Find the speed at which the kinetic energy of a particle will differ by 1% from its nonrelativistic value 1/2 m0v2.

As we know that Kinetic energy gained by the electron is due to change in mass of electron.


As E=K.E=


As we know relativistic Energy is always more than non-relativistic kinetic energy because Rest energy is always less then apparent mass energy


The relativistic value of Kinetic energy will be


As we know the moving object appears to be heavier in the moving frame that’s because of Lorentz transformation known as apparent mass which is given by


Where , V is velocity of moving object and C is speed of light in vacuum i.e.


K.E=



Let







As K= which is we can neglect





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