Question

A proton and a $\alpha$-particle are placed in uniform electric field. Accelerations produced in them are $a_p$ and $a_\alpha$ respectively. Then $a_p : a_\alpha$ will be ______.

• A. 1 : 2
• B. 4 : 1
• C. 2 : 1
• D. 1 : 4

Hint:

Even though the alpha particle has twice the charge (more force), it is four times heavier (more inertia), resulting in half the acceleration of a proton.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Force in an electric field is $F = qE$. According to Newton's Second Law, $F = ma$. Therefore, acceleration $a = \frac{qE}{m}$.
Step 2: Detailed Explanation:
For a Proton ($p$): Charge $q_p = e$, Mass $m_p = m$.
For an Alpha particle ($\alpha$): Charge $q_\alpha = 2e$, Mass $m_\alpha = 4m$.
$$a_p = \frac{eE}{m}$$ $$a_\alpha = \frac{2eE}{4m} = \frac{eE}{2m}$$ Ratio $\frac{a_p}{a_\alpha} = \frac{eE/m}{eE/2m} = \frac{2}{1}$.
Step 3: Final Answer:
The correct option is (c).