6. Hydrogen Atom Wavefunctions (Orbitals)

MIT 5.111 Principles of Chemical Science, Fall 2014
View the complete course: ocw.mit.edu/5-...
Instructor: Catherine Drennan
Where is that electron anyway? In this lecture, the probability of finding an electron at a particular distance from the nucleus is discussed. The concept of wavefunctions (orbitals) is introduced, and applications of electron spin are described. In particular, chemist Ben Ofori-Okai introduces us to the wonders of magnetic resonance imaging, also known as MRIs.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@sashafairyy]

Awesome. first year university student doing this topic and came upon this video. Cleared to concept up for me perfectly. THANK YOU

[@brijeshsurati7120]

Mane to taav aavi gyo lecture joine...

[@weixiong1.0]

Gotta love her shirts.

[@PhysiKarlz]

Psiphi (psee-fee)

[@randallmcgrath9345]

The guy who does videos for Fermilab also has cool dad nerd jokes and nerdy ass t shirts.

[@aelobalthrop1413]

Nano MRI sounds absolutely a fascinating concept!!

[@physics_enthusiast_Soorya]

Thank you for this video! Love your lectures and I'm grateful they are all free on youtube 😊

[@ArielLorusso]

17:57 Accurate description of 2020.

[@adityashankar5267]

Underrated comment

[@goldensiddiqui]

On her t shirt :- Sci-Fi

[@nuzlock4481]

I thought I was only one thinking this XD!

[@ryandsouza9093]

I clicked this video to like this comment.

[@culisteven4754]

that is why i like quantum, the wavefunction is huge

[@anilsharma-ev2my]

Sai shiva shanka 🕉🔱🕉 Phy physical phera pheromone saat ferocity fera phir phir phorna 📱

[@anilsharma-ev2my]

@Hinterfrage! Fatafat

[@shamsamir1698]

The beautiful use of educational tools and techniques! Wow!

[@MahardikaMatika]

18:05 "we're still very far away from having a real cure for the common cold" 18:11 person: **cough**

[@Name-jw4sj]

Wow, this comment has aged ironically.

[@jawden5638]

17:31 Was Nano MRI part of the COVID research. If so, big thumps up! We are soo close to being able to live life just as it was when this video was made!

[@hp127]

So great. Thanks MIT for providing these,

[@emanraafat4380]

coming from egypt . thank you very much 💗💗👀

[@vevo5086]

Lol I am also from Egypt

[@Habe111]

great teaching, thank you so much

[@zack_120]

A well done lecture critical for understanding wavefunctions - food for thought🍔

[@ronaldjorgensen6839]

YOU ARE THE BEST EXPLAINER EVER THANK YOU

[@mrozzy4442]

Great lecture - thank you!

[@aghamdahri7714]

Excellent Way of convying

[@MathPhilosophyLab]

So cool. The wavefunction is the same thing as the Orbital... Sweeeeet

[@schmetterling4477]

No, it's not.

[@indrajitbandyopadhyay9161]

Very nice! Could you please explain in the next video how we get different shapes of s, p, d, f orbitals with phases of lobes? This can be used to plot using Excel

[@josephmellor7641]

Look up "spherical harmonics".

[@RakeshLad-jv5jg]

At 9min 54sec... The Rydberg constant is incorrectly rounded to 2.8×10^-18 J. It should be 2.178x10^-18 J. It's then easier to understand why the constant divided by 4 gives you 5.45x10^-19 J.

[@moayadsrour4408]

This very helpful , thank you !

[@evgenytalantsev6995]

Problem on 36-38 min has two identical figures, i.e. figs. 2 and 3. And in addition, there is a mistake in the answer.

[@ot8479]

What's the mistake please? And why is it... ? Thanks!!

[@evgenytalantsev6995]

@@ot8479 Dear Catherine, I will reply you in couple days. Thank you.

@@evgenytalantsev6995 Any updates?

[@evgenytalantsev6995]

The student gave an excellent advice for the lecturer to count peaks instead of nodes, and lecturer even did not understand that this is the simplest method to answer the question, presumably becuase this was not in textbook the lecturer read. This lecture is indeed well below any acceptabable level.

[@goclbert]

There was a question in the lecture where the diagram had the same number of peaks but the incorrect number of nodes. Counting peaks is easier but it's not the right way to really look at things. Nodes are special because they are places where the sign of the wave function changes and that has later implications in molecular orbital theory.

[@dusaanna9458]

That is the problem: you can follow that "receipts" system without knowing anything about electro-magnetism which is at the basis of all these receipts. You can forget that everything is electro-magnetism in matter. As an example the PAULI principle indicate only that 2 magnets, in a stable position nearby cannot remain parallell north south. They will flip and go in opposite north. south. yes the electron is a small magnet as it spin with a charge around itsz center.

[@aliviamazumder3622]

THIS IS SO GOOD TYSM ❤

[@mohammadsalim1407]

Mam the value of En(j) for 1 orbital is wrong it is 2.1* 10-^18 j

[@talipgunes7022]

-2.18e-18 J to be more accurate.

[@thecritiquer9407]

very amazing

[@PhilipePXF]

Watching this video about nano RMI in 2020 gives me some weird vibes

[@meshukomoney9499]

Thanks alot Madam

[@gauravbhakar7207]

0:10everything is so clear

[@JS-rg7vo]

37:40 i felt bad for that guy

[@indiaview9414]

Probability of finding the wavefunction on t-shirt was really unpredictable

[@hailongwang5563]

the En @ 10:04 should be -2.18, not 2.8.

[@talipgunes7022]

You're right. It's -13.4eV for n=1 so is equal to 2.18e-18 J

[@SFYN..]

18:09 and we are on a break because of corona virus.. how about that nanoMRI..

[@KiFacil]

I lov u......Perfect!!!

[@VenturaStudio-f5d]

Wonderful intro miss oxygen 120% derusted massive thanks!

[@getyekefale8677]

Please upload the eigenfunction of hydrogen atom when the principal quantum number n is equal to 2 prove the phi (200)=(r, theta, phi) and phi(210)=(r, theta, phi) do it a step by step the radial and angular equation as soon as possible pardon me because I am interested with this lectures I am attend on online

[@ronaldjorgensen6839]

thankl you have been though the material need review uncertainty /1

[@mirdayyan4319]

Amazing....

[@Asdun77]

Thanks madam

[@consistentvillain]

Awesome lecture! So where can I buy those cool t shirts????

[@supreetsahu1964]

Sci-fi T-shirt. Genius

[@quarstrongforce]

At state university, chem class exam is acs exam.

[@jamesbnorman1]

If she wanted me to check her work, I would say I'm busy and to go with your gut on the answers.

[@rv706]

24:41 - Chemists can't draw graphs? Those graphs are not consistent with the functions that were in the previous table. For example, the wave function was, up to constants, of the form f(r)= b exp(- a r) with a and b some positive real constants. That's an inverse exponential: for r=0 it intersects the vertical axis in a finite number b, it doesn't have an asymptote (which the graph in the video maybe seems to have, but it's not so clear). And the "RPD", which would then be of the form b^2 exp(- 2a r), at r=0 is definitely not 0 but has the value of b^2. This returns to confuse everybody at 38:52 cause they're counting the origin as a "node". Edit: I watched another youtube video and now it's clear her confusion at 24:41. The "RPD" is _not_ the probability of finding the electron at a certain radius r, but the probability of finding the electron _inside_ a sphere of radius r. In other words, the RPD is the integral from 0 to r of the (squared modulus of the) wave function.

[@robertocolombo4622]

Sorry, but you seem to have missed the definition of RPD a minute later as "the probability of finding an electron in a spherical shell of thickness dr at distance r from origin", which would be something of the form (r^2)exp(-2r). See e.g. this other video: kzbin.info/www/bejne/qIG3kGqDidVpb6s

[@Az-cu2he]

How can it be that RPD is an integral?It would need to have negative probability to come down after the peak...

[@davidpradochible5702]

In the case of wavefunction, it wouldn't make sense to talk about a negative r, we are talking radially, therefore if r is equal to 1 that holds for every direction that is equidistant from the origin by 1 unit length. Then, that's why you do not see the intersection which would be the 'b' that you say times the constant of the angular wavefunction. It is there, but it isn't noticeable since we do not go to values at r < 0. As for the RPD, it indeed is explained wrong. The radial probability density is the wavefunction squared times the cross-sectional area, so it is not probability/volume, it is probability/radial distance. That's why it is 0 at r=0, because the area depends on r. As for the integral that you talked about, the RPD is the probability of finding the electron in between the points x and x+dx. However, if you want to know the probability of finding an electron in between the points x1 and x2 (so now we are not talking about an infinitesimal volume, in other words, a surface, since we are talking radially), then you do integrate over the distance dr.

[@sujeetiitd]

Question: While Px, Py, and Pz orbital probability plots make sense based on the symmetry, why should one of the D-orbitals (D_x2-y2) orient around the Z-axis? Ideally, as nature behaves uniformly and symmetrically along all dimensions to the particles/waves, I would think there should be 2 more D orbital counterparts: D_y2-z2 and D_z2-x2. So, why does the x2-y2 D-orbital have to always orient that specific way around Z-Axis?

[@schmetterling4477]

It's a convention. In an experiment an external electric or magnetic field will break the symmetry. Very often experimentalists will describe experiments with such fields in a way that makes them parallel to the z-axis. That, too, is a convention.

[@sujeetiitd]

@@schmetterling4477 I don't believe that. This is studying the mathematical models of orbitals with atoms in isolation - not sure what external fields are you talking about (Unless it's a Molecular structure, where there are external forces/fields from outside an atom).

[@schmetterling4477]

@@sujeetiitd You can believe whatever you want. We have religious freedom in this country. Nature simply doesn't know about your coordinate systems and it doesn't care, either. Not in classical mechanics and not in quantum mechanics. An orbital is simply not oriented unless you break the symmetry with an external field. You can see this in the degeneration of energies for these orbitals. The state for an atom in unbroken symmetry can be any linear combination of degenerate eigenfunctions. Turn on the field and then the one with the lowest energy will be preferred.

[@ZERO-mt1lv]

@@schmetterling4477 what's with religious freedom?

[@schmetterling4477]

@@ZERO-mt1lv Religious freedom is the simple legal right to make a complete fool out of yourself in public. Would you like a talking donkey with that? ;-)

[@nhra7110]

excellent professor!

[@ronaldjorgensen6839]

IMPOSSIBLE IS WERE REALITY GOES TO REST COLLAPSE OF ENERGETIC SYSTEM IS OUR AUDIO VISUAL SPECTRUM ALL AT RESTED STATE FREQUENCY OF 6-8 OR ZERO GROUNDED PERCEPTUAL FRAME?

[@kelechiosuoji]

I don't understand the ionisation energy states

[@Muleslover]

I like the class room

[@ChaineYTXF]

R_Y (in eV) not R_H (rydberg constant in m^{-1}), right..?

[@NothingMaster]

Those naughty little Hydrogen Atoms get into excited states quite easily.

[@31337flamer]

That Shirt makes Sci-Fi tangible

[@joshzeidner5412]

Who would pay mit tuition fees to listen to this person?

[@sunilparekh4581]

Me😁😁

[@amritpalsinghsaini2575]

How can we solve the part at 22:00 the column ?

[@sajjansingh4329]

I like scientific t- shirt. 🙏

[@aelobalthrop1413]

Cant wait until i can buy a nano probe and conduct real time microbiological, and cellular observation!

[@thevardhana2537]

In India we are taught this in high school

[@PandaCheeks]

Is that why it smells like dookie in india,lol.

[@Ava-fl7hd]

@@PandaCheeks it is why most of your country's corporate leaders are from India

[@PandaCheeks]

@@Ava-fl7hd who cares about corporate leaders though?lol

[@Ava-fl7hd]

@@PandaCheeks apparently your government does that's why they keep asking if Google's CEO will know they moved their phone LMAO

[@PandaCheeks]

@@Ava-fl7hd No one out here cares about corporate leaders and much less political ones at that...lol Sorry to bust your bubble kid haha

[@hugoapolaya7151]

08:46 I have a problem, here in my country I learned this in high school as Px -> m= -1 / Py -> m= 0 / Pz -> m= +1. So is this like, reglamented? and it was my high school's mistake or it's just a country difference thing? Thanks

[@johnsilverstein9862]

m = +1 and -1 are linear combinations of px and py. It's not so that m=1 corresponds to x or y directly.

[@prnv9876]

@@johnsilverstein9862 but m=0 is orbital on z axis so and I think it's some mistake

[@johnsilverstein9862]

@@prnv9876 yes, m=0 is the z component. Sorry i didn't read that properly.

[@iagojacob3785]

Mabie country difference or disparity of formalizations, happens all the time .- .

[@chandrashekariyer9329]

No. m=1, m=0, m=-1 can be assigned to any of px py pz

[@codingWorld709]

Thanks mam. Very helpful ❤❤❤🇮🇳🇮🇳🇮🇳🇮🇳

[@ShwetankT]

so is there any recommended text book along with the course?

[@ShwetankT]

found it - www.amazon.com/gp/product/B0071GCQ3U/ref=nosim/?tag=mitopencourse-20&linkCode=w61&imprToken=ny5eDbpouFeJnBhOLIfeOQ&slotNum=0

[@azulpurpura1230]

@@ShwetankT Thanks for sharing man, :D really.

[@davidwilkie9551]

To imagine the self-defining measuring/Superspin-spiral shaped cause-effect of potential possibilities, approaching zero-infinity difference distribution positioning in Singularity, in the i-reflection containment connection coordination of logarithmic numberness sequences dominance @.dt.., beginning with the Hydrogen orbital solutions. This is Eternity-now Interval Conception, wave-particle coordination-identification,in/of real-time e-Pi-i sync-duration scalar vector-values connectivity, projection-drawing 3D+T Perspective. (In plain words) A universe of time sync-duration connectivity, Math-Phys-Chem and Geometry functions of pure relative motion/energy in logarithmic circularity quantization/condenate.., is simultaneously self-defining elements of Mathematical law, ie relative projection-drawing positioning @.dt tangency of orbital density-intensity real-numberness. This is more muscle-memory, sum-of-all-histories experience than Pure Dynamic Mathematics, and the task for new Students with a blank screen.

[@dilawarhussain6509]

according to formula of nodes there should not be any node in 2p but in shape there is a nodal plane ???how ?

[@ManojKumar-cj7oj]

Total nodes= n-1=2-1=1 Angular node= l=1 Redial node = total nodes - 1 = 0

[@ronaldjorgensen6839]

I THINK IT IS IMPORTANT POINT NO 720 DEGREE SPINNERS IN SPECIFIED FUNCTIONSPINNERS WERE GOOD FOR VARIABLE MATH FUNCTION PRACTICE BUT NOT FUNCTION SPECIFIED ITSELF AT A FIXED POINT INTUITIVE OR MEASURED REACHING TOWARD 1/4 PI @90 DEGREE

[@ericstorm4613]

Finally understood why p have 6 e-.

[@miosoto]

Hi guys I checked ocw I could not find lecture on Organic chemistry , if anyone did , please share the link

[@drkrajkumar3620]

Dear Madam, your presentation about hydrogen atom wavefunction is very neat and clean message. Could you please give some PDF file or reference book details?

[@talipgunes7022]

You can find notes in the link under description which is ocw.mit.edu/courses/chemistry/5-111sc-principles-of-chemical-science-fall-2014/

[@nandanair1373]

Isn't this taught in indian high schools????

[@ramunasstulga8264]

No

[@cafe-tomate]

What does the Rmp represent ?

[@dilawarhussain6509]

is there diffrent formulas for radial and angular nodes ???

[@rihanakhtar]

Yes ofcourse there are ...

[@debtanaysarkar9744]

Radial nodes = n-l-1 Angular nodes = l where 'n' represents the principal quantum number and 'l' represnts the azimuthal quantum number.

[@sonarbangla8711]

No wonder why Einstein thought QM is incomplete, this lady shall need employment for a million years.

[@schmetterling4477]

Science is not what Einstein thought. It's what nature tells us. She isn't researching any of these things. She is simply teaching to students who are learning old material for the first time. Oh, wait... you don't know how school works... you weren't paying any attention. ;-)

[@InvinciblePepe]

​@@schmetterling4477what do you mean by "nature tells us"? Is nature or the universe conscious? This is what Schrodinger believed actually. He said consciousness is fundamental and it cannot be accounted for in terms of anything else.

[@schmetterling4477]

@@InvinciblePepe An experiment is a question to nature. The result of that experiment is the answer. Schroedinger had a really hard time with quantum mechanics. He made a few good guesses but then somehow got lost in the difference between the math and the actual physical reality, it seems. If you want to understand QM, Schroedinger and his confusion about it are among the least helpful sources. ;-)

[@elfullin]

@@schmetterling4477it can be an interpretation of a pattern observed in nature. Like an almost exact and equal description of a node that is interconnected with other nodes of the fabric of “reality.” Mathematics is one way of describing these nodes. Science is the closest approximation we have to understanding the natural world. Due to its intense focus on numbers and exactness, it is slow in painting the larger picture. I believe this is partially the reason why great scientists (men who knew limitations of science) could be very spiritually inclined. Who is to say that our consciousness, and bestowed intelligence has no fundamental connections to the broader network of reality at a spiritual level. That’s just my opinion tho.

[@schmetterling4477]

@@elfullin Yes, that was bullshit. ;-)

[@mynameisZhenyaArt_]

is there 2018 version? this is all good, but now people are using python to plot actual graphs instead of some hand-drawings.

[@moon-coder]

This is what I wanted to ask too. 28 years ago, when I was about to complete high school, with a friend we wrote a simple program that would draw orbitals for all elements in the periodic table. It was written in Borland's Turbo Pascal for PC (and DOS), using CGA, EGA, VGA graphics cards. Our chemistry teacher showed us some book for inspiration. Obviously, our program did not solve Schrödinger equations - we just tried to mimic 3D shapes that we saw in that chemistry book. Still, our program could draw the shapes in 3D (as "clouds of points", shapes similar to upload.wikimedia.org/wikipedia/commons/6/66/Porbital.png ). Edit: wikimedia deleted this image, help me find it! I could not find it anywhere, but wikimedia should not delete images permanently, right? Here is another depiction, not as good: i.stack.imgur.com/25yhY.png We then made the program shareware and tried to sell it to schools for $5, protecting the program by scratching 5.25" floppy discs to introduce bad sectors that would be impossible to copy, but that's another story. 28 years later, I would expect an online javascript app that would allow students to quickly see and compare all orbitals and their combinations based on real equations. Wait, a quick search finds an applet www.falstad.com/qmatom/

[@duraace6511]

@@moon-coder your reply is interesting, thanks.

[@samcoopermusic]

Why is nobody talking about her totally Sci-Fi t-shirt?

[@ravikumar-vr6zm]

I like two scifi

[@mayank9447]

Why these things are in my high school

[@fitnessdominator8146]

at 39:41 what was the difference between 2nd and 3rd graph

[@sujeetiitd]

Exactly my first reaction on seeing the plots... but the lady admitted it's "confusing" and probably copying issues from the Book.

[@securetech9798]

YEAH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[@anilsharma-ev2my]

Show the animation for this formula so we. Found its randomness in real time Shivalinga is ultimately the lingo for whole universe

[@iffatzahra3624]

Why r(2p)

[@erikumble]

Because the radius value (distance along r axis) is less (if you look at the plot of 2p, you can see that rmp occurs more to the left than the rmp for 2s)

[@anilsharma-ev2my]

Hydrogen atomic economy of universe Very cheap and accountability are automatically combined with inversely proportional to it's use 😀😀😃😃😃😃😃😃😃👽😃😃😀😀👽👽😃😃😀😀😀👽👽👽😃😃😀😀

[@apkapadosi3151]

We all know why we are here

[@Rajendra01350]

Can you provide me study materials??

[@mitocw]

See ocw.mit.edu/5-111F14 for the course materials. Best wishes on your studies!

[@kumarchandan8680]

Why Hydrogen atom produce magnetic field apart of other non-metal elements in human body.

[@yoshikagekira7600]

Its not about metal or non metal... It is about moving electron which produce magnetic field

[@tobiramasenju7530]

Because only atoms with uneven number of protons or neutrons produce magnetic field ( H-1, C-13, F-19, etc)

[@Bobsry16]

Hydrogen also, technically, in a condensed state can be a superconducting metal. An alkali metal and a halogen, oxidizer and oxidant depending on cercomstances due to that single electron.

[@brainstormingsharing1309]

👍👍👍👍👍

[@SampleroftheMultiverse]

Particle in a box model kzbin.info/www/bejne/raOlpKSfepWpfZYsi=waT8lY2iX-wJdjO3 Thanks for your well produced video. Your viewers might enjoy seeing my personal amateur science project in the visual aid linked below. It uses a sheet of spring-like material buckled from the ends to form a Gaussian curve. This is to represents a two dimensional field with the ends bounded. Seeing the mechanical effect may also takes some of the mystery of what the math is showing. See the load verse deflection graph in the white paper on my KZbin channel.

[@VishalSharma-pu9sw]

i love u

[@KartikPatel-nt4ff]

😅😅😮😅😮😅😅😮😅well information good show you 😅😅

[@uttampatra8395]

Sputnik ARJYABHATTA

[@wntu4]

Why is it no one in the academic community can manage to say Schrödinger's name correctly?

[@justinllih9]

Shut up nerd

[@steffanharmaajarvi2715]

Didn't she pronuounce it correctly?

[@maybewise]

Because it's an ethnic name. And nobody's Austrian.

[@stauffap]

@@steffanharmaajarvi2715 No, she didn't pronounce it correctly. Go to google translate select german and type in the name "schrödinger" and let google pronounce it. So you see that she pronounces the "g" incorrectly. It shouldn't be a "sh" shound, but more like the g in the word "singer".

[@tehyonglip9203]

Try deBroglie, almost pronounce it wrongly

[@johnfarmer3506]

d

[@bahaamohamed3625]

L

[@jimmythepowerful]

TRUMP 2020 ! TRUMP 2020 ! TRUMP 2020 ! TRUMP 2020 ! TRUMP 2020 ! TRUMP 2020 !

[@eityafackmullick]

Now I live sci fi

[@Etothe2iPi]

Who is Schrodindger? His name Schrödinger is pronounced like ˈʃreɪ-ːdɪŋər.

[@amanpandey4821]

Mam b.sc third year lecture done on solid state physics

[@HHHHHH-kj1dg]

Dude this is mit.usa. Not an outdated indian course.

[@videowithsongsandmotivatio4073]

Shi fhi mst h

[@phpART]

ok this is becoming a meme now

[@nuzlock4481]

Meme 4 what?

[@benheideveld4617]

This brilliant professor would be laughed at in France. Do you know why?

[@Cjendjsidj]

Why?

[@ramunasstulga8264]

In france they laugh at you

[@schmetterling4477]

She isn't brilliant. She is outright boring.

[@giakon1]

the orbital... abstraction of what? of where the "particle" called electron is spinning at speed (?) around another particle called a proton, or a bunch of particles called a nucleus ... what became the "particle" in QM? a field...a bunch of numbers in a region... nonsense....

[@schmetterling4477]

It's the same level of abstraction as a probability distribution for two dice.

[@giakon1]

@@schmetterling4477 ... non sense

[@DeltaVTX]

lol ψΦ

[@lordmomstealer]

....öô...