Electron accelerated by potential difference

[gillgill]

An electron is accelerated by a potential difference of, say, 100V. How much greater would its final speed be if it were accelerated with four times as much voltage?

 

[marlon]

The corresponding energy is eV where e is the elementary charge and v is the applied potential. Note that this energy is kinetic in nature and therefore equal to 1/2mv²

regards
marlon

 

[gillgill]

Ep=Ek
eV=1/2mv²
so...four times as much voltage= 16 times greater speed?

 

[marlon]

So if the potential is 4 times bigger then the kinetic energy will get four times bigger. If A = mv²/2 or v = sqrt(2A/m) ; well then after the increase : 4A = mv²/2 or mv² =8A or v = sqrt(8a/m). Now if you divide sqrt(8A/m) by sqrt(2A/m) you acquire : sqrt(4) = 2. So the speed would be doubled...you see

regards
marlon