Chatlog 11-05-08; Hydrogen energies part 2 <BrianQ> Well, ya recall we left off with the hydrogen atom (hurting yet?) <_Frank_> yes <Spauwe> I remember (@ pain level 1) <BrianQ> do y'all recall the symbols we use for quantum numbers of a hydrogen state? <doos_> n l m <BrianQ> very good! <BrianQ> remember their names? <Spauwe> m=magnetic <DragonStek> principle algular momentum <BrianQ> very good! <BrianQ> n is principle <BrianQ> L is angular <BrianQ> m is magnetic <BrianQ> and upon which quantum number does the energy of the state depend? <_Frank_> m <BrianQ> boo Frank <Spauwe> l (@ pain level 2) <Crystal> n <BrianQ> yes Crystal! <BrianQ> (boo Spauwe ;) ) <doos_> m and n are close to eachother on the keyboard <BrianQ> Recalling that E0 is some collection of constants... <_Frank_> yes it was a typo <BrianQ> The energy of a state is given by E_n = -E0/n^2 <BrianQ> we recall hydrogen energies are negative... <BrianQ> and that the lowest energy is n = 1, with energy E_1 = -E0 <BrianQ> next energy is E_2 = -E0/4 <BrianQ> etc... <BrianQ> now we mapped this out last time on an energy level diagram... DragonStek, did you see how that was done? <DragonStek> yes thanks <DragonStek> frank thanks <_Frank_> np <_Frank_> I've sent copies of the energy chats to barbra to post with the chats <Spauwe> cool <_Frank_> the drawings I mean <BrianQ> Recall we are interested in not only the energies of states, but also the difference in energies between states <BrianQ> So... as we increase n, what happens to the energy separations? <_Frank_> they get smaller <DragonStek> smaller <BrianQ> difference in energy between adjacent n values get smaller, yes <BrianQ> Do we recall what the collection of constants E0 gives us? <_Frank_> infinite energy <doos_> the energy at the ground state? <BrianQ> the energy of the ground state, yes.
<BrianQ> well, actually -E0 <BrianQ> and what does it mean if the electron has zero energy? <doos_> it can't exist <BrianQ> recalling that all our energies are negative <BrianQ> it can... in a way... <_Frank_> in it's hidden symetry? <BrianQ> it means that the electron can escape to infinity... otherwise known as? <Spauwe> ionisation (@ pain level 3) <doos_> ionizaztion <BrianQ> still poking for that easter egg, Frank <doos_> heh <BrianQ> yes, Doos <_Frank_> I'm giving the others a chance <BrianQ> So the difference between ground state energy and zero energy is called what? <doos_> inonization <BrianQ> ionization energy <DragonStek> ionization energy <DragonStek> opps <doos_> can't spell either today <BrianQ> yep.. <BrianQ> so... E0 is the ionization energy... which happens to be a number all atomic physicists <BrianQ> are required to memorize <BrianQ> 13.6 ev <doos_> we can do that <Spauwe> we can try (@ pain level 4) <doos_> question <BrianQ> Now... why are we so interested in "differences between energies"? <BrianQ> yes doos? <Spauwe> colour in my stones!! <BrianQ> yes spauwe <doos_> the 13.6 ev is for hydrogen or for all elements/molecules? <Spauwe> they're the key to understanding it <BrianQ> indeed <BrianQ> What was your question Doos? <doos_> the 13.6 ev is for hydrogen or for all elements/molecules? <BrianQ> only for hydrogen... <doos_> ok <BrianQ> other values for other atoms... and then it gets really tricky for molecules... <BrianQ> Because molecules can break apart (called dissociation) as well as lose electrons (called ionization) <BrianQ> and these two processes compete... so that the ionization of a molecule is more tricky to define <BrianQ> That happened to be my area of research a long time ago... my job was to make it even more tricky to define <_Frank_> lol thats a strange job description
<doos_> it means he can't sleep <BrianQ> my wife just called, asking me what was a substitute for mascarpone cheese <BrianQ> anyways, back on topic. <doos_> I know that.. uhm <_Frank_> creme Fraiche would work <BrianQ> cream cheese, apparently <BrianQ> yes, indeed <_Frank_> yes thats the one <doos_> yah, both <BrianQ> heh <BrianQ> ok then, these hydrogen states... they are "constant energy" states or what we've been calling <BrianQ> stationary states <BrianQ> This is as long as nothing else is happening. <BrianQ> But you introduce light, which we describe as a "photon field"... <BrianQ> and it can upset these stationary states. <BrianQ> The electron can be promoted to a higher energy state (higher n state) if it absorbs a photon <BrianQ> thus absorbing all the photon's energy <BrianQ> And an electron can drop to a lower energy state (lower n) if it emits a photon <doos_> question <BrianQ> emitting the energy in the form of light <BrianQ> yes Doos? <doos_> the n=1,2,3 states, were they formerly known as the K L M shells? <BrianQ> They actually are called that. We haven't gotten to the spectroscopic notation yet <doos_> ok <_Frank_> showoff <BrianQ> heh <doos_> piss off, monsieur tossier <BrianQ> ok... so as it happens, you can't partially absorb a photon... you either absorb it all or nothing <Spauwe> that's a french teacher of Franks kid <BrianQ> Then a photon has to have a certain exact energy in order for the hydrogen atom to make a transition from n=1 state to n=2 state <BrianQ> How much energy does it need? <doos_> 4EO <_Frank_> 13.6Ev <BrianQ> nope, and nope <Spauwe> ehm... 1eo (at pain level 5) <doos_> 0.25EV <BrianQ> nope <BrianQ> almost <doos_> -0.25EV <BrianQ> Let's put it this way... <BrianQ> Let's call the difference between energies of two hydrogen states de <BrianQ> for example, de_1,2 = E_2 - E_1
<BrianQ> is that too much? <doos_> no <_Frank_> no <BrianQ> just subtract one from the other, right? <doos_> yes <_Frank_> yes <BrianQ> What is the energy E_1 of the ground state? <doos_> -EO <BrianQ> yes <BrianQ> What is the energy of E_2, the first excited state? <_Frank_> de_1,2-e_2 = E1 <BrianQ> nope Frank <doos_> -0.25EV (-EO/4) <BrianQ> yes Doos <BrianQ> so, what is de = -E0/4 + E0? <_Frank_> ok I see that <_Frank_> 0 <BrianQ> nope <Spauwe>.75 <doos_> -0.25EV <BrianQ> 3E0/4... you forgot the E0, Spauwe <Spauwe> ghe <BrianQ> 0.75*E0 <BrianQ> Now we recall that E0 = 13.6 ev, so now we could figure out the energy of the photon needed to promote the electron from n=1 to n=2 <BrianQ>... so now we can see why we had to memorize E0... <doos_> 13.6/0.75 <Spauwe> yep, if only I could count <BrianQ> No Doos... multiply 13.6 by 0.75 <doos_> ok <BrianQ> 13.6*0.75 <_Frank_> 10.2 <BrianQ> Yep, something like that :) <_Frank_> eo <Spauwe> ghehe <_Frank_> 10.2E) <BrianQ> 10.2 ev <_Frank_> 10.2EO <BrianQ> ev stands for electron-volt and is a unit of energy. <doos_> that is alot of energy <BrianQ> E0 = 13.6 ev <doos_> not coming from any visible light <_Frank_> ok I see it <BrianQ> yes, it is not coming from visible light, that's for sure... that's what we want to know, in fact <BrianQ> so... <Spauwe> thats why hydrogen isn't a colouring element i guess * diamond-clutter has joined #gemology <_Frank_> Hi DC <BrianQ> indeed Spauwe, that's exactly why hydrogen isn't a coloring agent
<diamond-clutter> hey <Spauwe> hi clutter <Crystal> hi diamond <BrianQ> hi Diamond clutter <doos_> you would need a wavelength of about 90nm to do that <diamond-clutter> hey all <Keirkof> helloes " <doos_> hi will <BrianQ> probably so Doos, sounds about right... <BrianQ> That's where we are headed... <diamond-clutter> Howdy Doos <BrianQ> A photon's energy is related to light frequency... <BrianQ> E = hf... where E is energy, f is frequency, and h is a constant called Planck's constant <BrianQ> So higher energy... higher frequency <BrianQ> now light frequency is related to wavelength, via speed... <BrianQ> c = x * f, where c is speed of light, x is wavelength, and f is frequency <BrianQ> speed of light is constant (in the quantum world)... so... <Spauwe> yep we know that one... <BrianQ> as frequency increases... what happens to wavelength? <diamond-clutter> decreases <Spauwe> is hets shorter/ lower in value <doos_> decreases <BrianQ> yes, yes <BrianQ> So... let's review... increasing energy -> increasing frequency -> shorter wavelength <diamond-clutter> yep - energy as in potential - right <doos_> whats the english term? inverse proportional? <BrianQ> yes, inversely proportional. <BrianQ> energy, in that the photon has some energy which might be viewed as potential, as it could potentially excite the hydrogen <BrianQ> but we just say the photon has energy <diamond-clutter> k <diamond-clutter> ok <BrianQ> and either the hydrogen eats it, or doesn't... no partial snackes. <doos_> so electrons are male? <Spauwe> ghehehe <BrianQ> So we found that to promote the hydrogen from n = 1 to n = 2, we need an energy 10.2 ev (genderless, as far as I know... they don't reproduce themselves) <diamond-clutter> potentially - ;) <_Frank_> so if the electron absorbs the proton does the proton cease to exist completely? <BrianQ> yes Frank <_Frank_> k <doos_> photon <BrianQ> but not to worry, because in a beam of light, the number of photons is kazillions <_Frank_> yes photon
<diamond-clutter> the hydrogen then absorbs the energy of the photon as well? <BrianQ> Exactly... <diamond-clutter> got it <diamond-clutter> conservation of energy <BrianQ> Now as Doos rightly figured out... 10.2 ev corresponds to what kind of light? <BrianQ> yes <doos_> x-rays? <BrianQ> not quite... <doos_> gamma? <Keirkof> more like IR, no? <BrianQ> no... way out <BrianQ> nope <doos_> atleast very short waves <diamond-clutter> red <Spauwe> very short wave uv <doos_> no <BrianQ> it is ultraviolet <BrianQ> yes Spauwe <BrianQ> very short ultraviolet <diamond-clutter> ok <BrianQ> shorter than SWUV <Spauwe> yep <diamond-clutter> the tiniest bit into the uv in other words <doos_> where is the cut-oof between x-ray an uv? <Spauwe> 40 nm? <BrianQ> it is what is referred to as VUV (vacuum ultraviolet)... no, deep in the uv... getting close to xrays <diamond-clutter> ok <BrianQ> Usually it is considered to be around 100 ev <doos_> on the edge then <BrianQ> So light between 10-100 ev is called VUV, vacuum ultraviolet <BrianQ> as you mentioned... 10 ev ~ 90 nm sounds about right <BrianQ> recall that SWUV is ~ 250 nm <doos_> yes <BrianQ> LWUV is ~ 350 nm <BrianQ> and violet light is ~ 400 nm <doos_> yes <BrianQ> and red light is ~ 700 nm <BrianQ> so... high energy light... and... to promote the electron from the ground state to, say, the n = 3 state... would require even more energy <diamond-clutter> so the hydrogen gains an ionized atom and can later relax and release a photon as it changes energy states <BrianQ> The hydrogen gains an excited electron, that can later go back to ground state by emitting a photon <diamond-clutter> ok <BrianQ> If the hydrogen is ionized... then the electron is lost, and all the energy is lost with it. <BrianQ> you are left with a sad proton :(
<diamond-clutter> ok <BrianQ> ok... now what if we had a bunch of hydrogen, all it their ground state, and we shine a whole lot of 5 ev light upon it? <BrianQ> Can we excite the hydrogen? <Spauwe> nope <doos_> no <BrianQ> no we cannot... so what happens to the light? <Spauwe> its transmitted <doos_> goes straight through <BrianQ> yes, it passes through like nothing is there. <diamond-clutter> transmitted - I agree <BrianQ> What if we shine a bunch of light with energy 10.5 ev upon the hydrogen, can we excite the hydrogen? <doos_> yes <diamond-clutter> yep <Spauwe> nope <Spauwe> we need 10.5 <BrianQ> no we cannot... how much energy do we need to excite the hydrogen? <Spauwe> wrong <Spauwe> 10.2 <doos_> 13.6.. gawd damned <Spauwe> no munching on the sly <diamond-clutter> ok <diamond-clutter> oops <BrianQ> Yes, we need 10.2 ev and only photons with exactly that will excite the hydrogen to n=2 <BrianQ> if it has a little more it just passes through, if it has a little less it just passes through <BrianQ> Now, let's consider another case... <BrianQ> Let's imagine we have hydrogen in the n = 2 state <BrianQ> How much energy is required to promote it to the n = 3 state? <Spauwe> pain level 6 <BrianQ> heh <Spauwe> frank? <Spauwe> ;) <doos_> -5EO/9? <BrianQ> Let's start... what is the energy of n = 2? <diamond-clutter> 10.2 <BrianQ> I don't think so... but we'll check <Spauwe> (i've got selevtive absorbtion going on when it comes to physics info) <BrianQ> in terms of E0, what is the energy of n = 2 (and 10.2 ev is wrong... that is the difference in energy between n = 1 and n = 2) <doos_> 13.6 ev <_Frank_> -2/.25 = 8 <_Frank_> sorry -8 <diamond-clutter> just a guess - I missed the first part of the talk <BrianQ> I'll be right back... got to carry in some groceries <Spauwe> righto <doos_> -EO/n^2
<doos_> so in 2 it is -EO/4 <doos_> and in 3 it is -EO/9 <_Frank_> yes <doos_> s0 -EO/5? <doos_> so* <_Frank_> why 5? <doos_> or ((-EO/4) / (-EO/9)) <Spauwe> no doesn't work that way <doos_> that is more logical (the latter) <Spauwe> gotta calculate values and then substract <doos_> or ((-EO/4) - (-EO/9)) <doos_> sorry <BrianQ> yes, getting there... E_2 = -E0/4 and E_3 = -E0/9 <BrianQ> So de = E_3 - E_2 = -E0/9 + E0/4 <doos_> plus? <Spauwe> yeah I was getting to pain level 7 as well <BrianQ> two negatives make a plus <doos_> yes <Spauwe> ok <doos_> oh right.. got it <doos_> it's increasing energy, so must be plis <doos_> plus <BrianQ> The result is 0.139*E0 = 0.139 * 13.6 ev = <BrianQ> 1.89 ev <BrianQ> (rounding up) <doos_> yea I got that too <BrianQ> Now... what does that energy correspond to in terms of wavelength? <doos_> very very very small <BrianQ> nope <diamond-clutter> Since it takes nearly as much energy to excite the hydrogen atom's electron from n = 1 to n = 3 as it does to ionize the hydrogen atom, the probability of the electron being excited to n = 3 without being removed from the atom is very small. Instead, after being ionized, the electron and proton recombine to form a new hydrogen atom. In the new atom, the electron may begin in any energy... <diamond-clutter>...level, and subsequently cascades to the ground state (n = 1), emitting photons with each transition. Approximately half the time, this cascade will include the n = 3 to n = 2 transition and the atom will emit H-alpha light. Therefore, the H-alpha line occurs where hydrogen is being ionized. <_Frank_> near IR or nearly visible <doos_> oh right.. <doos_> inversley prop. <BrianQ> Nope, in fact... the transition from n = 2 to n = 3 is the H-alpha line <BrianQ> and Frank is correct... <_Frank_> yes and remember your Ev numbers on the visible spectrum <BrianQ> it is visible <BrianQ> it is somewhere in the red... i forget exactly... ~ 650nm? <Spauwe> where do I find ev numbers on the spectrum?
<_Frank_> read the fluorescent vhats <diamond-clutter> I am going to quit guessing ;( not having much luck <Spauwe> ok <_Frank_> chats <BrianQ> mm... I just do the calculation because I have h (Planck's constant) and c (speed of light) memorized <BrianQ> and also I know the conversion from ev to Joules. <BrianQ> But there really should be a light scale that compares energies and wavelengths. <doos_> ev = 1240 / wavelength <BrianQ> That's ok diamond-clutter, just keep trying. <doos_> that is how I remember it <BrianQ> yeah, and that little shortcut too! <Spauwe> ok <BrianQ> saves much effort compared to what I was suggesting. <doos_> 1240 comes from Planck's constant and the speed of light <_Frank_> have you dyed your hair doos? <BrianQ> hey... and it comes out to be... 656 nm... I was pretty close with my guess <doos_> yes.. reddish now :) <BrianQ> heh <_Frank_> lol...only 6nm Brian...good shot <doos_> BrianQ.. <diamond-clutter> 656.281 nanometer <BrianQ> I said "around 650 " always leave space for error ;) <doos_> so from 1 to 2 it takes much more energy than going from 2 to 3 <BrianQ> yes indeed, Doos <BrianQ> And we know this, because we've seen the spacing... <doos_> yes true <BrianQ> energy spacing goes down as n increases <BrianQ> That's why I keep referring to that point <doos_> for hydrogen only.. correct? <BrianQ> mm... not exactly <BrianQ> we shall have to wait and see... <doos_> lol <BrianQ> Now... back to hydrogen in n = 2... what energy to promote it to n = 4... <BrianQ> You guys should be able to look through the log and work this out... and then figure what the wavelength is... <BrianQ> You know it takes more energy... <Spauwe> pain level 8 <doos_> E_2 - E_4 <BrianQ> and so you end up moving a little further into the visible, yes <BrianQ> and it occurs in the "cyan" range of color... somewhere below 500 nm. <BrianQ> So, this is practice for the homework exercise... see if you can figure out exactly what wavelength corresponds to the transition energy from n = 2 to n = 4 <BrianQ> Then the homework problem is this... <Spauwe> can it skip n = 3?
<BrianQ> Yes, it can. <Spauwe> ok <BrianQ> So the homework... <BrianQ> figure out what wavelength corresponds to the transition from n = 2 to n = 5 states. <doos_> heh <BrianQ> This one too should lie in the visible spectrum <doos_> wouldn't be to hard to do <Spauwe> ghe <BrianQ> good! <doos_> thanks to your good formulas <BrianQ> and yours! <doos_> gem-a's <Spauwe> cool, thanks Brian... gotta go have to clean up shop <DragonStek> thanks brian another great chat <diamond-clutter> l8r thnx <Spauwe> all the rest: have a good week, see you next weekend <BrianQ> Ok very good <Crystal> Thanks Brian! * diamond-clutter has quit IRC ("ChatZilla 0.9.82 [Firefox 2.0.0.14/0000000000]") <DragonStek> night tim * Spauwe has quit IRC ("Java user signed off") <Crystal> bye Tim <doos_> thanks BrianQ, we are getting closer and closer <DragonStek> hehe fun for you doos <BrianQ> We'll carry on from here next time ;) <Crystal> my brain's scrambled like eggs <BrianQ> ciao ciao <doos_> yes it is, although my mind was not set to it tonight <Crystal> g'night <DragonStek> night * BrianQ has quit IRC ("Java user signed off")