Does a hydrogen atom have d orbitals?
Dave
forget it once the course was over) here is my current understanding of
quantum mechanics:
1. Orbitals are mathematical description of the wave functions
(representing electrons).
2. These functions are based on the nucleus of the atom in questions (i.e..
nuclear charge, etc).
3. One can solve the Schrödinger equation for a number of wave functions
for a give nucleus.
Am I right to assume that you can take ANY nucleus and solve for the 1s, 2s,
2p, 3s, 3p, etc?
So, even though the orbital is empty, does a hydrogen atom have a d orbital?
Dave
Uncle Al
If you pumped in enough energy you could populate a hydrogen
d-orbital. Otherwise, it is virtual.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
Repeating Decimal
wrote on 3/20/03 2:50 PM:
It is not that difficult to right down Schrödinger's equation for a high Z
atom, expecially if you have a computer program to help you get all the
terms. Actually, it is not so easy when you take all the electron-electron
interactions into account. But many of the terms can be neglected. What is
difficult is solving the equation, even in its approximation.
It turns out that the Schrödinger equation for a hydrogen atom is just about
completely soluble using analytic methods with very little approximation. It
is the only atom for which it is possible.
It should be possible possible to excite the electron into a 3e orbital. I
would be surprised if there is not spectroscopic evidence for that. I am
just not up to date.
Bill
Joshua Halpern
More precisely (and you did a pretty good job of
being precise) the d orbitals are empty in a
ground state hydrogen atom. However, you can
populate them in many ways: electron collisions
in a discharge, absorption of two photons, a
Raman process, energetic collisions of neutral
hydrogen atoms, via cascading after recombination
of a proton and an electron etc.
josh halpern
Terry Wilder
"Dave" <nob...@nowhere.com> wrote in message
news:v7khdoi...@corp.supernews.com...
"spectrums" of allowable solutions.
where these discrete structures fail to have any meaning
(at n=4 I believe) This is one of the hallmarks of QM.
See Sommerfelds' book on Wave Mechanics.
Repeating Decimal
terry....@gte.net wrote on 3/21/03 2:42 AM:
> Not necessarily, above a certain energy you begin getting continuous
> "spectrums" of allowable solutions.
> where these discrete structures fail to have any meaning
> (at n=4 I believe) This is one of the hallmarks of QM.
> See Sommerfelds' book on Wave Mechanics.
These still have meaning. Look up Rydberg atoms and the Bohr correspondence
principle.
Bill
Terry Wilder
spectrum as well.
Look up Rydberg spectrum and Ionization energy.
"Repeating Decimal" <Salm...@attbi.com> wrote in message
news:BAA0B31E.46F4E%Salm...@attbi.com...
Josh Halpern
Repeating Decimal wrote: SNIP....
It is not that difficult to right down Schrödinger's equation for a high Z atom, expecially if you have a computer program to help you get all the terms. Actually, it is not so easy when you take all the electron-electron interactions into account. But many of the terms can be neglected. What is difficult is solving the equation, even in its approximation. It turns out that the Schrödinger equation for a hydrogen atom is just about completely soluble using analytic methods with very little approximation. It is the only atom for which it is possible. It should be possible possible to excite the electron into a 3e orbital. I would be surprised if there is not spectroscopic evidence for that. I am just not up to date.
Quibble 2: 3f orbitals don't exist. The solution requires that L < n so you
can only have a 1s not a 1p orbital, 2s and 2p not 2d orbitals and 3s, 3p, 3d
but not 3f orbitals.
For this I deserve to be flamed. What the hell.
josh halpern
Bill
Philip Frampton
>>for a high Z atom, expecially if you have a computer program
>>to help you get all the terms. Actually, it is not so easy
>>when you take all the electron-electron interactions into
>>account. But many of the terms can be neglected. What is
>>difficult is solving the equation, even in its approximation.
>>
>>It turns out that the Schrödinger equation for a hydrogen
>>atom is just about completely soluble using analytic methods
>>with very little approximation. It is the only atom for which
>>it is possible.
>>
>>It should be possible possible to excite the electron into a
>>3e orbital. I would be surprised if there is not spectroscopic
>>evidence for that. I am just not up to date.
>>
> Quibble 1: e orbitals don't exist. The nomenclature goes spdfgh.....
>
> Quibble 2: 3f orbitals don't exist. The solution requires that L < n
> so you
> can only have a 1s not a 1p orbital, 2s and 2p not 2d orbitals and 3s,
> 3p, 3d
> but not 3f orbitals.
>
More quibbles...
1. Orbitals don't exist! They are (a) approximations (b) a way of representing
electron density.
2. Schrodinger equation is poor, Dirac is better --> gives spin!
3. You cannot truly solve for more than 1 electron. The 'orbitals'
for used for elements with more than 1 electron are hydrogenic. You
can calculate solutions to arbitrary precision but not solve
them algebraically.
So...
Hydrogen does have all the 'orbitals' 1s, 2s, 2p, 3s, 3p, 3d, .... and infinitum
You can effect transistions to them and solve exact equations for the
energies.
For atoms/ions with more than one electron there are many fudges to predict
energies but these are poor. The reason that all QM based chemistry breaks
down is the use of the orbital approximation.
People will probably reply to this with picky points but as it's 3am, and I've
had a long day in the lab I'm not bothered!
Philip
--
Philip Frampton
Inorganic Chemistry Laboratory, Oxford University, Oxford.
e-mail:philip....@chem.ox.ac.uk
Repeating Decimal
It should be possible possible to excite the electron into aQuibble 1: e orbitals don't exist. The nomenclature goes spdfgh.....
3e orbital. I would be surprised if there is not spectroscopic
evidence for that. I am just not up to date.
You should have known that I meant a 3d orbital. :=)
Quibble 2: 3f orbitals don't exist. The solution requires that L < n so you
can only have a 1s not a 1p orbital, 2s and 2p not 2d orbitals and 3s, 3p, 3d
but not 3f orbitals.
Did I mention a 3f orbital? If I did, it should have been a 4f orbital.
High n hydrogen wave functions are highly degenerate for most observations.
Bill
Joshua Halpern
SNIP....
> More quibbles...
>
> 1. Orbitals don't exist! They are (a) approximations
> (b) a way of representing electron density.
>
> 2. Schrodinger equation is poor, Dirac is better
> --> gives spin!
and quantum electrondynamics gives the Lamb splitting.
OTOH, we do have the issue of effort vs. reward.
> 3. You cannot truly solve for more than 1 electron.
> The 'orbitals' for used for elements with more than
> 1 electron are hydrogenic. You can calculate solutions
> to arbitrary precision but not solve them
> algebraically.
>
> So...
>
> Hydrogen does have all the 'orbitals' 1s, 2s, 2p, 3s,
> 3p, 3d, .... and infinitum
> You can effect transistions to them and solve
> exact equations for the energies.
>
> For atoms/ions with more than one electron there
> are many fudges to predict energies but these are
> poor. The reason that all QM based chemistry breaks
> down is the use of the orbital approximation.
I'm not sure I would go so far. Accuracy is in
the eye of the user and usually traded off for
time and effort. I think this is an area where
the magisterial wave of the hand will not do for
a sensible discussion. One must actually state
the limits of measurement and calculation at
the highest levels, for individual atoms. Not
a trivial or easy task.
I would also say...we can observe the energy
levels of the various atoms as we can with
hydrogen and construct accurate energy level
diagrams. For each energy level we can
assign term symbols and the configurations based
on hydrogenic orbitals which are approximate
(although usually very good approximations).
> People will probably reply to this with picky points
> but as it's 3am, and I've
> had a long day in the lab I'm not bothered!
Know your audience
josh halpern
Joshua Halpern
> "Dave" <nob...@nowhere.com> wrote
SNIPO...
> Not necessarily, above a certain energy you
> begin getting continuous "spectrums" of
> allowable solutions. where these discrete
> structures fail to have any meaning (at n=4
> I believe) This is one of the hallmarks of QM.
> See Sommerfelds' book on Wave Mechanics.
Since I know of studies where states with n > 100
have been characterized (and in a discharge it is
pretty easy to see transitions to n = 8 or more
with a 1 nm resolution spectrometer) I think
you have to up the ante.
The continuum starts above the ionization limit,
although there are any number of complications
experimentally.
josh halpern
Terry Wilder
"Joshua Halpern" <jhal...@neteze.com> wrote in message
news:2551c44c.0303...@posting.google.com...
> "Terry Wilder" <terry....@gte.net> wrote
> > "Dave" <nob...@nowhere.com> wrote
> SNIPO...
>
> > Not necessarily, above a certain energy you
> > begin getting continuous "spectrums" of
> > allowable solutions. where these discrete
> > structures fail to have any meaning (at n=4
> > I believe) This is one of the hallmarks of QM.
> > See Sommerfelds' book on Wave Mechanics.
>
> Since I know of studies where states with n > 100
> have been characterized (and in a discharge it is
> pretty easy to see transitions to n = 8 or more
> with a 1 nm resolution spectrometer) I think
> you have to up the ante.
Yes but then error factors or quantum defects comes into play, hardly the
common notion of an Atomic Orbital
Also they are restricted to using "Rydberg like" etc etc
Someone corrected me as n=6 for hydrogen,
n=4 being the case for the restriction of two degrees of freedom
>
> The continuum starts above the ionization limit,
> although there are any number of complications
> experimentally.
Band Gap Engineers were once the highest paid.
>
> josh halpern
sch...@gefen.cc.biu.ac.il
: Dave wrote:
:>
:> Since I only learned what I needed to pass physical chemistry (and quickly
:> forget it once the course was over) here is my current understanding of
:> quantum mechanics:
:>
:> 1. Orbitals are mathematical description of the wave functions
:> (representing electrons).
:> 2. These functions are based on the nucleus of the atom in questions (i.e..
:> nuclear charge, etc).
:> for a give nucleus.
:>
:> Am I right to assume that you can take ANY nucleus and solve for the 1s, 2s,
:> 2p, 3s, 3p, etc?
: If you pumped in enough energy you could populate a hydrogen
: d-orbital. Otherwise, it is virtual.
More to the point, the orbitals are the angular part of the wavefunction
for a single-electron atom or ion (e.g. H). Once you have more than one
electron in your atom, the "orbitals" are actually just an approximation.
So not only does H have nd orbitals (n>2), H (and H-like) atoms are in
some sense the *only* atoms that have d orbitals.
-----
Richard Schultz sch...@mail.biu.ac.il
Department of Chemistry, Bar-Ilan University, Ramat-Gan, Israel
Opinions expressed are mine alone, and not those of Bar-Ilan University
-----
"Contrariwise," continued Tweedledee, "if it was so, it might be, and
if it were so, it would be; but as it isn't, it ain't. That's logic."