Atomic Structure

CHARGE OF ELECTRON
            R.A Millikan in 1909 measured the absolute value of the charge on an electron. His experiment is called as OIL DROP EXPERIMENT.
The experiment used to determine electronic charge is called as Millkan’s oil drop method the apparatus used is given in the diagram:

The apparatus consists of two plates, which are 22cm in diameter and 1.6 cm apart indicated by A and B. The plates are placed in a container contain air at low pressure. These plats are connected to battery of a high voltage. (10kv) V. In the   upper plate which is positively charge is a small hole c,By means of an atomizer, a fine spray of a non-volatile oil was introduced above the upper plate. (note: Atomizer is instrument which break the oil into the very small droplets). When oil passes out from the atomizer a friction will make the droplet negatively charged. Extra negative charges was introduced by means of X-rays, due to which droplets got negative charge. One droplet was allowed to come down through the hole C and its motion was observed by means of a telescope. Droplet can be seen under light. First the droplet  is allowed to fall down under gravity.  The velocity at which it drops down under the influence of gravity is represented by v1. v1 is directly proportional to the weight of droplet i.e
                       
            As                                                                 
      Therefore 
            Or           (1)
                        m= mass of droplet
                        g= Gravitational Acceleration (9.8m/s2)
                        K= Proportionality constant.
The electric current was then applied across the plates, the droplet will rise up against the gravity (mg). The upward force acting on the droplet is due to the applied electric field this force is given by E en ie.
             
            Where E= Strength of electric field applied
                     en= charge on oil droplet.
As the droplet will be moving upward against the gravity, the net upward force, the droplet will be

The velocity    with which the droplet will be moving upward is directly proportional to the force applied  in upward direction i.e
                       
            Or           --------  (2)
                        K = proportionality constant.
            Equation  (1) can be rearranged as under:
                        ------------      (3)
                                                 
            Put values of equations on 3 in 2
             
                       
           
                          
           
Or         
           
Or                            (4)
                       
The above equation 4 shows the charge on one droplet. v1,v2, and m  for  oil droplet are calculated. The value of  “g” is known. Thus the value for ”en” is calculated. It was found that the charge on droplet (en) was always an integral i.e. whole number, multiple of a definite elementary charge of one election. The value calculated   was:
          

            MASS OF ELECTRON: -

   With the determination of e/m ratio and cater on determination of the carge an electron, the mass of electron can be caudated:
               (1)
                           (2)
            Putting value from  (1) in  (2) we get.
           
                 
            or         
                        =

Mass of electron in atomic mass units (amu): -

            We know that

           
           
          
                                   
            9.109x 10-27 gm= 1     x 9.1096x 10-27
                                       1.6x 10-24
                                    =  0.00055 amu

= 0.00055 amu