Re: What does Planck's constant really mean?
- From: franklinhu@xxxxxxxxx
- Date: 21 Jun 2005 00:12:36 -0700
Bjoern Feuerbacher wrote:
> franklinhu@xxxxxxxxx wrote:
> > Planck's constant is said to be the smallest amount of heat which can
> > be radiated at the vibration frequency v. (See.
> > http://www.hypertextbook.com/physics/modern/planck/)
>
> Can't you read? What the page *actually* says is that hv, i.e.
> Planck's constant *times the frequency*, is that "smallest amount of
> heat". (BTW, I would prefer using "energy" here instead of "heat").
>
>
> > This is in
> > accordance with the formula Energy = (any integer value representing
> > number of photons) X (Planck's constant 6.63 X 10^-34 J*s) X (frequency
> > in cycles/second).
>
> And where exactly did you get this formula from?
General Chemistry 3rd Edition Ebbing, pg.244. The other term besides hv
(n) is just a multiplier of the energy of a single photon which would
be hv.
>
>
> > My question is whether this also means that this is also the smallest
> > amount of energy difference between any frequencices.
>
> What is "energy difference between frequencies" supposed to mean?
>
You can calculate the energy of a single photon = hv. If you take 2
different frequencies, you should be able to calculate the difference
in energy between the frequencies.
>
>
> > In other words,
> > the amount of energy has to be some whole number multiple of 6.63 X
> > 10-34.
>
> If you didn't notice: in physics, quantities have *units*. h isn't
> simply 6.63 x 10^-34. It is 6.63 x 10^-34 Js (Joule times seconds)!
>
> Since energy is measured in J, not in Js, the answer to your question
> should be obvious...
>
So you have to multiply Planck's constant by a frequency which gives
you only the energy term. The reason why 1 hz is special is that this
makes the value of Planck's constant expressible directly in Joules.
>
> > The formula does not place any quantization limits on
> > frequencies, so an infinity of frequencies is allowed.
>
> Indeed. As long we talk about free particles...
>
>
> > This would also
> > imply that an infinity of energy amounts would also be allowed. But
> > this would seem to be in contradition with the whole idea that energy
> > only come in quantized packets.
>
> No, that is in no way in contradiction with that idea. Why do you
> think so? Perhaps you should educate yourself a bit on what is meant
> when one says that energy comes in "quantized packets"...
>
Perhaps there is no contradition, that is the heart of my question. I
had difficulty seeing how Planck had to invoke quantatization of energy
in solving the ultraviolet catastrophe. I still don't see how quanta
solved the problem. It just appeared that the probability of a black
body emitting a high frequency photon was reduced since it had to
absorb this same amount of energy in order to radiate. This statement
doesn't seem to have anything to do with quanta and would seemingly
apply to continuous energy spectra. Perhaps you can shed some light on
this.
According to the web site I had cited previously:
"Moreover, it is necessary to interpret UN [the total energy of a
blackbody radiator] not as a continuous, infinitely divisible quantity,
but as a discrete quantity composed of an integral number of finite
equal parts."
The contradition I am questioning is the infinity of energy states
versus the statement that the energy is a descrete quantity.
>
> > It would seem that one possible solution is that frequencies would also
> > have to be quantisized, meaning that only certain frequencies would be
> > allowed
>
> For bound systems, yes. For free, no.
>
>
> > and if you were to closely examine a spectra which
> > theoretically contained all possible frequencies, you would actually
> > see frequency bands corresponding to energy spacings equal to Planck's
> > constant.
>
> "energy spacings equal to Planck's constant" makes no sense. Again,
> see my comment about units above.
It does make sense if you multiply by 1Hz which does reduce to an
energy term which could be used to make energy spacings.
>
>
> > For example, if we simply the formula by using 1 as the integer amount
> > in the formula (energy of a single photon) and assume that the
> > frequency is 1 cycle/second,
>
> Why don't you say "1 Hz", like everyone? And why do you use that
> frequency? What's so special about it?
Ok, I'll use Hz. I have already explained why 1hz is special. It allows
you to use Planck's constant as if it were a unit of energy.
>
>
> > It appears that the seconds terms cancel
> > out leaving just Joules which is a measure of energy of 6.63 X 10-34
> > Joules.
>
> BFD!
No big deal here, just showing how the formula e=hv works out to just
Joules and that the Joules X second term dissappears.
>
>
> > Now the question is, can I modify the frequency to produce any
> > arbitrary amount of energy like 6.64 X 10-34 J,
>
> YES!
>
>
> > or would I have to
> > modify the frequency enough to produce another Planck constant worth of
> > energy or 13.38 X 10-34 Joules?
>
> NO!
>
> Why on earth do you even call 6.63 x 10^-34 J "a Planck constant wort
> of energy"???
>
Ok, thank you for the very clear response. Now please explain how this
infinity of energies fits with Planck's explanation of the spectrum as
integral number of finite equal parts. If any energy is allowed, how
could anything be equal? That is why it seemed sensible that 6.63 X
10^34 J of energy could be what the "equal parts" are made up of. This
appears to be a tiny amount of energy, but since a Joule is the energy
of 1 newton over 1 meter and a newton is the force required to
accelerate 1Kg to 1 meter/second, roughly speaking, this is the amount
of energy required to accelerate 6.63 X 10-34 kg of mass to 1
meter/second. Considering the mass of an electron is 9.1X10-28g, this
is enough energy to accelerate 1,374 electrons to 1 meter/second, which
doesn't appear to be very little at all.
>
>
> > If frequency can only come in particular quanta, some rough
> > calculations show that the frequency would have to differ somewhere in
> > the magnitude of 1 X 10-21 meters for such a small jump to occur.
>
> Huh? What has the units meters to do with frequency? You apparently
> mean the wavelength?
Sorry, yes I mean wavelength
>
> Could you show that calculation, please?
I can only estimate because I'd need a calculator with nearly 36
signficant digits. So I start with a specific example.
Energy of single photon at 672nm =2.95x10-19 J
The question is, what is the change in wavelength such that the energy
= 2.95x10-19 J + 6.63X10-34J. By doing some sample calculations, I find
that each signficant decimal digit affects the energy difference by an
order of magnitude, so at 671.1nm, this creates a difference of
4.42x10-23, 671.01nm creates a difference of 4.41x10-24 and so forth.
By walking this logic back, it appears that 1 X 10-21 (21 digits behind
the decimal point) creates an energy difference in the magnitude of
1X10-34 J.
>
>
> > This
> > would also imply that this would correspond to the maximum frequency
> > possible (based on the smallest possible weavelength of 1X10-21m) or
> > about 3 X 10^29 cycles/second. It might also imply that this is the
> > smallest possible unit of distance in the universe, since nothing can
> > seem to act at smaller distances that this. Going even further into
> > speculation, this could mean that space itself is quantized in 1 X
> > 10-21 m cubes and explains why we see quantized amounts of energy &
> > frequency and why we see Planck's constant. (Lots of speculation, but
> > an interesting idea, I think).
>
> Sorry, I don't see how your space quantization idea leads to the known
> formula E=hv.
You'd have to work your way back from the assumption that 6.63X10-34 J
is the absolute minimum quanta of energy. Then E=nhv is trivial since E
is always going to be some multiple of 6.63X1-34 J which happens to be
Planck's constant. Of course, none of this makes sense if E is allowed
to take on arbitrary values
>
>
> > There is some experimental evidence from the dropping of neutrons in a
> > gravitational field that would suggest that the neutrons cannot take
> > arbitrary positions in space, but must drop in specific quanta,
> > indicating that space is quantized.
> > (See:http://www.users.csbsju.edu/~frioux/neutron/neutron.htm)
>
> That has *nothing* to do with space quantization!!! These are simply
> the energy eigenstates of the neutrons in this bound state!!!
There is a lot of technical information to weed through, so perhaps
this abstract makes it clearer:
http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v415/n6869/abs/415297a_fs.html&dynoptions=doi1074722794
"the falling neutrons do not move continuously along the vertical
direction, but rather jump from one height to another"
While this is meant to show that neutrons can only take up fixed
positions in space, like electrons can only take up fixed positions
around a nucleus, the raw data shows stair step like quantization in
the movement of the neutrons. Now it could be that this disappears if
you remove the neutron from the gravitational field, but maybe it
doesn't. All we know is that it does appear to take discrete steps on
it's way down.
>
>
> > So this is not a wild idea.
>
> It is. Could you please get a basic education before talking about
> topics you understand only superficially?
>
>
> Bye,
> Bjoern
>
> > fhuplanck
> >
.
- Follow-Ups:
- Re: What does Planck's constant really mean?
- From: Bjoern Feuerbacher
- Re: What does Planck's constant really mean?
- References:
- What does Planck's constant really mean?
- From: franklinhu
- Re: What does Planck's constant really mean?
- From: Bjoern Feuerbacher
- What does Planck's constant really mean?
- Prev by Date: Re: Sunset at Old Man's Place
- Next by Date: Re: Best water wicking material?
- Previous by thread: Re: What does Planck's constant really mean?
- Next by thread: Re: What does Planck's constant really mean?
- Index(es):
Relevant Pages
|
