make more videos like this! Would be amazing to see your explanation of photoelectric effect, with historical progression and context as you so very well put it in your other videos!
or perhaps moving into quantum mechanics or optics would be amazing!
Bravo! I wish this were available 50 years ago when I took physical chemistry. I never quite grasped the interplay of the various early theories/models/equations and how Bohr synthesized them. I just subscribed. Count me in!
Glad you enjoyed it!
Splendid work as always! Hoping for a video on Heisenberg's Uncertainty principle soon
I will definitely be making a video on Heisenberg's uncertainty principle, watch this space
I really love your explanations! You don’t skip Important parts!
Glad you enjoyed it, thanks for the comment
I always wanted to be a physicist.. did my masters too.. but couldn’t pursue it further. Your videos exactly explaining not only the results and the flashy headlines but also the mathematics of how to get there make me relive my love for physics. Thank you so much for making them. Please keep making them.
Outstanding content and presentation. Please keep posting!
Very, very helpful information for anyone going through college-level physics or even chemistry and biology in some cases. BRAVO. This is WONDERFUL information and it's so easy to understand. You have no idea how much I appreciate this content! THANK YOUUUU!!!!!
Glad it was helpful!
Love your series. The histories are fascinating.
One thing I particularly like about these videos is they tie the reasonably-detailed algebra to experimental results. In this case, including the photograph of the spectral emission lines from hydrogen really brings home that all the maths leading up to that point is describing a real, testable phenomenon.
I gotta say Something, you are so awesome.
Explaining physics so good and mit leaving out the math!
Really well explained and understandable. Better than some of the actual physics classes I've had.
Excellent! Very complete! Thanks a lot!
Absolutely brilliant explanation! Thanks for the video :) Reminds me of my high school physics teacher, who used to explain things so neatly, I still remember it :)
Glad you liked it, thanks for leaving a comment!
I'm just becoming a fan of your simplistic explanation. You are doing a great job carry on.....wanna see more videos asap
Thanks for the feedback
This is great stuff - both from a technical and historical point of view. Very entertaining too - I often remember Bohr as "that guy who was always arguing with Einstein" but forget the brilliant early work that catapulted him to fame...
I love these reflections at the end of each video.
superb explanation ! many thanks .
I watched this film and immediately subscribed to the channel. Brilliantly explained!
Fantastic Job, outstanding quality.
Very much love the content. The prediction of the Balmer series at the end is quite a stunner
This is one of the most beautiful videos I've ever had the fortune to watch. Thank you.
Glad you enjoyed it!
Thanks, I've read about Electron Volts for decades, now I understand them!
Glad I could help!
I can't stop saying myself: this blows my mind and so beautiful indeed.
Love the channel! Keep up the good work man.
Thanks for the encouragement, much appreciated
Very meaty. Yet clear. Mostly clear. Also, fun. Will rewatch.
Great explanations.....much appreciated
My pleasure, thanks for the comment
This content is so easy to understand. Thank you!
Rewatching this - it is a brilliant explanation!
1, Do not stop doing this.
2. Your handwriting is beautiful as well, apart from the pictures used I believe it would take less time to produce videos with handwriting.
3. You may not do this a full-time job, but what you are doing is valuable and if you can mass produce these videos I am sure people will notice soon.
4. I don't know your education level, but if you can touch more advanced subjects it would be really nice.
Keep up the good work.
Thanks for your feedback. You are right, videos with hand-writing are far less time consuming. I will probably produce a mixture of videos in the future. I have a PhD in theoretical physics and have considered doing a series of videos on quantum field theory and string theory, but first I am going to cover the basics of quantum mechanics and special relativity
@@PhysicsExplainedVideos I could tell you know a lot on the subject, now I know it. You could do series like DrPhysicsA, which are basically a summary of Susskind's Theoretical Minimum. You have really nice dots as well, on your 'Estimating the number of atoms in the observable universe' video your dots are making me feel comfortable. So touching some Boltzmann subjects would be eye candy (with a lot of dots involved obviously!!!).
Also, your video titles are really nice; everybody is into well-delivered clickbait videos. Like 3b1b's hardest question on the hardest test, or most of the quantum mechanic videos.
I would say there are not that many string theory videos that are visually satisfying, given the complexity and math required to understand the topic (and it always feels like string theory is built upon the idea of unreasonable efficacy of mathematics, which is why its probably very promising theory as well.)
I feel like expanding this channel (which you should be doing given you are one of few physicists with good handwriting and deep knowledge on the subject) relies on well-delivered quantum mechanics videos. Not so surprisingly quantum videos are getting millions of views (probably due to magical interpretation of the subject by popular science), a well-delivered video explaining everything that led the development and implications of the subject will be well appreciated by the public.
Clearly getting clicks is not the main purpose of making educational videos. Learning more about the subject while delivering, teaching and ego-boosting are probably the main reasons behind it; but at the end of the day, we are animals that love positive feedback and social acceptance. So getting more views will ensure you will deliver more videos with higher quality.
Please use more handwriting and never shy away from diving deep into mathematics. Teach the rules and apply them to problems like how can you calculate gravitational constant, what really is an electron, infinite slit experiment or whatever comes to your mind. Keep it clickbaity, equation filled and comprehensive. Good luck!
I found your ultraviolet catastrophe video excellent as well as this one, and look forward to continuing to learn from your videos. It always helps to see things presented in several slightly different ways. I've been trying to make beginner's headway in MCQuarrie and Simon's _Physical Chemistry: A Molecular Approach_ as well as White's _Introduction to Atomic Spectra_ , having completed Chapter 1 of the former and being in the middle of Chapter 1 (devoted to pre-Bohr spectroscopy) in the other. Having viewed your latest video a couple times casually when it came out, I dedicated yesterday to reviewing the relevant section of McQuarrie and Simon and then looking ahead to part of White's treatment of the Bohr atom, before devoting a couple hours last night and this morning to reviewing your video in detail, checking everything.
I did notice a couple of errors in the expressions that appear. @13:25 the video has v = e^2/2πε_0n, whereas the actual expression that follows from the substitution shown should be v = e^2/2hε_0n. @15:05 the expression given to substitute for v^2, is the first such expression from earlier in the video, namely v^2 = e^2/4πε_0m_er, rather than the one actually needed for the substitution: v^2 = e^4/4ε_0^2h^2n^2.
I must confess being driven in my desire to learn more by criticisms which have been leveled against the nuclear theory itself, as well as interest in a related non-standard theory. Those criticisms remain almost unknown due to the historical fact that Bohr's contribution (in part due to its striking initial success) has been the focus of subsequent modifications, in effect shielding the nuclear concept itself from critical scrutiny. A brief-but-cogent presentation of the reasons may be found here: philpapers.org/rec/LARJHM-3
To the point here, the conclusion that "the basic idea of energy levels and electron transitions would ultimately account for the emission spectra of all the known elements," is marred by the lack of discrimination between the sound pedigree of the energy levels concept itself, and the historical predisposition to describe them in terms of "electron transitions."
To underscore this point, I'll close with an extended quotation from Larson's neglected classic _The Case Against the Nuclear Atom_ (1963). Would it not be healthy for physics if these criticisms were more widely appreciated?
The most astounding feature of this whole situation is that after having thrown the only connection between the atomic energy levels and the nuclear atom to the wolves, and putting nothing in its place - even going to the extent of contending that nothing _can_ be put in its place - the physicists still insist on using the genuine successes of the theory of atomic energy levels as evidence of the validity of the nuclear theory to which it is no longer even distantly related. Furthermore, the whole jargon of spectroscopy is based on the features of the original theory that have now been repudiated. While Schrödinger tells us that there really are no electrons in orbit, Heisenberg says that there actually is no physical electron at all, only a “symbol,” and the whole Copenhagen school insists that we cannot conceive of the atom or any of its parts in anything but purely mathematical terms, the spectroscopists tell us just how many electrons there are in the atom and exactly how they are arranged in “shells,” etc., and proceed on this basis with the calculation of spectroscopic terms to an accuracy of eight or nine significant figures. “The terms result from definite configurations and motions of the outer electrons of the atom and are explained by a well-established theory of spectral structure,” [Citation omitted] says the National Bureau of Standards.
This utterly ridiculous situation in which one group of physicists is defining specifically and in great detail the properties of entities which, according to an even more eminent group of physicists, have “no immediate and direct properties at all ” and do not even “exist objectively” is another example of the same confusion that was pointed out in connection with Moseley’s Law. Here again, as in the Moseley case, a name derived from currently popular theory has been arbitrarily attached to a particular physical phenomenon, and the scientific profession has fallen into the habit of accepting the connotations of that arbitrary nomenclature on the same basis as the observed properties of the phenomenon itself. The Bureau of Standards tells us, “…the atoms of a gas or vapor, when excited by radiation, absorb certain wavelengths corresponding to transitions of their outer electrons from lower energy levels to higher ones.” Here we have an assertion which contains three statements of totally different origin, all lumped together as if they were equally authoritative. The statement that the atoms absorb certain wavelengths when excited by radiation is a description of an observed fact. The statement that these particular wavelengths correspond to transitions from lower to higher energy levels is a theoretical conclusion which is strongly backed by evidence from experimental sources. The further statement that these energy levels are energies of electrons is pure hypothesis without the least vestige of experimental support. These levels are “Atomic Energy Levels” - the title of the Bureau of Standards publication from which the foregoing statement was taken - and that is all we know. Evidently some kind of units enter into the situation, but applying the name “electrons” to these units is pure guesswork.
Similarly the same N.B.S. circular says, “Each chemical element can emit as many atomic spectra as it has electrons,” but what is actually known is that the number of different spectra is equal to the atomic number; the further conclusion that this represents a number of electrons is wholly gratuitous, and the use of the name “electron” serves no purpose that would not be fulfilled equally well by any other name. As pointed out earlier, any theory of atomic structure that could be given any serious consideration at all must necessarily make some provision for a quantity corresponding to the atomic number, and the name of this “something,” whatever it may be, can be substituted for “electron” in the language of spectroscopy without affecting spectroscopic theory in the least. The current contention that the successful application of the theory of energy levels to the study of spectra constitutes an argument in favor of the nuclear theory of the atom is therefore pure fantasy.
sathearn thanks for the detailed comment and feedback, much appreciated. Thanks for spotting the typo involving epsilon nought. And yes, for simplicity I should have written an expression for v squared which did not involve r but hopefully anyone working through this will just substitute for r to get the correct expression. I really like the quote by the way, certainly something to think about
Really nice presentation. Really enjoyed it. It was a nice refresher with some additional insights that make my understanding a little deeper.
Glad it was helpful! Thanks for the feedback