3.3 (sspd_chapter 1_part 2 continued

Photo electric effect continued.

P (Joules/second) / (hν) = number of photons incident .

If quantum efficiency is 100% then each photon will cause photoemission of a corresponding electron.

Hence P (Joules/second) / (hν) = number of photoemitted electrons/second.

Assuming that all photo-excited electrons are picked up by the Anode , this will constitute the Photo-ionic Current. Hence

I _A (Photo-ionic Current) = q.P (Joules/second) / (hν)

This graph is a straight line graph passing through the origin and with a slope Tanα=[q/((hν)] where α is the angle of inclination of the straight line graph.

Fig(1.7) Photoionic Current versus Intensity of Light for a monochromatic light source.

Fig.(1.8) I A vs V A family of Output Curves for a constant Intensity but incident light frequency being increased in steps of ν Th .

Einstein was able to explain all the three graphs by assuming the quantum nature of light. Does this mean that Wave Nature of Light is wrong ? Absolutely not. We have studied Diffraction (aperture is comparable to wave length) and Interference pattern in Intermediate Physics and this can be explained only on the basis of Wave Nature of Light.

What this implies is that Electromagnetic Waves , which visible light is, manifests Wave Nature while interacting with Energy whereas it manifests Quantum Nature while interacting with Matter. Photo-Electric Effect and Compton Effect are two such examples.

The Photo-Electric also implies that every metal has its characteristics Work-Function and whenever the conduction electrons are energetic enough to overcome this Work-Function they will escape from the metal surface into vacuum.

Work-Function can be defined as follows:

It is the minimum energy required at zero Kelvin for a given metal for electron emission into vacuum.

A monochromatic light source emits photons of frequency ν at a constant rate of P/(hν) photons per second where P= Intensity of the monochromatic source in Joules per second. Each incident photon interacts with a single electron only and imparts the energy packet in totality to the electron with which it is interacting. If the incident photon’s frequency is less than the Threshold Frequency then no intensity of light will cause photo-ionic emission. This is because increase in intensity means increase in the number of photons but energy packet transferred from the photon to the interacting electron remains insufficient to cross the surface potential barrier. Hence below threshold frequency no amount of incident light will cause any photo-ionic current.

When the frequency of the monochromatic source is increased to become equal to the threshold frequency then photo-ionic emission will just occur with photo-emitted electrons having zero kinetic energy.

When the incident frequency exceeds the threshold frequency then photo-emitted electrons have finite kinetic energy (1/2)m _e v ² and photo-ionic current starts being detected as anode current. This kinetic energy can be measured by the application of retarding voltage at the anode. The application of positive Anode Voltage causes a potential downhill which accelerates the photo-emitted electrons. Hence positive Anode Voltage facilitates the collection of photo-ionic current as Anode Current. The application of negative Anode Voltage causes a potential uphill which retards the photo-emitted electrons and converts the kinetic energy of the photo-emitted electrons in potential energy and this prevents the collection of photo-ionic current as Anode Current and hence Anode Current decreases. As retarding voltage is increased the anode current decreases until at a retarding voltage V _R the anode current becomes zero. This gives the famous Einstein Equation: