Question

The ratio of momentum of an electron and \( \alpha \)-particle which are accelerated from rest by a potential difference of 100 V is:

• A. 1
• B. \( \sqrt{2m_e / m_\alpha} \)
• C. \( \sqrt{m_e / m_\alpha} \)
• D. \( \sqrt{m_\alpha / m_e} \)

Hint:

The momentum of a particle is proportional to the square root of its mass when accelerated by the same potential difference.

Answer 1

The Correct Option is B

Step 1: Momentum of the particle.
The momentum of a particle is given by: \[ p = \sqrt{2 m e V} \] where \( m \) is the mass, \( e \) is the charge, and \( V \) is the potential difference.
Step 2: Ratio of momentum.
Since the momentum depends on mass, the ratio of momentum between the electron and \( \alpha \)-particle is: \[ \frac{p_e}{p_\alpha} = \sqrt{\frac{2m_e}{m_\alpha}} \]
Final Answer: \[ \boxed{\sqrt{\frac{2m_e}{m_\alpha}}} \]