3.2 Sspd chapter 1_part 2_photoelectric effect  (Page 2/2)

Fig 1.3. Energy Band Diagram of a Metal.

The electrons in the Conduction Band are not localized to their host atoms but belong to the whole crystalline lattice of the metal. Hence they are free to conduct throughout the crystalline lattice. But when they come to the surface boundary of the crystalline lattice they face a Surface Barrier Potential φ _B . This prevents the conduction electrons from escaping to the vacuum space outside the metallic lattice. Hence the conduction electrons are referred to as semi-free electrons.

But if the conduction electrons acquire sufficient energy to cross the Surface Barrier Potential then indeed the conduction electrons will be emitted from the surface of the Cathode.

The Surface Barrier Potential φ _B implies that conduction electrons must acquire energy equal to or greater than qφ _B to escape into the vacuum. This quantity qφ _B is known as the Work Function (W _F ) of the Metal. Pure Tungsten has W _F = 4eV whereas Strontium Barium Oxide coated Thoriated Tungsten has W _F = 1 eV. The latter is used as the Cathode Material in all Vacuum Tube Devices.

Table 1.1. Work Function and Threshold Frequency.

If the conduction electrons become energetic enough to cross the Surface Barrier Potential by heating i.e. (3/2)kT>W _F then Thermo-ionic Emission takes place.

If the incident Photons have energy packets hν>W _F then Photo-ionic Emission takes place.

If the application of a very high field causes the surface barrier potential height to be lowered and surface barrier thickness to be narrowed then High Field Emission of conducting electrons occur by quantum mechanical tunneling. This is described in Section 1.7.3.

Presently we are concerned with Photo-ionic Emission.

Let the accelerating voltage be V _A ,

Let the incident photon have a frequency of ν ;

Let the Threshold frequency be ν _Th where hν _Th = W _F ;

As long as incident photon frequency ν<ν _Th , no photo-excitation takes place and hence no photo-ionic emission takes place and no Anode Current is detected irrespective of what the Anode Voltage is. The increase in the intensity of light will also not result in any photo-excitation and no Anode Current will be ever detected as shown in Fig 1.4.

Figure 1.4. Stopping Potential, V R , versus incident frequency.

But if the incident frequency is greater than the Threshold Frequency then even the weakest intensity light at minimum Anode Voltage will cause some photo-ionic current and a weak Anode current will be detected.

As the intensity of incident monochromatic light is increased the strength of the Anode Current increases .

Now if a decelerating voltage is applied to the Anode, the photo current detected decreases until at a given negative Anode Voltage the Anode Current becomes zero. For constant frequency but varying Intensity, the stopping potential is the same. Meaning by that stopping potential depends on frequency and not on intensity as shown in Figure 1.5.

On the basis of all the observations we arrive at the following graphs shown in Fig.(1.6), Fig.(1.7) and Fig(1.8).

hν – W _F = (1/2)m _e v ² =q |V _R | where, hν>W _F , is the necessary condition for photoemission

ν- W _F /h= ν – ν _Th = (q/h) |V _R |

or (h/q)ν – (h/q)ν _Th = |V _R | is a straight line equation like y=mx+c where |V _R | is the dependent variable y, ν is the independent variable x and (h/q) is the slope Tanθ where θ is the angle of inclination of the straight line.

Y axis intercept is = – (h/q)ν _Th

Fig.1.6. Photo- electric effect graph with a constant intensity source but variable frequency.

From graph given in Figure 1.4 and 1.6 the Universal Constant h, Planck’s Constant and Work Function of the metal of the cathode which is being illuminated by the monochromatic light can be determined. In 1930 Milikan, of Milikan drop experiment fame, carried out the experiment using Sodium as the cathode.

In his experiment he got the Plot as given in Figure 1.4.

According to that plot:

ν _Th = 4.39×10 ¹⁴ Hz .

This corresponds to visible light of wavelength λ _Th = 683nm (red light).

The slope = ∆E/∆ν = 4.1×10 ^-15 = h/e .

Multiplying by the charge of electron e = 1.6×10 ^-19 Coulomb ,

The value of Planck’s Constant = h = 6.6×10 ^-34 Joules.sec

[To be Continued in next module]