Particle and wave model understanding -- help please

[physics1999]

How does the photoelectric effect prove the wave-particle wrong? Higher intensity does not mean higher energy. If we were to assume the wave-particle model, an increase in intensity means an increase in the amplitude of the wave right? The energy of light is never dependent on amplitude, it is, however, dependent on the frequency/wavelength. So it makes sense that visible light is not ionizing radiation because the binding energy is higher than the energy visible light can offer. It also makes sense that ultraviolet light, x-rays, and gamma rays are ionizing radiation because they can provide energies equal to or greater than the binding energies of metals. Someone, please help I am so confused. I was looking at the youtube video and it just didn't make sense why the particle model described the photoelectric effect.

 

[Dale]

Higher intensity does not mean higher energy.

Intensity is the power transferred per unit area. So yes, if you keep the time and area the same then higher intensity does mean higher energy.

The energy of light is never dependent on amplitude, it is, however, dependent on the frequency/wavelength.

Classically none that is true. That is only true on a per-photon basis, but that concept had not been developed yet.

Someone, please help I am so confused. I was looking at the youtube video and it just didn't make sense why the particle model described the photoelectric effect.

I don’t know what to tell you. You seem to have some misconceptions about how classical EM works. You are stating things about photons that aren’t true about classical EM, and then of course you don’t see why these things were important discoveries.

 

[physics1999]

Intensity is the power transferred per unit area. So yes, if you keep the time and area the same then higher intensity does mean higher energy.

Classically none that is true. That is only true on a per-photon basis, but that concept had not been developed yet.

I don’t know what to tell you. You seem to have some misconceptions about how classical EM works. You are stating things about photons that aren’t true about classical EM, and then of course you don’t see why these things were important discoveries.

Okay, thank you for your answer. As you can tell, yes I am indeed VERY confused.

So you're saying that E = hv is only applied to photons (particle nature of light)? and there is another equation stating the energy of a wave as a function of intensity (power transferred per unit area)? Or...

When you mean classically, do you mean the wave nature of light?

 

[Dale]

So you're saying that E = hv is only applied to photons (particle nature of light)?

Yes, that is the energy for a single photon of frequency $\nu$

and there is another equation stating the energy of a wave as a function of intensity (power transferred per unit area)?

Yes, the classical energy flux density is given by the Poynting vector: $\vec S=\vec E \times \vec H$. This is proportional to the amplitude of both the electric and magnetic fields.

When you mean classically, do you mean the wave nature of light?

Yes, I mean light as described by Maxwell’s equations. These were observations that could not be explained by Maxwell’s equations. But at the same time, scientists had a lot of confidence in Maxwell’s equations because it predicted so much correctly.

 

[physics1999]

Yes, that is the energy for a single photon of frequency $\nu$

Yes, the classical energy flux density is given by the Poynting vector: $\vec S=\vec E \times \vec H$. This is proportional to the amplitude of both the electric and magnetic fields.

Yes, I mean light as described by Maxwell’s equations. These were observations that could not be explained by Maxwell’s equations. But at the same time, scientists had a lot of confidence in Maxwell’s equations because it predicted so much correctly.

Thank you so much, I will look into that.

 

[vanhees71]

First of all forget about everything they told you using the socalled "old quantum theory", describing the era between 1900-1925 where the first hints of what we call quantum phenomena today have been discovered. Unfortunately most popular-science books and even more embarassing also new introductory textbooks at the university level just start with ideas from this era in an attempt to tell the history of the development of modern quantum theory.

The problem with this historical approach is that the discovery of quantum phenomena starts with Planck's theoretical explanation on Dec. 14, 1900 of his just before found formula which describes the spectrum of thermal electromagnetic radiation, aka the black-body spectrum. Ironically Planck's careful description is not as bad as the popular-science picture based on Einstein's famous 1905 "heuristic aspects" paper about em. radiation. One should also know that Einstein was never satisfied with all the ideas about this problem till the end of his life, because of course he knew that "old quantum theory" is far from being a good physical theory but he also didn't like modern quantum (field) theory which is however the most successful physical theory ever discovered until today.

The modern understanding of electromagnetic radiation is that it is fundamentally a phenomenon best described by the field concept. Any attempt to think about it in terms of particles is flawed. You cannot even define an observable describing the position of the radiation as if it were a particle. So the field concept is the right starting point.

The field concept has been developed in the early 19th century by Faraday. The ingenious thought was to get rid of Newton's old description of interactions between (macroscopic) bodies at a distance. The macroscopic bodies around us of course can be described by classical physics and often they can be idealized to "point particles" if their extension doesn't play a significant role in the description of a pheonomen. E.g., to understand the motion of the planets around the Sun we can idealize them to point particles being attracted by the Sun due to the gravitational interaction, and Newton described it as an "action at a distance", i.e., he stated as a fundamental law of nature that two masses attract each other by a forces given by
$$\vec{F}_{12}=-\vec{F}_{21} = -G m_1 m_2 \frac{\vec{x}_1-\vec{x}_2}{|\vec{x}_1-\vec{x}_2|^3},$$
and if the bodies are moving against each other the force instantaneously adapts just to be precisely described by this expression. Newton himself already had some headaches about this, because it's hard to believe that there should be instantaneous influences over large "astrnomical distances". Nevertheless, Newton's theory describes the motion of the planets around the Sun very accurately, and so the issue was not that pressing to invent new concepts.

Now Faraday had the great idea give a more local explanation for the interaction, but he was mostly concerned with electromagnetic phenomena and so he was thinking mostly about the electric and magnetic forces between charged and magnetized bodies and electric currents etc. His idea was that due to the presence of electric charges and currents (being just moving electric charge) there is something around these charges and currents he called a field, which is extended through all space. So just having one charged body, his idea was that together with this charged body there was an electric field around it described by the already known Coulomb Law (valid if the charge is at rest for a very long time):
$$\vec{E}(\vec{x})=\frac{q_1}{4 \pi \epsilon_0} \frac{\vec{x}-\vec{x}_1}{|\vec{x}-\vec{x}_1|^3}.$$
This field, however, can only be detected by using another charge $q_2$ at a point $\vec{x}_2$, since due to the presence of the electric field at this (!) point there's a force acting on $q_2$ given by
$$\vec{F}=q_2 \vec{E}(\vec{x}_2),$$
i.e., now the force on $q_2$ is explained by a local concept: It's due to the presence of the electric field at the place $\vec{x}_2$ of the charge.

Similar if you have a permanent magnet or some moving charges (currents) these have a magnetic field around them, and there are magnetic forces on other moving charges due to the presence of the magnetic field at the very position of this charge. Having both an electric and a magnetic field leads to a force acting on a particle with charge $q$ located at $\vec{x}$ moving with a velocity $\vec{v}$ is given by
$$\vec{F}=q (\vec{E}[\vec{x})+\vec{v} \times \vec{B}(\vec{x})].$$

Now if everything is moving in general the electric and magnetic fields are also changing with time, and Maxwell took up both Faraday's qualitative concept of local field actions instead of action-at-a-distance forces a la Newton as well has his accurate quantitative results and came up with a comprehensive theory describing the electromagnetic field as a dynamical fundamental thing (and indeed there's no way to keep electric and magnetic fields separated; they have to be seen together to get a closed dynamical system). One of the most important conclusions of this theory was that changes in the motion of electric charges lead in the vacuum to electromagnetic waves with a finite propagation speed which numerically matched the then empirically known speed of light. This also implies that there the electromagnetic force between moving charges is not instantaneously acting at a distance but it takes a finite time for the electromagnetic field due to one charge to change at a (may be far distant place) of the other charge.

It also turned out that in order to have energy, momentum, and angular momentum to be conserved, given that the motion of one particle has no longer an instantaneous impact on another far distant particle, so that Newton's 3rd Law for the interaction between particles cannot hold anymore, one has to assume that the electromagnetic field itself carries energy, momentum, and angular momentum and it can exchange these quantities with the moving charged particles, but here this exchange of energy, momentum, and angular momentum is local, i.e., at the position of the charge and the corresponding changes travel as changes of the em. field with the speed of light.

Now finally we can look at Planck's black-body spectrum. It's just the radiation within a cavity with its walls being kept on some constant temperature for a long time. Now the cavity walls consist of charged particles and these are in thermal motion corresponding to the temperature the wall is kept and thus they radiate out em. waves, which are caught within the cavity. On the other hand these electromagnetic fields also lead to forces on the particles of the walls and thus the particles in the wall exchange energy with the electromagnetic field all the time. Keeping the temperature of the walls for a long time on constant temperature also the radiation comes to thermal equilibrium and its spectrum must be solely determined by this temperature. Thermal equilibrium means that per unit time the field transfers as much energy to the walls as the walls radiate off as radiation ("principle of detailed balance").

What Planck now figured out within about 10 years of struggle to find the spectrum of this thermal radiation, is that assuming the laws of classical electromagnetism (i.e., Maxwell's equations and Lorentz' force law for charged particles), which predicts that the walls and the field just exchange energy in arbitrary continuous amounts, leads to the impossible conclusion that the radiation in the cavity must have an infinite total energy.

Around 1900, however, he got very accurate data about this spectrum, and using a lot of his experience with thermodynamics he could guess a law describing it accurately, and it was different from all known laws considered before. The one based on classical electrodynamics, known as the Rayleigh-Jeans Law was good for the low-frequency part of the spectrum, another one based on an educated guess by Wien, worked fine for large frequencies. Planck then interpolated these IR and UV ends based on tricky thermodynamical ideas on the entropy of this radiation, and he needed a new fundamental constant of the dimension of an action, $h$, unknown to all classical physics known at the time.

Of course, as a theoretical physicist, Planck wanted to figure out what was behind his empirically found law, and the only way was to think in terms of statistical physics, which was also a pretty new subject at his days. Anyway, he applied the ideas of Boltzmann concerning the statistical physics of gases, assuming that gases consist of atoms or molecules (which was not an accepted hypothesis still in 1900 among physicists!). Planck's idea was to apply this idea to the exchange of energy between the em. field and the cavity walls. First to make his calculation easier he considered the radiation exchanging discrete portions of energy with the walls only. Of course, he thought, at the end he had to make these portions of energy arbitrarily small, finally describing the exchange of continuous amounts of energy between field and walls.

To his astonishment, however, all he had to do to get his radiation law was to assume that indeed the exchange of energy between field and walls has to be kept in discrete portions and that for each cavity mode of the field of frequency $\omega$ these portions must be $E_{\omega}=\hbar \omega$ (where $\hbar=h/(2 \pi)$ with $h$ is new action constant). Despite this enormous success, finding an entirely unknown law of nature and getting the Nobel prize for finding it in 1918, he never liked this conclusion and wanted to find a way out somehow describing the spectrum within classical physics.

The point, however, is that according to the new understanding about the must fundamental laws describing matter (as consisting of elementary particles) and radiation in terms of modern quantum theory, indeed radiation of frequency $\omega$ and matter only exchange energy in portions of size $\hbar \omega$. Einstein has drawn the conclusion that the em. field and the em. waves have some particle properties considering this discrete exchange of energy (and as followed a bit later also momentum and angular momentum) as if there where "light particles" exchanging energy with the particles making up matter in collisions (like the collisions of billard balls in our well-known macroscopic world). One should, however, note that at least for Plancks case of the thermal radiation in a cavity one doesn't need this "particle picture" of radiation. To the contrary, in a cavity one has well-defined "field modes", each representing a standing wave filling the entire cavity without any "point-like" properties but still exchanging only Planck's "energy quanta" of the size $\hbar \omega$. No particle-like aspects of radiation are necessary to get Planck's spectrum, the field picture works very well, however with the new "quantum rule" that energy exchange for each frequency of the field modes can only be in discrete portions of the size $\hbar \omega$.

With the new quantum theory (developed in 1925/26 by Born, Jordan, Heisenberg as well as Schrödinger and also Dirac in 3 different mathematical ways) applied to the electromagnetic field (the socalled quantum electrodynamics, first discovered by Jordan in 1926 and then again "rediscovered" independently by Dirac in 1927/28) this discreteness in the exchange of energy, momentum, and angular momentum follows from a consistent theory, which however is pretty abstract and leading to the conlusion that at the most elementary level the physical laws follow rules for random processes to be described by probabilities.

It's also interesting to note that the photoelectric effect also does not need any particle or even quantum descriptions of the electromagnetic field. It is sufficient to describe the light used to push out electrons from a metal's surface in terms of a classical electromagnetic field but the electrons within the metal by quantum theory. With this semiclassical theory you get precisely what Einstein predicted in terms of his "heuristic point of view" concerning "light particles".

Nevertheless that also the electromagnetic field has to be quantized is also very well established today. Already Plancks radiation law, when treated from the modern point of view of quantum kinetic theory, and as already discovered by a kinetic-theory argument by Einstein based on his old quantum theory inf 1917, needs the field quantization, because you need besides the absorption and induced emission of radiation by charged particles making up the matter, which both are understandable also assuming a classical electromagnetic field, also spontaneous emission, and this is only describable in terms of a quantum field.

Today there are of course many more experiments which demonstrate effects of field quantization, including the possibility to indeed operate with single photons, entangled photon pairs, etc.