Photoelectric effect theory (why does this text imply distribution of energies?)

[s3a]

Homework Statement

Problem:
Consider the experimental results of the photoelectric effect described in Sec. 1.1, i–iv. For each result discuss whether it would be expected on the basis of the classical properties of electromagnetic waves.

Sec. 1.1(iii):
For constant frequency and irradiance, the photocurrent decreases with the increase of the retarding potential V, and finally reaches zero when V = –VS.

Answer:
The result described in Sec. 1.1, iii shows that there is a distribution in the energies of the emitted electrons. The distribution in itself can, within the framework of the classical theory, be attributed to the varying degrees of binding of electrons to metal, or to the varying amount of energy transferred from the beam to the electrons. But the fact that there exsits a well-defined stopping potential independent of irradiance indicates that the maximum energy of released electrons does not depend on the amount of energy reaching the surface per unit time. Classical theory is unable to account for this.

Homework Equations

Photoelectric effect theory.

The Attempt at a Solution

I read the solution and while I understand most of it, I don't understand how what Sec 1.1(iii) says implies that there is a distribution in the energies of the emitted electrons. By looking at a schematic drawing of the apparatus for studying the photoelectric effect (from my book), it makes sense (assuming I am correct) that the radiant energy would bring a varying amount of energy based on distance differences from the source but I still can't see that from the text in Sec 1.1(iii).

If I have not given enough information, just ask me to.

Any help in understanding this would be greatly appreciated!
Thanks in advance!

 

[anathema]

Dear forum post author,

Thank you for your question. I can understand your confusion regarding the distribution of energies of the emitted electrons mentioned in Sec 1.1(iii). Let me try to explain it in simpler terms.

In the photoelectric effect, photons (packets of light energy) are incident on a metal surface, causing the emission of electrons. According to the classical theory of electromagnetic waves, the energy of a wave is proportional to its amplitude (or intensity). Therefore, one would expect that increasing the intensity of the incident light would increase the energy of the emitted electrons.

However, the experimental result described in Sec 1.1(iii) shows that this is not the case. Even when the intensity of the incident light is kept constant, the photocurrent (number of emitted electrons per unit time) decreases with increasing retarding potential. This means that the maximum energy of the emitted electrons (also known as the stopping potential) does not depend on the amount of energy reaching the surface per unit time.

This is where the concept of a distribution of energies comes in. The varying degrees of binding of electrons to the metal surface can explain why different electrons have different energies. But the fact that there is a well-defined stopping potential (independent of intensity) implies that there is also a maximum energy that the electrons can have. This maximum energy would be the same for all electrons, regardless of their initial binding energies.

I hope this helps to clarify the concept of a distribution of energies in the photoelectric effect. Please let me know if you have any further questions or if anything is still unclear. Keep up the good work in your studies!