EXPERIMENTAL STUDY OF PHOTOELECTRIC EFFECT -

The following fig depicts a schematic view of the arrangement used for the experimental study of the photoelectric effect.

Two metal plates C and A are sealed in a vacuum chamber. The light is falling on the plate C which is called the cathode or emitter. The electrons are emitted by C and collect by plate A called the anode or collector.

The potential difference between the cathode and the anode can be changed with the help of batteries and rheostat. The polarity of the plates C and A can be reversed by a commutator.

Light of different frequencies can be used by putting appropriate colored filters or colored glass in the path of light falling on the emitter.

(a) Effect of Intensity of light on the photoelectric current:-

Here the anode A is maintained at +ve potential w.r.t cathode C. Keeping the frequency of incident radiation and accelerating potential fixed. It is found that the photocurrent increases linearly with the intensity of incident light.

NOTE:-

(1) The intensity of radiation determined by the number of photons per unit area per unit time.

(2) Here Intensity of radiation can be changed by changing the distance between cathode C and the source of radiation.

Hence photocurrent is directly proportional to the intensity of the incident light.

(b) Effect of potential on the photoelectric current:-

We kept the anode at some A at some +ve potential w.r.t cathode C with radiation of fixed intensity(I).

If we increase the +ve potential on anode gradually, it is found that photoelectric current also increases till a stage comes when the photoelectric current becomes maximum( saturation current)

At this time all electrons emitted from the cathode are able to reach the anode. If we increase the intensity of light of some fixed frequency, then saturation current is more for more intense light. Because the greater the intensity of incident light cause emits more photoelectron from the cathode.

If the potential of the anode is made -ve w.r.t cathode, the electrons are repelled by the anode and only the most energetic electrons are able to reach the anode A. Due to this photocurrent is decreased, at a certain value of this -ve potential, the current is completely stopped. No photoelectron now has sufficient K.E to reach the anode A.

“The smallest magnitude of the anode potential which just stops the photocurrent is called the stopping potential or cut-off potential”

The stopping potential is related to the maximum K.E of electrons. To stop the current, we must ensure that even the fastest electrons fail to reach the anode.

Let the -ve potential of anode w.r.t cathode is $\fn_jvn V_0$ (stopping potential) when electron travel from cathode to anode. Its K.E decreases and is equal to the increase in P.E.
i.e If the fastest electrons just fail to reach the anode, then

$\fn_jvn \left [ eV_0=K_{max}=\frac{1}{2}mv^2 _{max} \right ]$

Stopping potential doesn’t depend upon the intensity of light (for fixed frequency)

(c) Effect of frequency of incident radiation on stopping potential:-

Here we study the relation between the frequency $\fn_jvn \large \nu$ of the incident radiation and the stopping potential $\fn_jvn V_0$ . Here we take the radiation of different frequencies but the same intensity.

The resulting variation is as

Here we observe that.

* The value of stopping potential is more for higher frequency. This implies that the value of maximum K.E depends on the frequency of incident radiation.

* The value of saturation current depends on the intensity of incident radiation but is independent of the frequency of incident radiation.

If we draw a graph between the frequency of incident light $\fn_jvn (\nu)$ and the stopping potential $\fn_jvn (V_0)$ at a constant intensity of the radiation ( for particular metal)

For different metal

The graph shows that.

(a) The stopping potential $\fn_jvn (V_0)$ varies linearly with the frequency of incident radiation for a given photosensitive material.

(b) There exists a certain minimum cut-off frequency $\fn_jvn (\nu_0)$ for which the stopping potential zero

These observations have two implications:-

(1) The maximum K.E of the photoelectrons varies linearly with the frequency of light but is independent of intensity.

(2) For a frequency lower than cut off frequency $\fn_jvn (\nu_0)$ , no photoelectron emission is possible even if the intensity is large. But for a frequency greater than $\fn_jvn \nu_0$ , causes photoelectron emission even if the intensity is very small. This minimum cut-off frequency $\fn_jvn \nu_0$ is called threshold frequency and it is different for different metal.

NOTE:-

Different photosensitive materials respond differently to light. Selenium is more sensitive than zinc or copper. The same photosensitive substance gives a different response to light of different wavelengths. For example, UV light gives rise to the photoelectric effect in copper while green or red light does not.

LAWS OF PHOTOELECTRIC EMISSION (SUMMERY)

1. For a given metal, there exists a certain minimum frequency of incident radiation below which no emission of photoelectron takes place. This is cut-off frequency is called threshold frequency $\fn_jvn \nu_0$

2. For a given metal and frequency of incident radiation ( above threshold frequency), the photoelectric current is directly proportional to the intensity of incident radiation.

3. Above the threshold frequency, the maximum K.E of the emitted photoelectron is independent of the intensity of the incident radiation bot depends only upon the frequency of the incident radiation.

4. The photoelectric emission is an instantaneous process. The time interval between the incidence of radiation and the emission of photoelectrons is less than $\fn_jvn 10^{-9}s$

IMPORTANT LINKS OF DUAL NATURE OF RADIATION AND MATTER
Introduction	Electron Emission
Photoelectric Effect	Experimental Study of Photoelectric Effect
Photoelectric Effect and Wave Theory of Light	Einstein’s Photoelectric Equation: Energy Quantum of Radiation
Particle Nature of Light: The Photon	Wave Nature of Matter
Davisson and Germer Experiment