Excited states of the hydrogen atom

Mike Fontenot

I understand that the electron of a hydogen atom can be
excited to an energy state higher than the ground state
if it absorbs the energy of an appropriate photon. But
can the electron be put into a higher state by other means?
In particular, suppose I have a large number of hydrogen molecules
(as a gas) confined to a box impermeable to radiation. Suppose
all of the hydogen atoms were originally in the ground state,
and that the box has been emersed in a constant-temperature
bath for such a long time that it has reached equilibrium.
Are all of the electrons still in the ground state, or have
some been excited to a higher level, purely by thermal
collisions between the molecules?

Mike Fontenot

Ray Tomes

Mike Fontenot wrote:

> I understand that the electron of a hydogen atom can be
> excited to an energy state higher than the ground state
> if it absorbs the energy of an appropriate photon. But
> can the electron be put into a higher state by other means?
> In particular, suppose I have a large number of hydrogen molecules
> (as a gas) confined to a box impermeable to radiation. Suppose
> all of the hydogen atoms were originally in the ground state,
> and that the box has been emersed in a constant-temperature
> bath for such a long time that it has reached equilibrium. ...

There is no such thing as impermeable to radiation. At any temperature
there is a certain amount of thermal radiation and it cannot be eliminated.

--
Ray Tomes
http://ray.tomes.biz/
http://www.cyclesresearchinstitute.org/

ebunn@lfa221051.richmond.edu

In article <43E7CD58.1CA4E0A8@comcast.net>,
Mike Fontenot <mlfasf@comcast.net> wrote:

>I understand that the electron of a hydogen atom can be
>excited to an energy state higher than the ground state
>if it absorbs the energy of an appropriate photon. But
>can the electron be put into a higher state by other means?
>In particular, suppose I have a large number of hydrogen molecules
>(as a gas) confined to a box impermeable to radiation. Suppose
>all of the hydogen atoms were originally in the ground state,
>and that the box has been emersed in a constant-temperature
>bath for such a long time that it has reached equilibrium.
>Are all of the electrons still in the ground state, or have
>some been excited to a higher level, purely by thermal
>collisions between the molecules?

Yes the atoms will be excited by collisions. This is known as
"collisional excitation" (unfortunately for those who would have
preferred something more interesting, like "horrendous space
kablooie").

-Ted
--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

Igor Khavkine

Mike Fontenot wrote:
> I understand that the electron of a hydogen atom can be
> excited to an energy state higher than the ground state
> if it absorbs the energy of an appropriate photon. But
> can the electron be put into a higher state by other means?
> In particular, suppose I have a large number of hydrogen molecules
> (as a gas) confined to a box impermeable to radiation. Suppose
> all of the hydogen atoms were originally in the ground state,
> and that the box has been emersed in a constant-temperature
> bath for such a long time that it has reached equilibrium.
> Are all of the electrons still in the ground state, or have
> some been excited to a higher level, purely by thermal
> collisions between the molecules?

The short answer is: some will be excited into higher energy levels
through collisions.

Here's a longer version. First, you have to realize that it is
impossible to exclude radiation, even from an insulated box (as you've
proposed). One reason is simply that there is no fundamental difference
between radiation or electrostatic or magnetostatic fields. They are
all states of the electromagnetic (EM) field. Since the interactions
between atoms (including collisions) are largely electromagnetic in
nature, the atoms will excite the EM field in many different ways,
including producing radiation. You may also be interested in one of my
recent posts about radiation and thermal equilibrium:

news:1138663836.929864.115300@z14g2000cwz.googlegroups.com
http://groups.google.com/group/sci.p...07864b87820717

Second, even if you idealize the situation to the point where the gas
is modeled by atoms that only interact through inter-particle
potentials and do not produce radiation, collisions will still excite
the internal states of each molecule to higher energy levels. Each
internal (bound) state of a Hydrogen atom represents a certain
configuration for the relative motion of the electron and the proton.
If you model collisions between individual atoms in such a way that the
electron and the proton collide independently, then it's easy to see
that in a generic collision the relative motions of the electron and
the proton will be altered, hence exciting the internal state of each
molecule to higher energy levels.

Finally, a note about the importance of collisional excitations in
gases. This possibility is what makes possible the construction of
He-Ne (Helium-Neon) lasers (like the kind you find in laser pointers).
In such a laser, Helium atoms are constantly pumped into a certain
excited state. Through interatomic collisions, Neon atoms get excited
as well, and then are stimulated into emitting photons at the frequency
to which the laser is tuned. An illustration and a more detailed
explanation can be found on the HyperPhysics website:

http://hyperphysics.phy-astr.gsu.edu...od/lasgas.html

Hope this helps.

Igor

Mike Fontenot

Ray Tomes wrote:
>
> Mike Fontenot wrote:
>
> [...] suppose I have a large number of hydrogen molecules
> > (as a gas) confined to a box impermeable to radiation. . ...
>
(Ray's response):
> There is no such thing as impermeable to radiation. At any temperature
> there is a certain amount of thermal radiation and it cannot be eliminated.

I meant that the box prevents any radiation entering from outside
the box. Did you mean that it's impossible to have thermal
conduction of energy into the box (from the constant-temperature
bath surrounding the box) if no radiation is permitted to enter
the box?

Mike Fontenot

Mike Fontenot

ebunn@lfa221051.richmond.edu wrote:
>
> In article <43E7CD58.1CA4E0A8@comcast.net>,
> Mike Fontenot <mlfasf@comcast.net> wrote:
>
> >Are all of the electrons still in the ground state, or have
> >some been excited to a higher level, purely by thermal
> >collisions between the molecules?
>
(Ted's response):
> Yes the atoms will be excited by collisions.

So presumably, for any specified temperature of the bath, it
should be possible to calculate the proportion of the atoms
that are in each state (or at least, the proportion that
are in each energy level). And I suppose that, if radiation
WERE allowed to enter the box from the outside, then those
proportions would change.

Mike

Mike Fontenot

Igor Khavkine wrote:
> The short answer is: some will be excited into higher energy levels
> through collisions.

OK, so given a specified temperature of the bath, the proportion of
hydrogen atoms that are in each energy level will be determined (at
equilibrium). And I suspect that this distribution will be
different for different assumptions about the nature of the
radiation barrier that the box is providing. I.e., I can prevent
any external radiation from entering the box by either arranging
for the box walls to absorb all incoming radiation, or else
to reflect all incoming radiation. And presumably these two
cases would likewise cause any radiation emitted inside the box
to be either absorbed when striking the walls, or else be
reflected when striking the walls.

> Here's a longer version. First, you have to realize that it is
> impossible to exclude radiation, even from an insulated box [...]

I was just excluding any external radiation from entering the
box, and thereby exciting the hydrogen inside...I wanted any
possible excitation of the electrons to be purely due to the
molecular collisions of the hydrogen (in turn due to thermal
conduction of heat into the box).

Mike Fontenot

Blackbird

Mike Fontenot wrote:
[...]
> I meant that the box prevents any radiation entering from outside
> the box. Did you mean that it's impossible to have thermal
> conduction of energy into the box (from the constant-temperature
> bath surrounding the box) if no radiation is permitted to enter
> the box?

The point is that the box itself will emit radiation, as long as it has a
temperature.

But to your original question; yes, electrons can be excited by other means
than absorbing radiation. Your average light bulb is an example of that;
turn on the current and the wolfram emits far more radiation than it ever
absorbed.

Blackbird

Igor Khavkine

Mike Fontenot wrote:
> Igor Khavkine wrote:
> > The short answer is: some will be excited into higher energy levels
> > through collisions.
>
> OK, so given a specified temperature of the bath, the proportion of
> hydrogen atoms that are in each energy level will be determined (at
> equilibrium). And I suspect that this distribution will be
> different for different assumptions about the nature of the
> radiation barrier that the box is providing.

No, that has little to do with the equilibrium distribution of the
atomic states. As long as the entire box is kept in a thermal bath, the
distribution of the atoms among the energy states is of the Gibbs form:
exp(-E/kT), where E is the energy difference between the excited and
ground states of an atom. That's the beauty of being in equilibrium.

Igor