DETERMINATION OF CHARGE ON ELECTRON BY MILLIKAN'S OIL DROP EXPERIMENT

DETERMINATION OF CHARGE ON ELECTRON BY MILLIKAN'S OIL DROP EXPERIMENT:-

C= Vacuumed Chamber     

W₁ & W₂= Two glass windows

P₁ & P₂=Two parallel metallic plates

H= Hole in upper plate

d= Separation between the plates

D= Oil drop

M= Magnified view of oil drop

x= Distance between oil drop with respect to lower plate

L= Convex lens

S= Source of light

A= Atomizer

V= Potential difference between the plates

Millkan used an apparatus as shown in fig to determine the charge on an electron. This apparatus consists of metallic chamber with air at low pressure in it.There are two electrodes in it upper electrode is acting as anode have hole in it as shown in fig and lower one is acting as cathode. Oil is sprayed over the upper plate by using atomizer. Oil moves downward through the hole due to gravity. Till yet battery is not connected. As the oil drop moves downward we apply X-Rays due to which air present in the chamber get ionized & air present loses electrons and these electrons are absorbed by the oil drops and oil drop gets charged. Now we connect the plates with the battery. As the oil drop is negatively charged and moves downward due to gravity but also the lower plate is cathode so it also repel the oil drop and potential difference is applied such that oil drop suspended at this position force due to gravity on oil drop and electrostatic force are equal ie

F_e=F_g -----(i)

We know that E=F_e

                         q

or F_e=qE-----(ii)

also we know that F_g=mg----(iii)

put (ii) & (iii) in (i) we get

qE=mg

or q= mg -----(iv)

          E  

We also know that E= V  ----(v)

                                  d

putting (v) in (iv) we get

q=  mgd------(vi)

        V  

in (vi) on right hand side all the values are known except mass of oil drop which can not be measured directly and is measured indirectly by following method.

We first measure the distance "x" by meter rod which is distance between the oil drop and the lower plate. We put the potential difference off and at the same time we start stop watch. The oil drop fall down due to its weight and because of its less mass very soon it attain terminal velocity. We measure the time of fall on lower plate by stop watch and then calculate terminal velocity using following relation

 v_t= x

       t

the drag force given by strokes law becomes equal to the weight of oil drop ie

 F_drag=W

   6πηrv_t=mg----(vii)

Also we know

  ρ= m

       V

or m=ρV----(viii)

For oil drop  V= 4 πr³ put this in (viii) we get

                       3   

 m= 4 πr³ρ-----(ix)

       3

Putting (ix) in (vii) we get

    6πηrv_t= 4 πr³ρg

                3

After cancellation we get

9ηv_t=2gρr²    

r²= 9ηv_t

         2gρ

taking square root on both sides we get

------(x)

where as ρ= Density of oil drop (known)

 g= Gravitational acceleration (known)

v_{t = Terminal velocity (known)}

η= Co-efficient of viscosity or air (known)

so indirectly radius of oil drop is measure by using relation (x). This radius is used in (ix) mass of oil drop is calculated and finally using this mass in (vi) the charge on oil drop is calculated.

CONCLUSSION:-

           Millikan repeated this experiment for number of oil drops and each time he found that answer is integral multiple of a constant minimum value (1.6 x 10^-19). He concluded that this common multiple value is actually magnitude of charge on an electron so the charge on an electron is

e= 1.6 x 10^-19 C