# Photoelectric effect [doubt]

1. Jan 2, 2008

### rohanprabhu

For the photoelectric effec to take place for a certain metal, there is a minimum frequency that the incident radiation must have, also called the threshold frequency. Let us call it $f_o$.

The electron is emmitted only when a minimum amount of energy is provided to it so that it can repulse the intermolecular forces. This energy, called the 'Work function' is $\phi = f_o$ [where 'h' is the Planck's constant].

Now, if the minimum energy is not provided, the electron is not emitted. No matter how high the intensity of the incident radiation is, the electron won't be emitted unless the radiation has a frequency $f_o$.

But, if it is energy dependent, won't increasing the Intensity increase the energy too? Because,

$$I = \frac{dP}{dA}$$

Therefore, if a radiation has a higher intensity, won't it be having a higher value of Power? Which means that the energy supplied per unit time should also be higher. So, for a higher value of Intensity, the energy is more... So why doesn't it show the photoelectric effect unless and until the metal is irradiated with a radiation having a frequency of $f_o$

2. Jan 2, 2008

### malawi_glenn

the thing is that the energy must come in ONE shot, the electron cant "gather energy".

The energy of a photon is given by its frequency, so you must have a frequency above a certain threshould. The energy of the beam is not the interesting thing, it is the energy of a the individual photons.

3. Jan 2, 2008

### rohanprabhu

ok.. so do you mean to say that an electron is ejected only when it annihilates a photon with the threshold frequency?

4. Jan 2, 2008

### malawi_glenn

yes, that is correct. (or higher frequency)

5. Jan 2, 2008

### f95toli

It is preumably possible to eject a photon even when the frequency is lower than the "threshold" using a multi-photon process. Two photon processes -where each photon has half the energy- are quite common and are used in spectroscopy. 3 photon processes are rare and higher order processes are as far as I know almost negligle in natural atoms (but can be seen in spectroscopy on e.g. Rydberg atoms). However, there are artifical systems ("quantum well") where tens of photons can "add up" (I think the highest I have ever seen is 13), the probability for such processes increases quite a lot in strongly anharmonic potentials.

Also, the intensity of the radiation DOES matter if it is very high. The reason is simply that the radiation itself can perturb the potential in such a way that the position of the levels are shifted; it is therefore possible to "hit" the resonance simply by driving the system very hard. Due to "ladder" proccess with virtual levels it is therefore possible to excite systems even when starting far from resonance if the drive amplitude is high enough. Unfortunately, the physics is VERY complicated since these processes can't be treated using perturbation theory and AFAIK there is no "simple" theory.

6. Jan 2, 2008

### malawi_glenn

of course more elaborate discussions about the photo electric effect can be made, but this has not so much to do what the OP asked about. He doubted the very basics about the photo eletric effect.

7. Jan 2, 2008

### rohanprabhu

OP??

another question is.. If there is a photon having a frequency higher than $f_o$, but not high enough so that the electron can accept it all [afaik, an electron can accept only a set of particular amounts of energy].. so is this remaining energy rejected? If it is rejected.. does it result in the creation of a new photon of a frequency such that it's energy is the energy difference between the nearest quanta of energy the electron could accept and the one brought in by the incident photon?

8. Jan 2, 2008

### malawi_glenn

op = original poster.

if the photons energy is not not enough to remove the electron from the atom, it can do other things, for example excite an atom or heat the solid etc.

9. Jan 2, 2008

### ZapperZ

Staff Emeritus
This is not correct. If the photon energy is larger than the threshold, then the "extra" energy is the kinetic energy of the emitted electron. That is why you see a spectrum of energy for all the photoelectrons emitted.

Zz.

10. Jan 2, 2008

### malawi_glenn

"If there is a photon having a frequency higher than , but not high enough so that the electron can accept it all " Seems like a condradiction.

11. Jan 2, 2008

### rohanprabhu

forget about the photoelectric effect for a moment. What about the electrons jumping orbits? If it receives photons that can make it jump to the 2nd orbit + a little extra energy, but not enough to make it jump till the 3rd.. does it reject it completely or reject just a part of it?

my teacher told me that it rejects it completely.. though i'm a bit reluctant to agree to that?

12. Jan 2, 2008

### malawi_glenn

it rejects it when chaning orbits yes.

But imagine the photo electric effect as ionization, the ionization energy of H is 13.6eV, if a photon of E = 20eV enters, the electron will be emitted with 6.4eV kinetic energy. The excitation energy for n=1 to n=2 is 10.4eV, and if the incoming photon has energy 11eV, then it can not excite the electron to that orbit, it does not interact with the atom at all here.

13. Jan 2, 2008

### rohanprabhu

thx a lot man.. it helped me understand a lot today :D

/offtopic: are u on this forum all day long?? :P

14. Jan 2, 2008

### malawi_glenn

I have nothing elso to do man ;) Shall ask some questions here my self, so I want to contribute to this lovley forum by giving answers to something that I understand :P

15. Jan 2, 2008

### dst

How about a photon with 20.8eV of energy? Any difference?

16. Jan 2, 2008

### malawi_glenn

energy is still too high right?.. ;)