Re: photoelectric effect (clarifications)

[John Denker <jsd@MONMOUTH.COM>]

Whenever I get a question that cannot be answered,
  1) On the first pass I try to avoid criticizing the question.  I try to
suggest ways the question could be rephrased to get a better result.
  2) If somebody really insists, I will explain why the original question
doesn't make sense.


At 04:05 PM 11/5/00 +0200, Savinainen Antti wrote:
> The question was: which version is consistent with the 19th century physics?
>
> Of course these versions cannot be experimentally tested because both are
> wrong.

Exactly!  Both are wrong.

> This was already known in 1902 when Lenard found that the kinetic energy
> of the electron emitted from an illuminated metal was independent of the
> intensity of the particular incident monochromatic light. Einstein's
> photon theory (1905) gave the explanation which was consistent with the
> experimental results.

If that is the question, then you have fully answered your own
question.  Both versions are wrong and nothing further need be said.

But if you want me to say more, I can make my position more
explicit:  Mother Nature has remained unchanged since the 19th century (and
long before that :-).  It is only our _understanding_ of the laws of nature
that has changed.

There is no universe that is fully described by the 19th-century
understanding.  There is absolutely no point in pretending that such a
universe exists.

To say the same thing yet again:  occasionally I hear somebody say "suppose
we take the true laws of physics and set hbar to zero, what happens
then?"  Well, then everything is broken:
  -- we have no photons
  -- we have no atoms and no metals
  -- we have no photoelectrons, and
  -- we have no physicists to worry about it.

==============

Returning now to constructive suggestions for rephrasing the question:  The
19th-century "laws" provide a reasonable description of the real universe
in certain limiting cases.

A) If you ask about a hydrogen atom in its ground state (L=0) then that's
not one of the cases where the 19th-century ideas are applicable.  End of
discussion.

B) If you ask about a hydrogen atom that starts out in a much higher state
(L>99,000,000) and meet certain other requirements, then the photoemission
process is relatively well described by the 19th-century ideas.  Such atoms
have been studied;  in the literature they are referred to as "Rydberg
atoms".  The situation is analogous to a marble in a 1/r dish, or to a
planet in the sun's 1/r potential.

In such a situation, the quantum states are so numerous and so close
together that you can average over them, whereupon the classical results
emerge.  They emerge not _instead_ of the true laws, but rather as a
_consequence_ of the true laws.

> My main concern was the intensity and its relation with the (maximum)
> kinetic energy.

Suppose we have a particle in a bound elliptical orbit.  Every time it
comes by we give it a small push.  It goes into higher and higher energy
states.  Eventually it will become unbound.  The energy with which it
departs cannot exceed the change in energy during the last push.  Therefore
the intensity (of the push) is relevant to the kinetic energy of the
departing particle.

> The second version states that the intensity doesn't affect the KE because
> the electrons are released immediately after they have gained enough
> energy from the interaction with the incoming light; the KE is very low no
> matter what the intensity is.

I suppose it is a true statement that the particle is unbound as soon as it
has picked up enough energy;  we probably want to take that as the
definition of "unbound".  If you stop pushing just at that moment, then all
particles depart with infinitesimal energy.  OTOH in the real world it is
quite likely that the push comes from an interaction that continues for a
while after the particle has enough energy to be unbound;  therefore the
particles will depart with a little extra energy in ways that depend on
intensity (and on various messy details).

On the third hand, if "the classical limit" includes passing to the limit
of a very large number of very small pushes, then infinitesimal unbinding
is the right answer.  I warned you that "the classical limit" is not
uniquely defined.


Note that for a 1/r potential we cannot take "leaving the vicinity" as a
definition of unbound;  we can have bound particles that go arbitrarily far
away and then return.

C) If you are not interested in Rydberg atoms, and have in mind some other
scenario in which 19th-century ideas describe (to a reasonable
approximation) the real universe, please describe your scenario more fully.