CHARGE TO MASS RATIO OF THE CATHODE RAYS
(Measurement of e/m value of Electron)
Crooks showed experimentally that cathode rays are negatively charged particles J.J Thomson now attempted to determine the quantity of charge on these particles. He was not successful in determining the charge and mass of the particles (Electrons) separately; anyhow in his attempt he was able to determine the charge to mass ratio (e/m ratio) of the particles, through his experiment.
He carried out his experiment in cathode ray tube (Gas discharge tube) with little modifications. It is shown in the figure.
Cathode rays are produced and passed through the slit. When there was no electric and magnetic fields, the electrons (cathode rays) traveled in straight beam, and stroked at point B. When Electric field was applied alone, the beam was deflected and it strike at point, C .when the magnetic field was applied alone the beam stroked at point A. At this stage Electric field and Magnetic field was applied simultaneously in such a way that they balanced each other and the beam of cathode ray was able to strike it point B again.
The electric field and magnetic field were both calculated and were used in the determination of e/m.
When magnetic field was applied alone, the electron farmed a circular path with radius “r” and velocity “ v ” in the magnetic filed.
As the electron is now in circular path, thus its centrifugal force can be given as:
Where m= Mass of electron
v= Velocity of electron
r= Radium of circular path.
Centrifugal force on the electron is balanced by the magnetic force as given below:
 --------- (1)
Where
B= Magnetic field strength
E= Charge on electron
v= Velocity of electron
or 
 ---- (2)
Radius “r” can be determined from the tube and the displacement of the electron spot on the screen.
When electric field applied in balanced by the magnetic field, we can write that
Magnetic field = Electric field
Or  where E= Strength of electric field.
Orr 
Or  -------(3)
Putting value of equation 3 in 2 we get
 ----------- (4)
E the electric field strength, B, the magnetic field strength and radius ”R” values are determine these values are inserted in equation 4 and value for e/m was calculated.
The value of  = 
J.J Thomson used different gases and calculated e/m ratio for them. He obtained the same value, regardless of what gas was used and what kind of electrodes were used. He deduced that these negatively charged particles are present in every kind of substance.
|
