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Is the fact on which the working of a cyclotron depends i.e. "The frequency or time period of revolution of a charged particle is independent of its ‘speed’ or radius of its orbit" consistent with the theory special relativity about which we learn in the Cyclotron's limitations that "It cannot be used to accelerate electrons because electrons are of very small mass. Thus, the ‘velocity’ will be increased to such a great extent that the electron will be thrown out of the step with the oscillating field." In one statement speed doesn't matter but in the limitations, it matters? How and why?

Is the fact on which the working of a cyclotron depends i.e. "The frequency  or time period of revolution of a charged particle is independent of its ‘speed’ or radius of its orbit" consistent with the theory special relativity about which we learn in the Cyclotron's limitations that "It cannot be used to accelerate electrons because electrons are of very small mass. Thus, the ‘velocity’ will be increased to such a great extent that the electron will be thrown out of the step with the oscillating field."
 In one statement speed doesn't matter but in the limitations, it matters? How and why?

Grade:12

1 Answers

Harsh Pandey
14 Points
2 years ago
Dear Abdul
 In case of electron also the frequency does not depends upon the speed of the electron . It only depends upon its mass.
 
Since according to “EINSTEIN’s SPECIAL THEORY OF RELATIVITY” 
 
 M = m/\sqrt{1 - v^2/c^2} ; M ---> moving mass & m---> rest mass
In case of electron ; the mass is very small in comparison with +ve H-like ions due to which speed of electron becomes comparable with the speed of light during acceleration & its MASS changes which is not true in case of other +ve H-like ions because here V ---> 0 and hence its mass remains same.
 
As I stated above that the frequency depends upon the mass of the charged particle.
Hence, the frequency of the electron becomes out of step with the cyclotron frequency.

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