# Why does the fact that the max. KE of photoelectron increases with increasing frequency of light contradict with the classical theory

It is stated that the experimental result from photoelectric effect that

The max. Kinetic Energy of the photoelectrons after the emission from the surface depends upon the frequency of the incident light.The max. KE increases with increasing frequency.

First of all, what was the prediction of the classical electromagnetic theory ? And secondly, in exactly which point that this contradicted with that wave theory of light ?

I mean the energy transferred by a wave is proportional with its frequency square, so if we increase the frequency, it can deliver more energy per unit time. I must also ask that how does the classical theory expects electrons's to have a KE after the emission ? I mean after the emission will the electron still absorb light during its movement to anode according to the classical wave theory of light ?

In the classical case, the energy of the wave depends both on the frequency and the amplitude. Hence, a low frequency wave with sufficient amplitude can transfer enough energy to the electron to eject it (in the classical case).

Suppose you observed that you need 200 nm light or shorted to observe a photoelectron ($\hbar c \approx 200\, {\rm eV\cdot nm}$), so you go to the lab and use 300 nm light with 1.5 (15, or 15,000) times the power: no photoelectron, ever.

In the quantum case, the photoelectron is bound with 1 eV, and it can only absorb 1 photo, so it must be at least 1 eV to eject it with no energy-call the threshold $E_0$.

If you now use 100 nm light (2 eV) you observe a photoelectron with $T=1\,$eV. The interpretation is:

$$T_{max} = \hbar\omega - E_0$$

with absolutely no energy dependence on the intensity of the light. You can have blinding 300 nm light do nothing, but even the weakest possible 100 nm light can kick out an electron.

The interpretation is that at any frequency there is a minimum field excitation with energy $\hbar \omega$, and the electron can absorb 1 of them. That excitation is called a photon.

• This does not answer any of my questions. – onurcanbektas Feb 28 '18 at 3:05
• @onurcanbektas (1) In your question you ignore amplitude and energy, so I corrected that. (2) The classical theory predicts that the moment the electron accelerates it obtains infinite energy through self interaction, regardless of external field, so there's really nothing else to say about it. – JEB Feb 28 '18 at 3:10
• infinite energy ? it does not sound right, even for a second year physics student. – onurcanbektas Feb 28 '18 at 3:15
• By the way, the fact that you are giving this response on comments proves my point in the first comment :) – onurcanbektas Feb 28 '18 at 3:16

According to the classical theory, the electrons would gain their Kinetic Energy due to the electormagnetic field inside the light. Therefore, their KE should not be a function of the frequency of the light.