(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a) What potntial difference will accelerate an electron to the speed of light according to classical physics?

b) With this potential difference, what speed will the electron acheive relativistically?

c) What is the relativistic mass at that speed?

d) What is the relativistic kinetic energy?

2. Relevant equations

see solution

3. The attempt at a solution

a) [tex]q_{e} \Delta V = \Delta K = \frac{1}{2}m_{e}c^{2}[/tex]

[tex]\Delta V =\frac{m_{e}c^{2}}{2q_{e}}=255,499 Volts[/tex]

b) here i'm assuming that i can say (is this assumption valid??):

[tex]q_{e} \DeltaV = \gamma m_{e}c^{2}-m_{e}c^{2} [/tex]

then solve for [tex]\gamma[/tex],

[tex]\gamma=\frac{q_{e}\DeltaV}{m_{e}c^{2}}+1[/tex]

the velocity follows immediately

c) [tex]m = \gamma m_{e}[/tex]

d) here's where I get confused, if i calculate kinetic energy using:

[tex]K=\gamma m_{e}c^{2}-m_{e}c^{2}[/tex]

I get the same kinetic energy ([tex]q_{e} \Delta V [/tex]) I assumed in part b (obviously)... now this makes some sense to me, in the respect that the classical kinetic energy at the speed the electron would obtain relativistically is lower than this, but it is also equal to [tex]\frac{1}{2}m_{e}c^{2}[/tex]... i don't think this is a contradiction, but it seems strange... is my underying assumption in part b wrong?

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# Relativistic Electron

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