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Why electrons cannot be accelerated using a cyclotron?

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In a cyclotron, the most important condition is that of the cyclotron frequency. The frequency of the square wave oscillator connected to the dees of the cyclotron must match the frequency of revolution of the charged particle being accelerated.

For ordinary ions, once the  frequency is set there is no need to change or adjust the frequency.

The equation for cyclotron frequency is

As it is clear from the above equation that the cyclotron frequency is inversely proportional to mass of the ion. The frequency of revolution is apparently constant for ordinary ions.

If an electron is accelerated in a cyclotron, it quickly picks up high-speed comparable to the speed of light because of its light mass. The speed comparable to the speed of light is called relativistic speed. At relativistic speeds, mass is not constant but varies according to the relation.

As per the equation as speed increases, relativistic mass increases. This will change the frequency of revolution and the revolution will go out of phase. The acceleration will stop.

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