Answer to Question #184222 in Electric Circuits for Koali

Question

An electron and a proton are accelerated through the same potential difference

A. The electron has lower KE

B. The proton has lower speed

C. The proton has lower KE

D. The electron has lower speed

Explain why is that your answer.

Answer 1

The change of kinetic energy is equal to the work of the electric field:

$A = |q| \Delta U.$

Therefore, due to the equality of the moduli of proton and electron charges, the kinetic energies will be equal.

$\text{KE}_p = \dfrac{m_pV_p^2}{2}, \; \text{KE}_e = \dfrac{m_eV_e^2}{2}$

Due to the equality of kinetic energies we may write

$m_pV_p^2 = m_eV_e^2$ or $\dfrac{V_p^2}{V_e^2} = \dfrac{m_e}{m_p}$ .

The mass of the electron is smaller, than the mass of proton. therefore the velocity of proton will be smaller, than the velocity of the electron.

So B is the correct answer.