Photoelectric Effect with changing electric field

In summary, the conversation discussed finding the maximum momentum of electrons emitted from the surface of Li metal under the projection of EM radiation. The electric component of the radiation is a function of time and the maximum momentum is reached when the energy of the radiation is at its maximum. The conversation also discussed the use of Einstein's theory and the concept of light as photon. It was concluded that the highest frequency of the electric field corresponds to the most energetic photon, leading to the maximum momentum of the photo-electron.
  • #1
liorda
28
0
The Question:
Find the maximum momentum of the electrons emitted from the surface of the Li metal, under the projection of the metal with EM radiation, when the electric component of the radiation is a function of time: E(t) = a(1+cos[w*t])*cos[w0*t]

a= 18 [V/m]
w= 6E14 [1/sec]
w0= 3.6E15 [1/sec]
Phi[Li]= 2.39 [eV]

My Problem:
I know the photoelectric effect is E= U - Phi.
The emitted electrons' momentum is (p^2)/2m = E, Hence: p = Sqrt[2m*U-Phi], where U is the energy of the radiation.

I believe the maximum p will be reached when U is in its maximum.
I have used vector Poynting on an EM field and found that U=(c/4pi)*E^2.

I can't find where U is in its maximum.

Does my way of solution correct? How to find the maximum value of U?

Thanks.
 
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  • #2
Hi, I think you have chosen the Einstein's theory but you do not take the light as photon. Try this:
[tex]E=a(1+\cos\omega t)\cos\omega_0t=a(\cos\omega_0t+\cos\omega t\cos\omega_0t)
=a\left[\cos\omega_0t+\frac{1}{2}\cos(\omega_0+\omega)t+\frac{1}{2}\cos(\omega_0-\omega)t\right][/tex]
,which means there are three kinds frequencies in the incident light.
The maximum momentum photo-electron comes from the highest frequency photon.

Hope it helpful.
 
Last edited:
  • #3
I got it. The heightest frequency of the electric field is the frequency of the most energetic photon.

Thank you.
 

1. What is the photoelectric effect?

The photoelectric effect is a phenomenon in which electrons are emitted from a material when it is exposed to light. This effect was first observed by Heinrich Hertz in 1887 and later explained by Albert Einstein in 1905.

2. How does the electric field affect the photoelectric effect?

The electric field affects the photoelectric effect by providing the necessary energy to the electrons for them to be emitted from the material. When an electric field is applied to a material, it creates a potential difference that can accelerate the electrons and increase their kinetic energy.

3. How does the intensity of the light affect the photoelectric effect?

The intensity of the light affects the photoelectric effect by determining the number of electrons that are emitted from the material. An increase in light intensity leads to a greater number of photons hitting the material, resulting in a larger number of electrons being emitted.

4. What is the work function in relation to the photoelectric effect?

The work function is the minimum amount of energy needed for an electron to escape from the surface of a material. It is a characteristic property of the material and determines the threshold frequency of light needed to cause the photoelectric effect.

5. How does the photoelectric effect support the particle nature of light?

The photoelectric effect supports the particle nature of light by demonstrating that light is made up of individual particles, called photons. These photons transfer their energy to the electrons in the material, causing them to be emitted. This is in line with Einstein's explanation of the photoelectric effect using his theory of light as discrete packets of energy.

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