Question

The de Broglie wavelength of a proton and α-particle are equal. The ratio of their velocities is :

• A. 4 : 1
• B. 4 : 2
• C. 4 : 3
• D. 1 : 4

Hint:

Mass of $\alpha$-particle is $4u$ and charge is $2e$. Mass of proton is $1u$ and charge is $1e$. These ratios are essential for dual nature and electrostatics problems.

Answer 1

The Correct Option is A

Step 1: de Broglie wavelength $\lambda = \frac{h}{mv}$.
Step 2: If $\lambda_p = \lambda_\alpha$, then $m_p v_p = m_\alpha v_\alpha$.
Step 3: The mass of an $\alpha$-particle is $4 \times$ the mass of a proton ($m_\alpha \approx 4 m_p$).
Step 4: $m_p v_p = 4 m_p v_\alpha \Rightarrow \frac{v_p}{v_\alpha} = \frac{4}{1}$.