From: Ronald Wong (ronwong@inreach.com)
Date: Wed Jan 24 2001 - 17:27:51 PST
Message-Id: <l03102800b6945676e43a@[209.209.19.165]> Date: Wed, 24 Jan 2001 17:27:51 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: Re:...and Quantum Mechanics
Jennifer Paillet brought up the following:
>...
>2. I just today taught that Rutherford's model of the atom didn't explain
>what was keeping the electrons from collapsing in on the positive nucleus;...
By the end of the 19th century, a scientist by the name of J.J. Thompson
had determined that the atoms of matter possessed negatively charged
particles which we now call electrons. Since the atoms are electrically
neutral, there had to be positive charges associated with the atoms as well.
It was Rutherford who discovered that the positive charge was concentrated
in the heart of the atom. This left the electrons to fend for themselves
somewhere else in the atom.
Now the electrons weren't just sitting around inside the atom because,if
they were, the electrostatic force of attraction between them and the
positively charged nucleus would draw them into the heart of the atom and
reduce the charge of the nucleus to zero - which it isn't. So they must be
moving around in the atom.
But there is a problem with having the electrons moving around in the atom.
According to classical electromagnetic wave theory, this motion leads to
the emission of radiant energy. If a charged particle gives off radiant
energy, it comes at the expense of it's mechanical energy. This causes it
to speed up and, in the process, move into a position that places it closer
to the nucleus. Since this doesn't stop it's motion, it will continue to
radiate energy away and continue to move closer to the nucleus until
finally it falls into it. At that point the nucleus becomes electrically
neutral - something which Rutherford's discovery had shown not to be true.
In addition, the radiation given off as the electron spirals into the
nucleus would extend over a continuous range of frequencies in the
electromagnetic spectrum - according to classical theory. This was not
observed so apparently the electron was not spiraling into the nucleus.
----------------------------------------
>what does? (this probably involves quantum mechanics-yuk)
You're right, it's quantum theory.
As Neil said in his message, it comes in the form of Bohr's model for the
atoms of matter.
It's not so yukky in retrospect.
Bohr "simply" said that since the heart of the atoms are indeed positively
charged the electrons moving around the atom just don't spiral into the
nucleus as one might expect based on the electromagnetic wave theory. They
must be allowed to move in prescribed orbits without radiating energy away.
What determines these orbit is, in general, the angular momentum of the
orbiting electron (objects moving in a straight line have linear momentum
and objects moving around have angular momentum). In the case of the
simplest atom, hydrogen, he found that the prescribed angular momenta were
apparently integral multiples of Planck's constant divided by 2Pi. In other
words, the angular momentum is quantized. This leads to discrete orbits of
a pre-determined size for the electron.
At this early stage in the development of his model, Bohr could use his
model to determine the size of the smallest orbit and thus the size of an
atom of hydrogen. The value agreed quite well with the suspected size based
on the kinetic properties of hydrogen as a gas.
Normally, the electron of the hydrogen atom is in the lowest orbit. When
the gas is ionized (as in a discharge tube), the electron acquires energy
and moves away from the nucleus to a higher prescribed orbit. Since it's
normal state is in the smallest orbit, it tends to fall back down into this
orbit - sometimes cascading from one prescribed orbit to another in the
process. Since these are discreet steps, the energy radiated away in the
form of electromagnetic (EM) waves have discrete frequencies. If the
electron falls into the second-to-the-lowest energy level the frequencies
are in the visible region of the EM spectrum. Bohr calculated the
frequencies of the visible radiation using his model. He made the
delightful discovery that they corresponded to the known frequencies of the
visible light given off by hydrogen when it is excited.
Scientists were also aware of two sets of infrared line spectra given off
by hydrogen and his model produced values consistent with those
observations as well.
If you don't have gas discharge tubes of your own, call any high school and
ask their physics or chemistry teacher for theirs and the equipment needed
to produce the discharge. To see the line spectra, don't forget to ask for
a class set of diffraction gratings as well (or buy a set for your class -
they're cheap and you can use them for other purposes). Make sure you have
one containing hydrogen in the set. The spectrum for it as well as the
others was a great mystery in the 19th and early 20th century (why a series
of lines? and why THESE lines?). The continuous spectrum of the sun has
blank spaces where the lines of the hydrogen line spectrum should be -
another mystery (there's a great demonstration of this at the Exloratorium.
You can find it on the elevated exhibit area. Just pick a sunny day if you
are interested).
Bohr's model solved these mysteries with it's initial explanation for the
visible hydrogen lines.
(When my students were studying light, we would use the
diffraction gratings and the hydrogen discharge tubes to
determine the wavelengths/frequencies of the visible
spectrum of hydrogen. At the end of the semester, they had
enough of a background in electricity and magnetism to allow
them to understand the problem of Rutherford's model of the
atom and to derive the expression for determining the
wavelengths/frequencies of the hydrogen atom based on Bohr's
assumption that the orbits depended on the angular momentum
being quantzed. It was a lot of simple, algebraic hocus pokus
but, when they got to the final, "simple" expression and
plugged in the numbers 2, 3, then 4, and then 5 into the
expression, many of them were just as delighted as Bohr must
have been)
In addition, Bohr's model predicted that electrons falling into the lowest
level of the hydrogen atoms would give off EM waves in the ultraviolet
region and those falling into levels above the fourth level would give off
infrared radiation in the far IR. His model allowed him to predict the
frequencies of radiation that would be found in these areas of the EM
spectrum. When scientists looked to see if ionized hydrogen gas were indeed
giving off UV as well as far IR, they not only found them but they found
that they had line spectra similar to the visible radiation and that the
frequencies matched those predicted by Bohr based on his model.
----------------------------------------
If you feel a little adventuresome and have a little time on your hands (a
56K modem, DSL, or T1 connection is preferable to a 34K modem but any
connection will work), take a look at:
http://www.Colorado.EDU/physics/2000/quantumzone/bohr.html
(This is one of the topics covered at a website called
Physics 2000 from Univ. of Colorado at Boulder City,
http://www.Colorado.EDU/physics/2000/index.pl,
which "...relies heavily on the use of interactive "applets...
These are different from the typical animations you see on
the Internet because you can actually interact with them."
You might want to check out the site for your kids.)
Be brave and go to the "Extra for the Advanced Student" link on that page
to get some important information. The "Previous" button on that page will
bring you back to the original web page and you can continue on. Your kids
might find it interesting too. The trick is to stay on the main track the
first time through and avoid the temptation of clicking on every link you
come across. You'll be there forever if you do and, although you may learn
a lot in the process, you'll probably lose your way.
Enjoy! - ron
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