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# Lecture 13. Hydrogen Atoms

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#### Automatisierte Medienanalyse

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but were continuing on with the exposition about the hydrogen atoms when we last left our hero we had separated into angular and radio equations and we had made a substitution you is equal to our times are and then we'd shown that if we make the substitution would get a much simpler equation to solve now what we're going to do today we're going to talk about the radio functions and solutions of the time independent showing their equations but we will get these letters states that Rittenberg observed experimentally and his spectroscopic investigations and fit that famous formula the difference between the inverse squares let's then tackle our problems 1st by setting a little L is equal to 0 we know that a solution for the particle on a sphere and we can put that and if we put little Ellis equal to 0 and the term won over our square is out of our hair make gives us a much easier equation is solved my far squared over to new times the 2nd derivative of view with respect are minus eastward over 4 by epsilon are and you is equal to the what we want figure out then is what is you and what is he for this equation and now we've got a little bit of experience with Icahn value equations like this we've got derivatives of things and then we get a copy of the thing and every time it seems that the exponential function comes in when we've got stuff like this furthermore we can make an argument that look the way function has to go away 1 little or against big because the chance that the electron is going to be very very far away From the protons In a hydrogen atoms In the ground statelets say has got to be very small and in particular it has to go away when AZ infinity so we can't possibly have a polynomial and because 1 gets bigger upon only only the blows up
that's kind of difficult plot because it has a real part of an imaginary part and they all have the same energy because the energy only depends on an doesn't depend on or am I so well foreign observers and therefore we can just take combinations of different values of em such that we get something that's nice plot and that therefore if we have the 2 the I am Friday and we combine it with you to the minor and 5 if we Adam up we get to and if we subtract them we get up
result that's important and the 2nd thing is that the 2 of electrons can penetrate there's a little
blip inside near to the nucleus and so the 2 us electrons can spend some time quite near the nucleus even inside where the 1 s electrons it could be they work both there together as they will be in some other atoms and that's an important feature as well because it means that the 2 US electron knows what the nuclear charges and like helium lithium in a way that the Tupi electrons doesn't have any chance of being at the nucleus cannot and in multilateral Adams will see that that changes the energy quite a bit then over 3 for the electron density for the 3 us I see there's a little blip nearby and then another little blips and then there is a big blow and it
gets big again right where the other 1 dies out so this is a picture that the ad is like and shelves like an onion it has shells and they can be occupied by electron that's that's a very important thank to to realize In spherical polar coordinates we can we can calculate the probability of being at a certain volume and Florida as an example problem let's just do this calculation for a hydrogen atoms in a wondrous electrons unless to following let's calculate the chance that the electron is within a sphere of radius knocked border regions so this is practiced problem 17 I just figure out the probability above what's the per cent chance the unified the electron nearer to the proton the border radius near equal well have we really know the way functions for sigh 1 we can square there's no complex numbers so we don't have to worry about the complex conjugate we square and we know what DVDs the volume for spherical polar coordinates are squared signed data Dee thing defiled and so were left doing an integral which I've written here the way things used to be written in books I have a triple integral From fight will 0 5 calls to pilots and bring them here from data equals 0 0 to the it's that part and from our equals 0 a non that's what I'm stopping but the wave function square defiance Sunday at the Theatre Arts where and did this dependence is pretty easy because the way functional independence on
R and decided that positive at the great so we can do that but it's it's much better I think to right the formula this way what I've done here is I have had the right fight 0 2 5 was to high because what I've done is I've put the deed something right next to the integral part the integral defile and then I just say 0 2 Part
it's understood that's referring to fight and I have been in grant and then I had the next 1 the data next Dr and then I don't think I can clean it up so it's a little bit nicer the Honourable Elsie iDecide I but you know I don't have to look back 1 because that 1 could be easier the inability whatever it is the whatever benefit in I'm integrating from 0 to piety to Pineland 0 I get too for the data I just have to integrate from 0 price signed dated the data that's minus co-signed data it's not a big deal and if I couldn't find 0 idea minus minus 1 and minus -minus 1 and careful and to therefore if I do those 2 integral and left with the following I get to high from the fight 2 from the theater and then I are square and I have this thing the wave function square interface square opining on the game minus 2 0 on the nite so I can clean things up I get following in a goal to do for times won over enough to the times integral from 0 to a knot of our square either minus 2 our upon a new deal as a one-dimensional integral and you can look this up and what I've done here as I've taken a screenshot From the roles . com and I've put in you have to put it in terms of that's not are not very smart that way but I don't put an X squared exponential function minus 2 eggs over a nod In click here and it gives me this format about whether this is the time to compute was a hundredth of a 2nd and it says it's minus 1 for the cannot be utilized to acts upon a knot times you may not square close to a Nymex to square so I just grabbed that and that's pretty easy if I accept that that's true enough I doubt it's true I can certainly take the derivative and see if it's true I don't know if there is a derivative stock ,comma maybe that's too easy and I put that in and I simplify it and put in the limits of 0 for acts or on parties and I put in the limits a knock on the top of the what I it is I get a knock you go over 4 -minus 5 a not you over 4 times each to where he is now the natural laws he not the electric charge and if I evaluate 1 minus 5 minus 2 I get the number . 3 2 3 excuse me 3 2 3 2 3 sometimes they not you for now I go back and collect everything together that I've got the ah I have I had 4 has 1 over a not too and then I get a knock you go over 4 great Everything goes away and the only thing that's left is this . 3 to 3 and so the answer is but the probabilities . 3 2 3 and that means but it's only 32 . 3 per cent likely that if we take a hydrogen atoms and we measure the position electron that's going to be within what we think of normally as the size Of the hydrogen as we usually think of a on something like the radius of the hydrogen atoms but it turns out that this much squishier than that it's only 32 per cent time Maryland and these arrests the timing of the electron is roaming around pretty far from home but kind of rather surprising so the interpretation is the electron is free to roam and can get pretty far away and that could be very important because when it gets far away it may have a chance of being picked up by by some of the positive nucleus may actually go somewhere and make a chemical reaction if you were held to tightly very close to the that would have it
that would have ramifications for reactivity and although the border radius is the radius where it's most likely in that show it's not actually so likely to be with American actually the outside that as well In higher orbitals the chance that the knew the electron can be far away From the ad it is very very high the saw 3 S 3 is not that high in energy in terms of quantum numbers it is actually when you look at -minus 9 versus minus 1 it's 90 per cent of the way toward disappearing into a
Protonierung
Derivatisierung
Kryosphäre
Elektron <Legierung>
Fülle <Speise>
Chemische Formel
Nanopartikel
Funktionelle Gruppe
Lösung
Atom
Lösung
Mineralbildung
Symptomatologie
Zellkern
Lösung
Konkrement <Innere Medizin>
Edelstein
Aktionspotenzial
Altern
Derivatisierung
CHARGE-Assoziation
Nanopartikel
Elektronegativität
Chemische Formel
Funktionelle Gruppe
Zunderbeständigkeit
Systemische Therapie <Pharmakologie>
Atom
Lösung
Entfestigung
Elektron <Legierung>
Symptomatologie
Potenz <Homöopathie>
Krebs <Medizin>
Zellkern
Querprofil
Quellgebiet
Rydberg-Zustand
Tellerseparator
Protonierung
Stickstofffixierung
CHARGE-Assoziation
Chemische Formel
Mannose
Bohrium
Single electron transfer
Zellkern
Ordnungszahl
Orbital
Lösung
Atom
Chemische Struktur
Kryosphäre
Sense
Nanopartikel
Uranerz
f-Element
Operon
Wasserwelle
Funktionelle Gruppe
Atom
Lösung
Konjugate
Kryosphäre
Elektron <Legierung>
Symptomatologie
Potenz <Homöopathie>
Quellgebiet
Zuchtziel
Protonierung
Mischen
Emissionsspektrum
Alignment <Biochemie>
Zetapotenzial
Chemisches Element
Chemische Forschung
Mineralbildung
Laichgewässer
Zellkern
Ordnungszahl
Lösung
Teststreifen
Simulation <Medizin>
Elektron <Legierung>
Alkoholgehalt
Funktionelle Gruppe
Wasserwelle
Systemische Therapie <Pharmakologie>
Atom
Lösung
Aktives Zentrum
Zelle
Elektron <Legierung>
Wasserstand
Fülle <Speise>
Gangart <Erzlagerstätte>
Mähdrescher
Stoffdichte
Ausgangsgestein
Toll-like-Rezeptoren
Erdrutsch
Emissionsspektrum
Chemischer Prozess
Zellkern
Elektron <Legierung>
Elektron <Legierung>
Lithium
Helium
Lactitol
Ordnungszahl
Konjugate
Kryosphäre
Elektron <Legierung>
Atomsonde
Nahtoderfahrung
Konkrement <Innere Medizin>
Schelfeis
Protonierung
Protonenpumpenhemmer
Chemische Formel
Elektron <Legierung>
Chemische Formel
Massendichte
Funktionelle Gruppe
Click-Chemie
Humangenom-Projekt
d-Orbital
Grenzfläche
Elektron <Legierung>
Chemische Reaktion
Zellkern
Reaktivität
Klinischer Tod
Orbital
Stockfisch
Derivatisierung
Kryosphäre
Elektron <Legierung>
Sammler <Technik>
Massendichte
Bohrium
Blätterteig
d-Orbital
Wasserstand
Elektron <Legierung>
Symptomatologie
Reaktivität
Dipol <1,3->
Ordnungszahl
Lösung
Chemische Struktur
Kryosphäre
Übergangsmetall
Elektron <Legierung>
Wildbach
Pharmazie
Spektralanalyse
Bisacodyl
Massendichte
f-Element
Ionisationsenergie
Containment <Gentechnologie>