# Photoelectric Effect with changing electric field

1. May 10, 2007

### liorda

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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 10, 2007

### variation

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