An electron is accelerated through a potential difference of 0.20 v. How much greater would its final speed be if it is accelerated with four times as much voltage?

v₂ = 2* v₁

Explanation:

Assuming no friction present, the change in the electrostatic potential energy of the electron, must be equal in magnitude to the change in the kinetic energy:

       

We know that ΔV = 0.2 V, so we can write the following equality:

       

Now, if the voltage increases 4 times, we can write the following equality:

       

Dividing both sides in (1) and (2), and simplifying common terms, we get:

       

Taking square roots at both sides, we get:v₂ = 2* v₁The final speed, if the electron is accelerated through a potential difference four times larger, will be double than the one for a potential difference of 0.2 V.