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An electron initially at rest accelerates through a potential difference of 1 V, gaining kinetic energy KEe, whereas a proton, also initially at rest, accelerates through a potential difference of - 1 V, gaining kinetic energy KEp. Which of the following relationships holds?

a) Cannot be determined from the given information.
b) KEe > KEp
c) KEe < KEp
d) KEe = KEp

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Answer:

d) KEe = KEp

Explanation:

According to the law of conservation of energy, the electric potential energy is converted into the kinetic energy of the particle:

[tex]KE=U\\KE=qV[/tex]

Here, q is the particle's charge and V is the potential difference.

The charge of the electron is -e. So:

[tex]KE_e=-eV\\KE_e=-e(1V)[/tex]

The charge of the proton is e. So:

[tex]KE_p=eV\\KE_p=e(-1V)\\KE_p=-e(1V)[/tex]

So [tex]KE_e=KE_p[/tex]

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