An electron and a proton starting from rest get accelerated through potential difference of 100 kV. The final speeds of the electron and the proton are V$_e$ and V$_p$ respectively. Which one of the following relations is correct?
”V<tex>$_e$</tex>
”V<tex>$_e$</tex>
”V<tex>$_e$</tex>
”Cannot
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CDS-1 – 2019
(1/2)m_e * V_e^2 = (1/2)m_p * V_p^2
m_e * V_e^2 = m_p * V_p^2
V_e / V_p = sqrt(m_p / m_e)
Since the mass of the electron (m_e) is significantly less than the mass of the proton (m_p), the ratio m_p / m_e is greater than 1. Therefore, V_e / V_p > 1, which means V_e > V_p. The lighter particle (electron) achieves a much higher speed than the heavier particle (proton) for the same kinetic energy.