Very little energy is expended to achieve high eV...
Since " eV" (an Electronvolt) is a unit of energy (equal to 1.602176634×10 −19 Joule) then this sentence fragment can be rewritten as: " Very little energy is expended to achieve high energy..." Which appears self-contradictory unless the energy "expended" comes from a different source than the energy "yielded". This then begs the question: What is that source ?
Alternatively, the author might have meant to write: " Very little energy is expended to achieve many meters per second..." Which is very plausible for an electron, since even a 1 Volt potential difference accelerates an electron to 593km/sec (368 miles/sec). ..doubling the velocity (eV) moves the energy from 200 to 800
Again, the SI unit of velocity for an electron is the [meter/second] - not the Electronvolt [eV]. Anyway, it is true that doubling the velocity of an electron quadruples its kinetic energy in the Newtonian formula. However, that is a double edged sword in classical physics, because the same formula applies to the: 1) energy expended in accelerating the electrons. 2) energy yielded from decelerating the moving electrons. ...which then yields more energy than expended in accelerating the electron...
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