Question

The mass of proton is 1836 times that of an electron. An electron and a proton are projected into a uniform electric field in a direction perpendicular to the field with equal initial kinetic energies, then:

• A. the electron trajectory is less curved than the proton trajectory
• B. the proton trajectory is less curved than the electron trajectory
• C. both trajectories are equally curved
• D. both trajectories will be straight

Answer 1

Answer: (A)

the electron trajectory is less curved than the proton trajectory

$KE=\frac{1}{2}{mv}^2$

Given, $\frac{K{E}_p}{K{E}_e}=1$

$⟹\frac{v_e}{v_p}=\sqrt{\frac{m_p}{m_e}}...............\left(i\right)$

Charge on electron is equal to charge on proton.

$F=qE$

$\therefore F_e=F_p$

This force provides the necessary centripetal force as it is perpendicular to the direction of motion.

Centripetal force at point is given by, $F=\frac{{mv}^2}{R}$

$⟹\frac{v_e}{v_p}=\sqrt{\frac{R_e}{R_p}}.............\left(ii\right)$

From (i) and (ii),

$\frac{R_e}{R_p}=\frac{m_m}{m_e}=1836$

Since radius of electron trajectory is more than radius of proton trajectory, the electron trajectory is less curved than proton trajectory.