Answer :

Given:


Potential difference between collector and emitter = 500V


Specific charge of electron (charge per unit mass e/m) = 1.76 × 1011 C


Kinetic energy of an electron is given by:


…(1)


Where,


M = mass of electron


v = velocity of electron


e = charge of electron


V = potential difference (accelerating potential)


(a) From equation (1), we can write


…(2)


By putting the values in equation (2) we can find electron velocity.



v = 1.327 × 107 ms-1


(b) Accelerating potential, V = 10MV = 106V


Let speed of electron be v1


Again putting the values in equation (2),


v1 =


v1 = 1.8 × 109ms-1


This result is wrong as we understand that speed of light


(i.e. 3 × 108 ms-1) is the theoretical limit of the speed.


Such problems can be dealt using relativistic mechanics,


Relativistic mass is given by:


m =


Where,


m = relativistic mass


m0 = rest mass


v = velocity of particle


c = speed of light


At relativistic speeds, kinetic energy is given by,


KE = mc2-m0c2


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