Stopping Potential

Concept of Stopping Potential in Photoelectric effect

Definition

         Stopping Potential is defined as the value of the reversed voltage applied where the velocity of the ejected electron become zero

Now to know about stopping potential we have to see the variation of photoelectric current and the potential difference through a simple experiment

Experiment:

Let us consider evacuated tube A as an emitter metal plate and B as a collector metal plate. Light strike on the ejector metal strap and the frequency and intensity of light remain constant

Case 1: when no external voltage is applied

When light/photon with energy hv strike on the collector metal plate surface and give the energy to the electron and the electron use the energy to overcome the threshold barrier and the remaining energy use in the kinetic energy of the ejected electron. The ejected electron go toward the collector metal plate and the small current start flow in the circuit and ammeter show some current at zero voltage. As shown in fig. below

Case 2:   when external voltage is applied

Positive (+ve  ) terminal of the battery is connected to the collector metal plate and negative(-ve) terminal of the battery is  connected to the ejection metal plate as shown in the fig.

 As the +ve terminal of the battery is connected to the collector metal plate. The +ve potential difference increase on the collector plate due to this the photocurrent start increases. After some time Photocurrent reaches saturation point this is called saturation current state as shown in the fig. below.

Case 3: when an external voltage is applied

Positive (+ve) terminal of the battery is connected to the ejection metal strap and negative(-ve) terminal of the battery is connected to the collector metal strap as shown in the fig.

Now the ejection plate become +ve hence the photon require more energy to eject the electron from the ejector metal plate as we have fixed frequency only few-electron will get out, on the other hand, the collector plate become -ve that is it also start repelling the electron as shown in fig. below

Therefore photocurrent start decreasing and reach to the point where photocurrent become zero (when -ve potential of collector plate and the kinetic energy of the electron becomes equal) from here the concept of stopping potential rise

Conclusion

Effect of frequency and intensity photocurrent and potential difference

Effect of Frequency

i.e. when photocurrent reaches to zero

Kinetic Energy of electron           =     -ve potential of collector plate (stopping potential)

                   (E_K.E.)_e = ev_s                 -------------1

e-electronic charge

v_s-stopping potential

Therefrom photoelectric effect equation

                     hv = hv₀ + ½ mv²

                             (E_K.E.)_e =hv-hv₀

Form equation --------1

                           ev_s = hv - hv_o

now from above equation

e,h,hv_o are constant

Therefore stopping potential (v_s) depend on Frequency (v)

 Conclusion

i.e.

·       if we increase the frequency the stopping potential increases.

·       There is no effect of frequency on photocurrent.

     As shown in the graph.

Effect of intensity

If we increase the intensity of light the number of photon strike on the ejector metal plate increase i.e. more electron eject from the metal strap therefor photocurrent increase but stopping potential remain the same

                     Intensity= n_pehv/area per unit time  

Conclusion

·       If we increase the intensity the photocurrent increase

·       There is no effect of intensity on stopping potential
     As shown in the graph.