Charge on Electron – How charge on an electron is calculated

Charge on Electron:

R.A. Millikan in 1909 performed an experiment to determine charge on electron.

The apparatus is shown in figure.

It is a glass box having two  metallic plates, one act as +ve  plate while other acts as –ve plate.                                                                

The upper plate has a hole in it.

These plates are 1.6 cm apart.                                                                 

10000 V voltage was applied  across the plates.                                                       

Oil was sprayed by atomizer.                                                              

X-rays were introduce to charge oil drops negatively also due to friction provided by atomizer, the oil drops were charged.                            

The area between two plates was

illuminated by light to see oil drops.                                                                                         

Some of oil drops entered into area between two plates. The drops fell under the influence of gravity.

Velocity ‘v1’ of an oil drop was calculated by noting its time of flow from upper plate to the lower one.                      

     v1         ∝        mg                

  Where k = proportionality constant

      v1         =          kmg…………. (1)  

     mg = weight of oil drop

   g = acceleration due to gravity

Then electric field was switched on and the oil drop started moving in the upward direction again upward velocity was determined by noting the time of flow from lower plate to the upper one. 

The upward velocity v2 depends upon charge on oil drop and strength of electric field.

      v2         ∝        Een – mg

       v2         =          k (Een – mg)….. (2)

Dividing equation-1 by eqation-2                 

v1            =              k mg          

v2                     k (Een – mg)      

v1         =                 mg           

v2                     (Een – mg)   

Een – mg         =         v2 mg                


Een      = v2 mg   +   mg


Taking LCM

Een      = v2 mg       +        mg      

      v1                        1

Een      = v2 mg  +  v1mg


Taking common

Een      = mg (v2  +  v1)



Charge on oil drop  =  en        = mg (v1 + v2)    



en = charge on oil drop

mg = weight of oil drop

v1 = downward velocity

v2 = upward velocity

E = strength of electric field

In this way charge on oil drop was determined. Millikan repeated this procedure for several hundred oil drops and found that charges on these oil drops were some whole number multiples of 1.6022 x 10-19 coulomb. From these investigations he concluded that this is the charge of an electron.

On the basis of these experiments following characteristics of cathode rays are noted:

  1. Cathode rays travel in straight line
  2. They cast shadow of opaque objects on fluorescent screen.
  3. Cathode rays deflect from their straight path when passed through electric or magnetic fields.
  4. Cathode rays are negatively charged.
  5. Cathode rays are stream of material particles which possess energy and momentum.
  6. They are capable of doing work.
  7. Cathode rays heat up thin metal film placed in their path. Kinetic energy of cathode ray particles changes to heat energy.
  8. High speed cathode ray particles when strike metallic anode, X-Rays are emitted.
  9. Their e/m ratio is independent of nature of gas as well as nature of cathode.

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