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:
The force on a charged particle in an electric field $E$ is $F = qE$. According to Newton's second law, $F = ma$. Therefore, acceleration $a = \frac{qE}{m}$.
Step 2: Formula Application:
For a proton: $q_p = e$, $m_p = m$. So, $a_p = \frac{eE}{m}$. For an $\alpha$-particle: $q_\alpha = 2e$, $m_\alpha = 4m$. So, $a_\alpha = \frac{2eE}{4m} = \frac{eE}{2m}$.
Step 3: Explanation:
The ratio is: $$\frac{a_p}{a_\alpha} = \frac{eE/m}{eE/2m} = \frac{1}{1/2} = 2$$
Step 4: Final Answer:
The ratio $a_p : a_\alpha$ is 2 : 1.