Physics PHOTOELECTRIC EFFECT

Photoelectric Effect :

The phenomenon of emission of electrons from the surfaces of certain substances (mainly metals) when irradiated with light of suitable frequency is called photoelectric effect. The emitted electrons are known as photoelectrons .
(The phenomenon of photo electric effect was discovered by hertz and later verified by the scientists such as J .J . Thomson, R. A. Millikan etc.)
The apparatus consists of two photo sensitive surfaces `A` and `B` enclosed in an evacuated quartz bulb. The plate `A` is connected to `-ve` terminal of the potential divider while plate `B` is connected to the positive terminal through a micro ammeter. In the absence of any light there is no now of current and hence there is no indication in the micro-ammeter, but when mono chromatic light is allowed to fall on the plate `A`, a current starts flowing in the circuit which is shown by the microammeter.

The significant features of this experiment are:

1 . No photo emission (the emission of electrons from a metal after it has absorbed light energy) is observed to occur below a critical cutoff frequency `n^TH` (and above the corresponding cutoff wavelength `I^(TH)`) of the incident light.

2. When a photo material is illuminated by a light with `n > n^(TH)` , the electron emission begins instantaneously without any observable time delay, even if the light intensity is very low.

3. For incident light with frequency `n > n^(TH)` the number of electrons liberated is directly proportional to the light intensity

4. For positive anode voltages, the electric field established in the tube effectively pulls all the liberated electrons to the positive terminal. If we increase the source potential difference `V` in the circuit of figure, no increase in the current occurs, because all the emitted electrons reach the anode. The current established in the circuit in this case is called saturation current.

5. If we reverse the polarity of the potential difference, the photo current decreases. The direction of electric field has reversed, it prevents some of the electrons from reaching the anode. Only the electrons with kinetic energy greater than `e(V)` can make it to the negative plate and contribute to the current. When this reversed electric field is large enough, no electrons are collected and the current is zero. This observation proves that the emitted charge is negative and has range of kinetic energies from essentially zero up to a maximum value `KE_(max)` .
At some voltage -`V_s` called stopping potential, no current will flow between the electrodes. The kinetic energy of electron is converted into electric potential energy as the electrons approach the negatively charged anode. At stopping potential the kinetic energy of even the fastest electron is completely converted into electric potential energy.

`KE_(max) = eV_s`

The observation that the photo current is proportional to the intensity of light is in accordance with the classical wave theory . In this theory the electric field of a light wave interacts with the electrons at the surface of the material and sets them into oscillation. The intensity of an oscillating electric field is proportional to the square of amplitude of the field vector, so the average kinetic energy of the emitted electrons is proportional to the intensity of light.

The problems with classical wave theory in explaining photoelectric effect:

1) The existence of a threshold frequency: According to wave theory, the photoelectric effect should occur for any frequency of light, provided only that the light is intense enough to supply the energy needed to eject the photo electrons. However experiments show that no photoelectron emission occurs below a certain threshold frequency.

2) The immediate emission of electrons: According to wave theory, there should be a sufficient time lag before any electron is emitted when we start to irradiate the metal. Since it would take up time for the electron to collect the diffused energy supplied by light ( in accordance with wave theory). But it is observed that there is immediate ejection of photoelectrons.

3) Maximum Kinetic energy of electrons is independent of light intensity: According to wave theory the energy supplied by light to the electrons should be proportional to the intensity of light and hence the `KE` of ejected electrons should also be dependent on the intensity. Experiments prove this to be false.

Certain graphs relating to the experiment :

(a) Photo current as function of the voltage applied for a given frequency n of light for three different light intensities.

(b) The photoelectric current I is shown as a function of applied voltage for three different light frequencies. The stopping potential ` V_s` is different for each `n` and is more negative for large `n` .

(c) For `n >n^(TH)` the photo current is proportional to the incident light intensity.

 
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