Q 12-11-058JEE MainJEE Main 2024 (1 Feb, Shift 1)Easy
The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2\lambda$ respectively. The ratio of the velocities of the proton and the $\alpha$ particle will be
Answer: (D) $8:1$
$\lambda = \dfrac{h}{mv} \Rightarrow v = \dfrac{h}{m\lambda}$.
$$\frac{v_p}{v_\alpha} = \frac{m_\alpha\lambda_\alpha}{m_p\lambda_p} = \frac{4m\times2\lambda}{m\times\lambda} = 8$$
So $v_p : v_\alpha = 8:1$.
Solution by Sreeraj P, M.Sc Physics