Photoelectric effect and the work function

[BlackWyvern]

Homework Statement

Let's just say some photons hit the anode in a photo-tube, and the light's frequency is the threshold frequency.
Will the electrons have momentum when they leave the electron?
Or will they simply leave the electron, only to come back because of the closer proximity anode's electric field?
Or, will the electron displacement get electrons from lower down in the anode, until the cathode is positively charged, and the electrons are attracted to it?

The Attempt at a Solution

I thought that it was the last option, where electrons from atoms lower down in the anode gave electrons to the higher-up part, and this continued until the cathode was positively charged? I also don't know if the electrons leave the atom with any momentum. I know that they have zero Ek relative to the nucleus, but does this mean that they don't have momentum and will just stop?

 

[anathema]

I would like to clarify some misconceptions and provide a more accurate explanation of what happens in a photo-tube.

Firstly, when photons hit the anode in a photo-tube, they transfer their energy to the electrons in the metal atoms of the anode. This energy is used to overcome the binding energy of the electrons and they are ejected from the atom. This process is known as the photoelectric effect.

The electrons that are ejected from the atom do indeed have momentum. This is because they were originally in motion within the atom and when they are ejected, they continue to move in the same direction with the same velocity. This is known as the conservation of momentum.

The electrons do not simply leave the anode and come back because of the electric field of the anode. Once they are ejected, they are free to move and are not affected by the electric field of the anode. However, they may be attracted to the positively charged cathode due to the electric field between the two electrodes.

The electron displacement that occurs in the anode does not involve electrons from lower down in the anode giving electrons to the higher-up part. Rather, it involves the movement of electrons within the metal atoms to fill the vacant energy levels left by the ejected electrons. This process continues until the cathode becomes positively charged and the electrons are attracted to it.

In summary, when photons hit the anode in a photo-tube, they eject electrons from the metal atoms which have momentum. These electrons are not affected by the electric field of the anode but may be attracted to the positively charged cathode. The displacement of electrons in the anode involves the movement of electrons within the metal atoms.

 

[ogb p]

I can provide some insights on the photoelectric effect and the work function. The photoelectric effect is a phenomenon where electrons are emitted from a material when it is exposed to electromagnetic radiation, typically in the form of light. This effect was first observed and studied by Albert Einstein, who explained it using the concept of photons and their energy.

The work function, on the other hand, is the minimum amount of energy required to remove an electron from the surface of a material. It is a characteristic property of the material and can vary depending on the type of material and its surface properties.

Now, to answer the question at hand, when photons hit the anode in a photo-tube with a frequency equal to the threshold frequency, the electrons in the material will absorb the energy of the photons and become excited. If the energy of the photons is greater than the work function of the material, the electrons will have enough energy to overcome the attractive forces of the atomic nucleus and leave the material as free electrons.

These free electrons will have a certain amount of kinetic energy and momentum, which is determined by the energy of the photons and the work function of the material. This momentum can be calculated using the formula p = h/λ, where p is the momentum, h is Planck's constant, and λ is the wavelength of the light.

As for the second part of the question, the electrons will not simply leave the material and come back due to the electric field of the anode. Once they have enough energy to overcome the work function, they will be emitted from the material and travel towards the anode. The electric field of the anode will then accelerate these electrons towards the cathode, where they will be collected.

In terms of the last option, where electrons from lower down in the anode give electrons to the higher-up part until the cathode is positively charged, this is not the case in the photoelectric effect. The emission of electrons is a one-to-one process, where one photon interacts with one electron in the material. The electrons that are emitted will not cause a positive charge on the cathode, as they will be immediately collected by it.

In conclusion, the electrons emitted in the photoelectric effect will have momentum and will not simply come back to the material. They will also not cause a positive charge on the cathode. Understanding the concepts of the photoelectric effect and the work function is crucial in explaining this phenomenon and its applications in various fields