5. Hydrogen Atom Energy Levels

00:41:39
https://www.youtube.com/watch?v=kO0VmaLkgj8

概要

TLDRVideoen omhandler fysikeksperimenter med hydrogenlamper til at studere fotonemission og absorption, samt hvordan Schrödinger-ligningen blev brugt til at beregne energier. Den forklarer eksperimentelt, hvordan lysspektre fra elektroner i hydrogen kan observeres, og hvordan Schrödinger-ligningen forudsiger disse energier præcist, som demonstreret af Balmer-serien. Desuden forklares forskelle mellem emission og absorption af fotoner, og vigtigheden af ioniseringsenergi og bindingsenergi diskuteres. Videoen indeholder en praktisk demonstration og diskussion af teoretiske koncepter. Forelæsningen dækker også over, hvordan man kan beregne fotonfrekvenser og -bølgelængder, samt hvordan disse tilsammen bekræfter energiforskellene som forudsagt af Schrödinger-ligningen.

収穫

  • 📚 Schrödinger-ligningen forudser energiniveauer præcist i hydrogen.
  • 🔬 Eksperimenter anvender hydrogenlamper for at se lysspektre.
  • 🌈 Fotonemission sker ved elektron-overgange i atomer.
  • ⚡ Ioniseringsenergi er positiv og bindingsenergi er negativ.
  • 🔍 Balmer-serien demonstrerer emission af synligt lys.
  • 🧪 Praktiske eksperimenter viser Schrödinger-ligningens gyldighed.
  • 📉 Energibindinger og ioniseringsenergier er centrale koncepter.
  • 🕵️ Beregninger bekræfter forskelle i energitilstande.
  • 💡 Lighed i lysbølgelængder giver indsigt i atomer.
  • 🎓 Uddannelse med praktiske fysikdemonstrationer.

タイムライン

  • 00:00:00 - 00:05:00

    Introduktion til kursets indhold og motivation for at deltage. Diskussion af røntgenstrålingens bølgelængde og intensitetens betydning for billeddannelse af proteiner. Eksempler på brug af synkrotroner til hjemme-dataindsamling.

  • 00:05:00 - 00:10:00

    Forklaring af Schrödinger-ligningen og dens anvendelse på hydrogenatomer. Diskussion af bindingen af elektroner til deres kerner og begrebet bindingsenergi. Introduktion til problematikken med at bekræfte data gennem eksperiment.

  • 00:10:00 - 00:15:00

    Detaljer om hydrogenatomets energiniveauer og hvordan bindingsenergien beregnes ud fra hovedkvantetallet. Diskussion om begrebet ioniseringsenergi og dets sammenhæng med bindingsenergi, herunder signernes betydning.

  • 00:15:00 - 00:20:00

    Beskrivelse af ioniseringsenergi fra grundtilstanden og op til højere energitilstande. Brug af klikker spørgsmål til at engagere studerende i at forstå energiovergange og ioniseringsprocesser.

  • 00:20:00 - 00:25:00

    Introduktion til konceptet med enelektron-ioner og hvordan Z (atomnummer) påvirker bindende energi. Diskussion af hvordan Schrödinger-ligningen anvendes for disse ioner. Klikker spørgsmål for at teste forståelse.

  • 00:25:00 - 00:30:00

    Gennemgang af hvordan fotonudsendelse fungerer, når elektroner skifter fra højere til lavere energitilstande, og hvordan dette relaterer til forskelle i energiniveauer. Visualisering af eksperimenter og fotonens energi.

  • 00:30:00 - 00:35:00

    Demonstration af lysspektre udsendt af hydrogen, og hvordan eksperimentelle resultater kan bruges til at teste Schrödinger-ligningens forudsigelser. Diskussion af de forskellige serier og deres bølgelængder.

  • 00:35:00 - 00:41:39

    Sammenfatning af absorption og emission af fotoner, herunder forskellen mellem processerne og hvordan man beregner frekvenser med Schrödinger-ligningen. Opsummering af læring og præsentation af klikker konkurrencevinder.

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マインドマップ

Mind Map

よくある質問

  • Hvad er Balmer-serien?

    Det er et lysmønster opstået ved elektronovergange i atomer, specifikt hydrogen, der afgiver lys ved emission.

  • Hvordan kan man se lys spektrum fra hydrogen?

    Det sker ved eksitering af elektroner gennem elektrisk spænding eller lysindfald, hvorved lys spektrum kan ses.

  • Er Schrödinger-ligningen en god model for energiniveauer i hydrogen?

    Ja, Schrödinger-ligningen kan præcist forudsige energitilstande i hydrogen, som verificeret af Balmer-serien.

  • Hvorfor er ioniseringsenergi positiv og bindingsenergi negativ?

    Ioniseringsenergie er positiv fordi det kræver tilførsel af energi for at fjerne en elektron, mens bindingenergi er den energi der frigøres ved binding.

  • Hvad sker der ved fotonemission i et atom?

    Elektroner udsender fotoner når de hopper fra et højere til et lavere energiniveau, og fotonen har energi svarende til forskellen mellem niveauerne.

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  • 00:00:48
    ok let's just take 10 more seconds
  • 00:01:15
    okay
  • 00:01:19
    does someone want to explain the answer
  • 00:01:22
    here give it a try um so it says in the
  • 00:01:38
    problem that the X rays have the same
  • 00:01:40
    wavelength so you know that they also
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    have the same frequency so that
  • 00:01:43
    discounts one two and five and six so
  • 00:01:46
    then it's just a choice between three
  • 00:01:47
    and four and in like the video the other
  • 00:01:50
    day you said in order to like say to
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    image these proteins you need a high
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    intensity light so three yep that's a
  • 00:01:57
    great explanation here I don't really
  • 00:01:59
    know what these these might come in
  • 00:02:01
    handy today I don't know okay yeah so
  • 00:02:07
    the trick was sort of better quality
  • 00:02:09
    data so you probably figured out that
  • 00:02:11
    that then was the higher intensity so
  • 00:02:14
    this is this is a true thing so we have
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    data collection there's equipment here
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    at home and a lot of universities have
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    what they call home data collection
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    equipment but we often travel to
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    synchrotrons where we have higher
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    intensity ie more photons per second and
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    then you get better quality data and so
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    these are sometimes people do these
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    things remotely where you ship your
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    samples and someone else collects it but
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    my lab likes to go and you stay up all
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    night and collect great data and it's
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    it's a bonding experience you saw a
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    little bit that of that on the video
  • 00:02:53
    okay we ended last time looking at the
  • 00:02:58
    Schrodinger equation and seeing that the
  • 00:03:00
    Schrodinger equation could be solved for
  • 00:03:03
    a hydrogen atom giving information about
  • 00:03:06
    binding energy the binding of electron
  • 00:03:09
    to its nucleus and also a wave function
  • 00:03:12
    which we haven't talked about yet so
  • 00:03:14
    we're going to continue talking about
  • 00:03:15
    this binding energy and then next week
  • 00:03:18
    we're gonna move into wave functions or
  • 00:03:19
    orbitals so the binding energy that
  • 00:03:22
    comes out of the Schrodinger equation no
  • 00:03:25
    one should ever just kind of believe
  • 00:03:26
    things it looks fancy but you know does
  • 00:03:28
    it really
  • 00:03:29
    is it really doing this right estimation
  • 00:03:32
    and again it just kind of came out of
  • 00:03:34
    Schrodinger's mind so it's always nice
  • 00:03:36
    to verify that this equation is is
  • 00:03:39
    working pretty well so today we're going
  • 00:03:41
    to talk about how we were able to verify
  • 00:03:44
    that the binding energy that the
  • 00:03:46
    Schrodinger equation was predicting
  • 00:03:48
    actually agrees with experiment so we're
  • 00:03:53
    going to continue talking about binding
  • 00:03:54
    energies then go on to the verification
  • 00:03:57
    with a demo of how they how people were
  • 00:04:00
    able to show that there was good
  • 00:04:02
    agreement here all right so let's
  • 00:04:04
    continue with binding energies so we're
  • 00:04:07
    still talking about the hydrogen atom in
  • 00:04:09
    energy levels and we saw last time that
  • 00:04:11
    the Schrodinger equation could be
  • 00:04:14
    derived for a hydrogen atom such that
  • 00:04:18
    the binding energy or e to the n was
  • 00:04:21
    equal to minus this Redbird constant RH
  • 00:04:24
    over N squared where n is the principal
  • 00:04:27
    quantum number and so this is what we
  • 00:04:30
    saw last time and now we have a
  • 00:04:32
    graphical depiction of this and you'll
  • 00:04:35
    note that this is a negative value over
  • 00:04:38
    here so if n is 1 and we have the
  • 00:04:43
    principal quantum number of 1 we have
  • 00:04:45
    minus RH over 1 squared and so we just
  • 00:04:50
    have the negative value for the rigvir
  • 00:04:52
    constant 2.18 times 10 to the minus 18
  • 00:04:56
    joules and as we go up here in energy we
  • 00:05:01
    would get to an energy of 0 and if
  • 00:05:05
    energy here is 0 what must be true about
  • 00:05:09
    n what kind of number is in here
  • 00:05:13
    infinity right so if this is infinity
  • 00:05:18
    that number goes to 0 and so if the
  • 00:05:22
    electron is infinitely far away from the
  • 00:05:25
    nucleus it's basically it's a free
  • 00:05:27
    electron it doesn't feel any kind of
  • 00:05:30
    attraction it's infinitely far away then
  • 00:05:32
    your binding energy would be 0 ie it's
  • 00:05:36
    not bound and that would be true at this
  • 00:05:39
    infinitely far away
  • 00:05:40
    distance and then in between the N
  • 00:05:43
    equals 1 to N equals affinity we can use
  • 00:05:47
    this equation for the hydrogen atom to
  • 00:05:49
    figure out what these energy levels are
  • 00:05:53
    so when we have the N equals 2 state it
  • 00:05:58
    would be minus RH over 2 squared or 4
  • 00:06:01
    and so we can calculate what that number
  • 00:06:04
    is here minus 0.5 for 5 times 10 to the
  • 00:06:09
    minus 18 joules N equals 3 so we have
  • 00:06:14
    our H over 3 squared we can do the math
  • 00:06:18
    over here for you get the idea
  • 00:06:22
    minus RH over 4 squared and we have then
  • 00:06:27
    over 5 squared over 6 squared and you
  • 00:06:30
    can see the energy and you can calculate
  • 00:06:34
    the energy levels here all right so when
  • 00:06:39
    you have an electron in this N equals 1
  • 00:06:42
    state that's the lowest energy it's the
  • 00:06:46
    most negative number and that's known as
  • 00:06:49
    the ground state and when you have an
  • 00:06:51
    electron in this ground state that's the
  • 00:06:54
    most stable stable state for the
  • 00:06:57
    hydrogen atom so again from these lower
  • 00:07:00
    ground state up to this state here now
  • 00:07:04
    we're going to introduce another term
  • 00:07:06
    which you'll hear a lot and this is
  • 00:07:10
    ionization energy so the ionization
  • 00:07:14
    energy the amount of energy you need to
  • 00:07:16
    put in to ionize an atom or a release
  • 00:07:19
    and electron so the ionization energy of
  • 00:07:23
    a hydrogen atom in the enth state is
  • 00:07:26
    going to be equal to the binding energy
  • 00:07:28
    but the signs of these are going to be
  • 00:07:31
    different so we have this equation where
  • 00:07:33
    binding energy equals minus ie the
  • 00:07:36
    ionization energy so we talked about the
  • 00:07:40
    fact that the binding energy is negative
  • 00:07:42
    and the ionization energy is always
  • 00:07:46
    positive so for the binding energy when
  • 00:07:49
    the binding energy is zero it means the
  • 00:07:51
    elect
  • 00:07:51
    isn't found so a negative value for
  • 00:07:53
    binding energy means that the electrons
  • 00:07:56
    being held by the nucleus the electrons
  • 00:07:58
    bound for ionization energy that's the
  • 00:08:02
    energy you need to add to the system to
  • 00:08:04
    release the electron and you're always
  • 00:08:06
    going to need to add some energy so
  • 00:08:08
    that's a positive number so when you
  • 00:08:10
    think about ionization energy you're
  • 00:08:11
    going to be thinking about it's it's a
  • 00:08:13
    positive number that you're going to be
  • 00:08:15
    expecting there now we can consider this
  • 00:08:19
    same diagram and we already talked about
  • 00:08:22
    these energy levels and now we can think
  • 00:08:24
    about these in terms of ionization
  • 00:08:27
    energies as well so the difference from
  • 00:08:30
    this state where energy is 0 to the
  • 00:08:33
    ground state down here the ionization
  • 00:08:36
    energy the energy it's needed to ionize
  • 00:08:39
    an electron that's an N equals 1 here is
  • 00:08:41
    going to be equal to minus the binding
  • 00:08:45
    energy of that electron in that N equals
  • 00:08:47
    1 state so again here it's not too hard
  • 00:08:51
    if you know this information and this
  • 00:08:54
    equation to figure out what the
  • 00:08:56
    ionization energy is so that's just then
  • 00:08:59
    going to be the positive value of the
  • 00:09:02
    binding energy so binding energy minus
  • 00:09:05
    red Burke's constant here 2.18 times 10
  • 00:09:09
    to the minus 18 joules so the ionization
  • 00:09:12
    energy then for a hydrogen atom in the
  • 00:09:15
    ground state is positive two point one
  • 00:09:17
    eight zero times ten to the minus
  • 00:09:19
    eighteenth and I'm just going to try to
  • 00:09:21
    use the same number of significant
  • 00:09:23
    figures I always try to pay attention to
  • 00:09:25
    my significant figures all right so we
  • 00:09:28
    can do this again for for at the N
  • 00:09:32
    equals 2 state or the first excited
  • 00:09:36
    state so here's the N equals 2 state so
  • 00:09:41
    now we're going to be talking about this
  • 00:09:42
    differential energy here so the
  • 00:09:47
    ionization energy for an electron in
  • 00:09:50
    this first excited state again that will
  • 00:09:53
    be ionization energy equals minus the
  • 00:09:56
    binding energy for that state and so
  • 00:09:59
    that's gonna be then the positive value
  • 00:10:01
    here
  • 00:10:02
    so the binding energy
  • 00:10:03
    - if we do this in if we change this to
  • 00:10:08
    it
  • 00:10:08
    this is eighteen point five to the 18 or
  • 00:10:11
    five point zero to the minus 19 joules
  • 00:10:14
    try to keep the significant figures the
  • 00:10:16
    same all right so why don't you give
  • 00:10:19
    this a try now we'll have a clicker
  • 00:10:22
    question
  • 00:11:13
    okay ten more seconds
  • 00:11:31
    stop very long one second okay
  • 00:11:40
    interesting
  • 00:11:43
    so maybe you can talk to your neighbor
  • 00:11:49
    and and someone can tell me what the
  • 00:11:52
    trick is here
  • 00:12:10
    okay we have someone who's going to tell
  • 00:12:13
    us what the trick is the ground state is
  • 00:12:20
    N equals one and from there the excited
  • 00:12:23
    States go up one so the first excited
  • 00:12:26
    state is N equals two and then so the
  • 00:12:28
    third one will be N equals four and
  • 00:12:30
    since you're looking for the ionization
  • 00:12:32
    energy you go to the energy for N equals
  • 00:12:37
    four and you multiply by negative one
  • 00:12:39
    which is four zero point one four to the
  • 00:12:42
    negative great yeah so see what I have I
  • 00:12:49
    need to get some more stuff sorry okay
  • 00:12:52
    so the trick it's not a hard problem you
  • 00:12:57
    just had to figure out what the third
  • 00:12:59
    excited state meant so that was a good
  • 00:13:07
    extension we made that mistake you will
  • 00:13:10
    not make that one again all right so now
  • 00:13:13
    we can think about this also in more
  • 00:13:16
    general terms only kind of slightly more
  • 00:13:18
    general terms frankly which is to
  • 00:13:21
    consider for other one electron ions we
  • 00:13:28
    can have a more general equation so we
  • 00:13:31
    had for the hydrogen atom the the
  • 00:13:34
    binding energy en is minus red bursts
  • 00:13:38
    constant rh / N squared and now I've
  • 00:13:41
    added Z squared which is the atomic
  • 00:13:44
    number and for hydrogen it's one so it
  • 00:13:47
    wasn't it wasn't around we didn't need
  • 00:13:49
    it before but we can consider other ions
  • 00:13:53
    that also have one electron they will
  • 00:13:55
    also work with this equation so there's
  • 00:13:59
    a couple of things that kind of fall out
  • 00:14:01
    of this one that an electron is going to
  • 00:14:04
    be bound more weakly when N is a big
  • 00:14:07
    number here and so that that that makes
  • 00:14:11
    sense from what we were looking at
  • 00:14:12
    before and that an electron is also
  • 00:14:17
    going to be bound more tightly when Z
  • 00:14:20
    is big and we hadn't really talked about
  • 00:14:22
    that because we've just been talking
  • 00:14:23
    about the hydrogen atom and so it always
  • 00:14:26
    has the same Z but if you have a
  • 00:14:29
    difference II you're gonna have a bigger
  • 00:14:30
    positively charged nucleus and so it
  • 00:14:34
    sort of makes sense that you would then
  • 00:14:36
    have a tighter binding electron alright
  • 00:14:39
    so you might think what are other things
  • 00:14:41
    that have just one electron that this is
  • 00:14:44
    going to apply to and so far of course
  • 00:14:46
    we've just been talking about our friend
  • 00:14:48
    a hydrogen that has its one electron and
  • 00:14:51
    z equals one but we have ions that can
  • 00:14:55
    also have one electron so helium plus
  • 00:14:58
    and it has a z of two but when it's
  • 00:15:01
    helium plus it only has one electron
  • 00:15:04
    lithium plus two also only has one
  • 00:15:09
    electron and it has a Z of three and
  • 00:15:12
    then what about something that's a one
  • 00:15:16
    electron system with a plus 64 without
  • 00:15:21
    looking at your periodic table what does
  • 00:15:23
    the Z have to be here yeah so 65 so when
  • 00:15:29
    working these kinds of problems if
  • 00:15:31
    you're not if you're talking about a one
  • 00:15:33
    electron ion or atom and it's not
  • 00:15:36
    hydrogen don't forget about Z we need to
  • 00:15:39
    have that in our equation all right so
  • 00:15:45
    talking about these binding energies now
  • 00:15:48
    out of the Schrodinger equation you can
  • 00:15:51
    calculate ionization energies if you
  • 00:15:54
    know the binding energy all of this is
  • 00:15:55
    good but how do we know that we can
  • 00:15:57
    trust the Schrodinger equation that
  • 00:15:59
    those equations really are working so
  • 00:16:02
    the way that they figured this out is
  • 00:16:04
    from experiment and particularly
  • 00:16:07
    experimentally figuring out what the
  • 00:16:09
    energy levels were and and thinking you
  • 00:16:12
    know does this match with the
  • 00:16:13
    Schrodinger equation so they were able
  • 00:16:16
    to use photon admission to be able to do
  • 00:16:19
    this so let's let's consider what photon
  • 00:16:23
    admission is and then we're going to
  • 00:16:26
    prove that this equation that I've been
  • 00:16:28
    showing you actually holds so photon
  • 00:16:32
    admission
  • 00:16:32
    this is a situation that occurs when you
  • 00:16:36
    have an electron going from a higher
  • 00:16:39
    initial higher energy initial state
  • 00:16:42
    going to a lower energy state and as it
  • 00:16:47
    goes from this high energy state to the
  • 00:16:50
    low energy State
  • 00:16:51
    there's a difference between these two
  • 00:16:54
    energy states Delta e and that's going
  • 00:16:57
    to be equal to the higher energy initial
  • 00:17:00
    state minus the energy in the final
  • 00:17:03
    state so there's this difference in
  • 00:17:05
    energy between the two states and the
  • 00:17:08
    photon that gets admitted when this
  • 00:17:12
    energy transition happens has the same
  • 00:17:15
    energy as the difference between those
  • 00:17:17
    so the energy of the admitted photon is
  • 00:17:21
    also Delta e so you admit all of that
  • 00:17:24
    energy as you have that change so the
  • 00:17:28
    difference here we can consider an
  • 00:17:31
    actual kind of case where we're going
  • 00:17:33
    from an energy difference of N equals 6
  • 00:17:37
    to an energy a level of N equals 2 and
  • 00:17:41
    we can think about what the energy
  • 00:17:43
    difference is between these two and we
  • 00:17:46
    can just write that equation out so the
  • 00:17:49
    initial energy the electron started at N
  • 00:17:52
    equals 2 so the energy or N equals 6 the
  • 00:17:56
    energy of the N equals 6 state and it
  • 00:17:58
    goes to the energy of the N equals 2
  • 00:18:01
    state so in energy and equals 6 minus
  • 00:18:04
    energy n equals 2 all right so of course
  • 00:18:10
    if you know energy you can know a lot of
  • 00:18:12
    other things about the photon so you can
  • 00:18:16
    calculate frequency of that admitted
  • 00:18:19
    photon so again we have our energy
  • 00:18:21
    difference here and we can then solve
  • 00:18:25
    for the frequency of the admitted photon
  • 00:18:28
    which is equal to the energy difference
  • 00:18:30
    that energy divided by Planck's constant
  • 00:18:34
    and you could also write it out the
  • 00:18:38
    initial energy minus the final energy
  • 00:18:40
    over H all of these are equivalent
  • 00:18:42
    things
  • 00:18:44
    and from when you know frequency we're
  • 00:18:46
    talking about light here so you can
  • 00:18:49
    calculate the wavelength so let's think
  • 00:18:53
    now about what we might expect in terms
  • 00:18:56
    of frequencies and wavelengths depending
  • 00:18:59
    on the energy difference between the two
  • 00:19:02
    different states so here if we think
  • 00:19:06
    first about this electron with the
  • 00:19:08
    purple line we have a large energy
  • 00:19:11
    difference here between this state and
  • 00:19:15
    this state down here between N equals
  • 00:19:18
    five to N equals one so when we have a
  • 00:19:21
    large difference in energy what do we
  • 00:19:23
    expect about the frequency of the
  • 00:19:26
    emitted photon is it going to be a high
  • 00:19:28
    frequency or low frequency high yeah so
  • 00:19:34
    large energy high frequency and so then
  • 00:19:37
    what would be true about the wavelength
  • 00:19:39
    of that emitted photon short right now
  • 00:19:46
    if we had a small difference say N
  • 00:19:48
    equals 3 to N equals one which is a
  • 00:19:50
    smaller difference in energy what's true
  • 00:19:53
    about the frequency here right low
  • 00:19:57
    frequency and wavelength right long
  • 00:20:00
    wavelength all right so now we're
  • 00:20:05
    actually going to see some photons being
  • 00:20:09
    admitted and let me just kind of filled
  • 00:20:12
    in to this experiment a little bit so we
  • 00:20:16
    have we have a fill a vacuum filled with
  • 00:20:21
    hydrogen and if you have negative and
  • 00:20:24
    positive electrodes you can admit light
  • 00:20:27
    from this and then analyze the different
  • 00:20:31
    wavelengths so we are not going to be
  • 00:20:35
    the first people to see this but we're
  • 00:20:37
    going to try this and this is a we
  • 00:20:40
    should observe these different
  • 00:20:42
    wavelengths coming off and after we
  • 00:20:45
    observe them we will try to calculate
  • 00:20:47
    what they're due to and then
  • 00:20:50
    if this experiment if the experimental
  • 00:20:52
    results of the wavelengths and frequency
  • 00:20:55
    observed can be explained by the
  • 00:20:57
    Schrodinger equation but first let's
  • 00:20:59
    actually see the visible spectra that is
  • 00:21:03
    created by hydrogen and so we have our
  • 00:21:06
    demo tas and actually if all our TAS can
  • 00:21:08
    help pass out some little glasses to
  • 00:21:11
    help everyone see this and when we're
  • 00:21:15
    ready we're gonna do lights down but
  • 00:21:18
    let's get everything handed out first
  • 00:21:23
    alright here are the lights
  • 00:21:28
    so this is a hydrogen lamp and you turn
  • 00:21:32
    it on electricity excites all the
  • 00:21:35
    hydrogen's inside it and then you see
  • 00:21:37
    this glow from the electromagnetic
  • 00:21:39
    radiation being emitted by these excited
  • 00:21:42
    hydrogen's relaxing down to the ground
  • 00:21:44
    state
  • 00:21:53
    I'm gonna try there like
  • 00:21:57
    so we're gonna try this for those of you
  • 00:22:00
    who don't have the glasses but let's see
  • 00:22:03
    if this works it was kind of there is
  • 00:22:11
    that what they're supposed to see hey
  • 00:22:14
    you're supposed to see all of them I
  • 00:22:15
    guess you can't really it's depending on
  • 00:22:19
    how you move this thing
  • 00:22:25
    it's not working
  • 00:22:32
    we're not working
  • 00:22:34
    now
  • 00:22:38
    yeah I know I mean
  • 00:22:42
    kind of worse depending on how I believe
  • 00:22:44
    this thing
  • 00:22:48
    sometimes it works really well
  • 00:22:59
    - just try walking can we hold it up and
  • 00:23:04
    see whether people also can see all
  • 00:23:06
    right so we're gonna hold it up see if
  • 00:23:08
    you guys without the without the camera
  • 00:23:15
    okay so you should be able to see for
  • 00:23:21
    those of you that have your glasses is
  • 00:23:22
    the continuous spectrum with the various
  • 00:23:26
    colors
  • 00:23:32
    I might have to get the angle right they
  • 00:23:35
    say our people in the middle of the room
  • 00:23:36
    able to see it
  • 00:23:46
    can anyone can anyone see it yeah people
  • 00:23:51
    on the edge of the room can you see it I
  • 00:23:53
    think it's harder from when the camera
  • 00:23:57
    is blocking people a little bit it works
  • 00:24:01
    I can see it do you want to move it up
  • 00:24:04
    farther like in front of that
  • 00:24:16
    turn around
  • 00:24:19
    all right you will turn it slightly and
  • 00:24:22
    then people can we can come down maybe
  • 00:24:25
    and try it after class if it's not
  • 00:24:27
    working very well
  • 00:24:41
    when it's tilted are you having better
  • 00:24:43
    luck over here all right
  • 00:24:51
    all right I guess we'll bring the lights
  • 00:24:52
    back up and I'll show you what you sort
  • 00:24:54
    of seen if it didn't work for you so how
  • 00:25:00
    many how many people were able to see
  • 00:25:02
    see the spectra okay all right so a good
  • 00:25:05
    number of people great
  • 00:25:06
    I feel like this room is not as perfect
  • 00:25:10
    for this as some other rooms but there's
  • 00:25:13
    some rooms that actually don't get dark
  • 00:25:15
    at all and then you can't really see
  • 00:25:17
    anything
  • 00:25:18
    all right so maybe if you have a chance
  • 00:25:25
    we can try again at the end all right so
  • 00:25:28
    this is what you should have seen you
  • 00:25:33
    should have seen these different series
  • 00:25:35
    of lights our series of colors coming
  • 00:25:38
    off and this was we're not the first
  • 00:25:41
    people to see it so the ball JJ Balmer
  • 00:25:46
    in 1885 reported seeing these colors and
  • 00:25:51
    he wanted to calculate the frequencies
  • 00:25:53
    of the lights that he were seeing
  • 00:25:56
    admitted from this and so he did
  • 00:25:59
    calculate the frequency and then he
  • 00:26:01
    tried to figure out the mathematical
  • 00:26:03
    relationship between the different
  • 00:26:05
    frequencies of light that he was
  • 00:26:06
    observing and he found that the
  • 00:26:08
    frequency equaled 3.29 times 10 to the
  • 00:26:11
    minus r 10 to the 15th per second times
  • 00:26:15
    1 over 4 minus 1 over some number and
  • 00:26:19
    where n was either 3 4 or 5 and he
  • 00:26:23
    really didn't understand what the
  • 00:26:25
    significance of this was but it was
  • 00:26:27
    pretty you had a hydrogen in the sealed
  • 00:26:30
    tube and there were colors that came off
  • 00:26:32
    and they had frequencies so that's kind
  • 00:26:36
    of where where that stood for a little
  • 00:26:38
    while so now let's think about what
  • 00:26:40
    those different color lights were due to
  • 00:26:43
    so we have here energy levels and the
  • 00:26:50
    transitions that we were observing are
  • 00:26:52
    all going to the N equals 2 final state
  • 00:26:57
    and we can think about why
  • 00:27:00
    see any transitions to N equals one
  • 00:27:02
    think about that we'll come back to that
  • 00:27:04
    in a minute
  • 00:27:05
    but there were these different
  • 00:27:06
    transitions that were being observed
  • 00:27:08
    from three to two for two to five to two
  • 00:27:12
    and six to two so now let's think about
  • 00:27:14
    which colors which wavelengths are due
  • 00:27:19
    to which of the transitions so for the
  • 00:27:22
    red one what do you think three four or
  • 00:27:26
    five transition to two three
  • 00:27:30
    it is three and you could think about
  • 00:27:33
    that in terms of the smaller energy
  • 00:27:36
    that's the smallest energy so that would
  • 00:27:39
    be a low frequency and a long wavelength
  • 00:27:42
    so the one with the longest wavelength
  • 00:27:45
    and red is the longest wavelength so
  • 00:27:48
    that must be the transition from initial
  • 00:27:51
    end of three to N equals two and then we
  • 00:27:55
    can fill in the rest so this one over
  • 00:27:58
    here must have been N equals four to two
  • 00:28:03
    this one here then would be the blue N
  • 00:28:07
    equals five to two and then the purple
  • 00:28:11
    or indigo at the end N equals six to N
  • 00:28:15
    equals two so we saw they saw these four
  • 00:28:18
    colors there were these different
  • 00:28:20
    transitions and so then now we can
  • 00:28:23
    calculate what the frequencies of these
  • 00:28:26
    are and think about this then in terms
  • 00:28:29
    of Schrodinger's equation and kind of
  • 00:28:32
    test row dangers equation to see if it
  • 00:28:34
    predicts this so we can calculate the
  • 00:28:38
    frequency then of the admitted photons
  • 00:28:41
    and we had frequency equals the initial
  • 00:28:45
    energy minus the final energy state or
  • 00:28:49
    this Delta e over Planck's constant and
  • 00:28:54
    from the Schrodinger equation we know
  • 00:28:57
    about what these energy levels are from
  • 00:29:00
    Schrodinger and this is again for
  • 00:29:02
    hydrogen so Z equals one so these isn't
  • 00:29:05
    shown we have the binding energy equals
  • 00:29:09
    minus RH rid BER constant
  • 00:29:12
    and squared and now we can put these
  • 00:29:15
    equations together so we can substitute
  • 00:29:18
    these energies in using these and so we
  • 00:29:23
    can do that here we'll pull out Planck's
  • 00:29:26
    constant so one over H and then we can
  • 00:29:31
    substitute in - RH over the initial
  • 00:29:36
    enter the initial end level squared
  • 00:29:40
    minus - minus RH over the final n
  • 00:29:46
    squared and we can also simplify this a
  • 00:29:50
    little more pull out our H over here and
  • 00:29:53
    now we just have one over the final we
  • 00:29:57
    have minus a minus so we've rearranged
  • 00:29:59
    this one over n final squared minus 1
  • 00:30:03
    over n initial squared and we have an
  • 00:30:08
    equation that solves for the frequency
  • 00:30:11
    in terms of red burg Planck's constant
  • 00:30:14
    and what the principal quantum numbers
  • 00:30:18
    are what n is so let's look at this a
  • 00:30:21
    little more now remember this is all
  • 00:30:24
    going to and final of two and so we can
  • 00:30:29
    put that equation up here again so when
  • 00:30:32
    this is 2 2 squared is 4 and if you
  • 00:30:35
    remember back Balmer had a 4 had this
  • 00:30:39
    part of the expression but he had kind
  • 00:30:42
    of a strange number over here that he
  • 00:30:44
    experimentally determined but if you
  • 00:30:47
    take our H and divide by Planck's
  • 00:30:50
    constant rigvir constant divided by
  • 00:30:52
    Planck's you get that number that bomber
  • 00:30:55
    had found back in 1885 3.2 9 times 10 to
  • 00:31:01
    the 15th per second so when we plug in
  • 00:31:04
    the values from Schrodinger's equations
  • 00:31:07
    you come up with the experimentally
  • 00:31:10
    determined values for frequencies or
  • 00:31:13
    wavelength of the admitted light and of
  • 00:31:15
    course from the frequency you can
  • 00:31:17
    calculate the wavelength and the
  • 00:31:19
    wavelengths that were observed
  • 00:31:20
    experimentally agreed with a wavelength
  • 00:31:24
    you would
  • 00:31:24
    callate from the Schrodinger's equation
  • 00:31:26
    to one part in times 10 to the 8th so
  • 00:31:30
    the agreement was absolutely amazing
  • 00:31:32
    so Schrodinger's equation which was
  • 00:31:35
    taking into account the wave-like
  • 00:31:36
    properties of the electrons were able to
  • 00:31:40
    predict for a hydrogen atom
  • 00:31:42
    what wavelengths you should see admitted
  • 00:31:45
    in that hydrogen atom spectra so this
  • 00:31:48
    was really exciting Schrodinger equation
  • 00:31:51
    was working we had a way of describing
  • 00:31:54
    the behavior that we were observing for
  • 00:31:57
    these electrons and that was that was
  • 00:31:59
    really incredible and I think bombers
  • 00:32:02
    should get a lot of credit as well for
  • 00:32:04
    all of this and and the people who are
  • 00:32:06
    doing these early experiments they
  • 00:32:08
    didn't know what it was meaning but they
  • 00:32:09
    were coming up at the data that allowed
  • 00:32:10
    to test theories later on ok so this was
  • 00:32:14
    a series going to a final n of 2 and so
  • 00:32:19
    we have the Balmer series that was the
  • 00:32:21
    visible series that we were seeing so
  • 00:32:25
    what about why wasn't anything going to
  • 00:32:29
    N equals 1 and that's a clicker question
  • 00:33:16
    so at the end I'm going to ask you to
  • 00:33:18
    put up the winners
  • 00:33:26
    it's my number good okay ten more
  • 00:33:29
    seconds
  • 00:33:47
    okay
  • 00:33:50
    so seventy seventy one percent so the
  • 00:33:54
    trick here is to think about well
  • 00:33:56
    actually someone could tell me maybe
  • 00:33:57
    what was the trick here to think about I
  • 00:34:04
    get a little exercise okay oh come on
  • 00:34:07
    how's everyone doing up here so
  • 00:34:13
    therefore the Lyman series there's like
  • 00:34:15
    a more difference from the Balmer series
  • 00:34:17
    and so there's like more energy in the
  • 00:34:19
    transition when it goes down back to the
  • 00:34:20
    ground state so for that with more
  • 00:34:22
    energy it's gonna be a shorter way of
  • 00:34:24
    playing than that and that's ultraviolet
  • 00:34:26
    so here would be convenient to remember
  • 00:34:29
    kind of your orders of what are short
  • 00:34:31
    and long wavelength kinds of light okay
  • 00:34:40
    so we have the UV range then and so
  • 00:34:44
    that's why you didn't observe it it was
  • 00:34:47
    happening but you didn't see it because
  • 00:34:49
    it was in the UV alright so then we can
  • 00:34:53
    go on and look at the other things that
  • 00:34:56
    can happen here so we can have an final
  • 00:35:00
    of three and you don't need to know the
  • 00:35:03
    names of the series but that would be
  • 00:35:06
    near near IR N equals four would be in
  • 00:35:11
    the IR range so only some of what's
  • 00:35:14
    happening is actually visible to us we
  • 00:35:17
    see beautiful colors from transitions
  • 00:35:20
    but there's other things happening too
  • 00:35:22
    that are not visible to us so at this
  • 00:35:27
    point we're feeling pretty good about
  • 00:35:30
    those energy levels about the
  • 00:35:33
    Schrodinger equation being able to
  • 00:35:35
    successfully predict what kind of energy
  • 00:35:39
    levels you have that binding energy and
  • 00:35:44
    now that was from this this verification
  • 00:35:47
    was good from your photon emission but
  • 00:35:51
    there's another property that you can
  • 00:35:52
    have which is photon absorption so why
  • 00:35:56
    don't we do yet another clicker question
  • 00:35:58
    is a competition after all about
  • 00:36:02
    absorption
  • 00:36:51
    okay ten seconds okay
  • 00:37:10
    so now we're talking about a different
  • 00:37:14
    process we're talking before about
  • 00:37:16
    electrons they're starting up in a
  • 00:37:19
    higher energy level going lower
  • 00:37:21
    but with photon absorption we're going
  • 00:37:23
    the other direction so we're going from
  • 00:37:25
    a lower state we're being excited
  • 00:37:28
    they're absorbing energy and being
  • 00:37:30
    excited so we have a final state that is
  • 00:37:34
    higher and the energy is gained in this
  • 00:37:37
    process so it's being excited all right
  • 00:37:43
    so we can think about the same things
  • 00:37:45
    then in terms of absorption so if we
  • 00:37:49
    have a big energy difference if it's
  • 00:37:51
    absorbing a lot of energy big energy
  • 00:37:56
    difference it's going to be absorbing
  • 00:37:58
    light with a high frequency and a short
  • 00:38:02
    wavelength if there's a small energy
  • 00:38:05
    difference it'll absorb a photon with a
  • 00:38:08
    low frequency or a long wavelength and
  • 00:38:12
    we'll come back to some of these ideas
  • 00:38:14
    actually well into the course and we'll
  • 00:38:16
    actually look at some pretty colors so
  • 00:38:19
    in this case now we can calculate
  • 00:38:22
    frequency again but our equation is a
  • 00:38:24
    little bit different so we have the
  • 00:38:27
    Redbird constant and Planck's constant
  • 00:38:29
    again but now we have 1 over initial n
  • 00:38:33
    squared minus final n squared and so
  • 00:38:37
    this term should be a positive term we
  • 00:38:41
    should be getting out a positive
  • 00:38:43
    frequency so if I take this again and
  • 00:38:47
    just kind of put it up here you want to
  • 00:38:50
    think about whether you're if you're
  • 00:38:51
    talking about absorption or admission
  • 00:38:54
    that's what's telling you if the energy
  • 00:38:56
    is being gained or lost so you're not
  • 00:39:00
    going to have negative frequencies in
  • 00:39:02
    one case you're gonna be absorbing a
  • 00:39:04
    light of a particular frequency or
  • 00:39:07
    admitting light of a frequency so pay
  • 00:39:10
    attention to your equations and think
  • 00:39:12
    about whether your answer actually makes
  • 00:39:14
    sense when you do them and again all
  • 00:39:16
    these equations are going to be provided
  • 00:39:18
    to you in an equation sheet ok so let's
  • 00:39:21
    consider the sort of summary of both
  • 00:39:24
    these things now so we're talking about
  • 00:39:26
    admission versus absorption and so we
  • 00:39:29
    have this Rydberg formula which is what
  • 00:39:31
    this is called and it can be used to
  • 00:39:34
    calculate the frequency of either
  • 00:39:36
    admitted admitted photons or absorbed
  • 00:39:41
    photons so from either process and if we
  • 00:39:45
    want to make it more general again it's
  • 00:39:46
    just a one electron case but we can put
  • 00:39:49
    our Z in for any one electron ion so
  • 00:39:53
    frequency equals Z squared
  • 00:39:55
    Redbird constant over Planck's constant
  • 00:39:58
    and we have one over final the final
  • 00:40:03
    minus initial or initial minus final
  • 00:40:06
    depending on which process you're
  • 00:40:09
    talking about and over here where you'd
  • 00:40:11
    be talking then about admission so our
  • 00:40:15
    initial our initial energy is higher
  • 00:40:18
    going to lower and when that happens
  • 00:40:20
    you're going to be releasing light with
  • 00:40:24
    the enter energy difference that is due
  • 00:40:27
    to the difference between these states
  • 00:40:29
    so we're gonna have our electron it's
  • 00:40:32
    going to admit this energy in the
  • 00:40:35
    absorption process for this equation
  • 00:40:37
    we're gonna go from a initial state
  • 00:40:41
    that's lower to a higher state so our
  • 00:40:45
    our final will have a final state that's
  • 00:40:47
    higher than initial that's absorption
  • 00:40:50
    it's absorbing energy it's getting
  • 00:40:51
    excited and so the electron is absorbing
  • 00:40:55
    that energy so this really kind of
  • 00:41:00
    summarizes now what we need to know
  • 00:41:02
    about binding energies Schrodinger
  • 00:41:05
    equation also tells us about wave
  • 00:41:09
    functions which is what we're moving
  • 00:41:10
    into next so that's all for today except
  • 00:41:14
    we have a very important announcement
  • 00:41:16
    which is congratulation to recitation
  • 00:41:22
    six Lisa you are the first winner of the
  • 00:41:26
    clicker competition
  • 00:41:29
    have a great weekend everybody
タグ
  • Schrödinger-ligning
  • hydrogen
  • fotonemission
  • energibinding
  • Balmer-serien
  • ioniseringsenergi
  • bølgefunktioner
  • fysikeksperiment
  • lyspektre
  • elektronovergange