3.3 (sspd_chapter 1_part 2 continued  (Page 2/2)

hν – W F = (1/2)m e v 2 =q |V R | 1.5

where hν>W _F is the necessary condition for photoemission

ν- W F / h = ν – ν Th = ( q / h ) | V R | 1. 6

or (h/q)ν – (h/q)ν Th = |V R | 1.7

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.

The y intercept in Eq.(1.7) is – (h/q)ν _Th = -W _F /q = Surface Barrier Potential φ _B ;

The x intercept in Eq(1.7) is ν _Th ;

Thus from the straight line graph |V _R | vs ν (the incident photon frequency) , Fig(1.4), we can obtain Surface Barrier Potential φ _B and Planck’s Constant h .

In Fig(1.7) the straight line graph I(Anode Current) vs P(Incident light Intensity) is obtained. Here the incident frequency, which is greater than the threshold frequency, is kept constant while the intensity of the incident light is increased.

At frequencies greater than threshold frequency, each incident photon causes corresponding photoemission of a single electron . Because of the one to one correspondence the Anode Current ,which is the collection of photo-ionic electrons per second, is directly proportional to the incident light intensity provided we have a constant positive Anode Voltage. This results in a straight line Graph passing through the origin.

Fig(1.8) is the family of curves comprising of the static output characteristics of Photo-Electric Device. The static output characteristic is I _A vs V _A for a given incident frequency and which is a multiple of threshold frequency and for a given intensity of light.

In the first quadrant of the Graph if we do not enter high field emission region then for a given incident frequency we have a constant Anode Current with respect to Anode Voltage provided the intensity of light is kept constant. Constant light intensity implies constant number of incident photons. If quantum efficiency is 100%, constant incident photons number implies constant photo-emitted electrons. Hence no matter what the anode accelerating voltage is, a constant number of photo-emitted electrons are collected. That is the Photo-Electric Current Device acts as constant current source as long as the incident light intensity is constant.

Here we may define Constant Current Sources and Constant Voltage Sources. A Constant Current Source delivers a constant current irrespective of the load voltage whereas a Constant Voltage Source will give a constant terminal voltage irrespective of the load current.

The I-V curve of a Constant Current Source will be a horizontal line as it is in the case of Photo-Electric Current Device whereas the I-V curve of a Constant Voltage Source will be a vertical line.

For this simple but elegant explanation of Photo Electric Effect , Albert Einstein was awarded Nobel Prize in 1921.

These photons are virtual particles but they exhibit all the properties of material particles. They have translational momentum and hence exert force and pressure. Had the pressure of sun-light not been considered, Viking would have missed Mars by about 15,000 km.

Insolation in the upper most part of Atmosphere= 1400W/m ² ;

Force (F) = rate of change of translational momentum (dp/dt) 1.8

Force.displacement = F.Δx

= ΔU ( incremental work done on incremental displacement)

F.Δx = (dp/dt). Δx = Δp.(dx/dt) = Δp.v 1.9

In case of light in free space : ΔU = Δp.c;

Therefore Δp = ΔU/c;

Therefore Δp/∆t = ΔU/∆t /c = (1/c)(dU/dt) = Force = F (Newtons) 1.10

dU/dt = rate of energy incidence;

dU/dt/m ² = Energy falling per unit time per unit area = Insolation;

Eq.(1.10) gives:

F/m ² (Pressure)= (1/c)(dU/dt)/m ² = I (intensity)/c ;

Given I(intensity) =

Insolation of sun-light in the upper part of the atmosphere = 1400W/m ²

Resulting pressure= I (intensity)/c

= 1400W/m ² ÷(velocity of light in vacuum)

=4.7×10 ^-6 N/m ² ;

1mW/m ² is equivalent to 3.3pN/m ² ;

Total force exerted on Earth by Sunlight = (F/m ² ) × (πR _EARTH ² )

= 4.7×10 ^-6 N/m ² × π×(6.37×10 ⁶ ) ² m ²

= 6×10 ⁸ N= 6×10 ⁸ N/(10 ⁴ N/metric Ton)

= 60,000 metric tons.