Accelerating an electron to the speed of light

_AVG_

According to classical mechanics, I calculated that if an electron were to be accelerated through a potential difference of about 257 kV, it would breach the speed of light. Now, according to relativistic mechanics, this is obviously untrue. So, what are the mathematical corrections to be made whilst calculating the speed attained?

What I did was:

qV = (mv^2)/2 [Electrostatic potential energy = Kinetic energy]

How do I correct this using relativistic mechanics?

Indi

The relativistic kinetic energy is (γ - 1) × m₀ × c², where γ is the Lorentz factor.

If you use that in your equation, 257 kV will accelerate an electron to 0.747 c. (And, for reference, a potential of ten times that - 2,570 kV - will accelerate an electron to 0.986 c. A hundred times that - 25,700 kV - to 0.9998 c. And a thousand times that - 257 MV - to 0.999998 c.)

DoctorBeaver

You can't use classical mechanics where particles or high speeds are concerned.

chatrack

You should follow classical mechanics

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