Physics - Modern Physics Question with Solution | TestHub

According to question, ${\lambda }_p={\lambda }_{\alpha }$ Using, $\lambda =\frac{h}{p}=\frac{h}{mv}$ $$\begin{array}{rl}& \text{ So, }\frac{h}{m_p\times v_p}=\frac{h}{m_{\alpha }\times v_{\alpha }}\\ & \Rightarrow \frac{v_p}{v_{\alpha }}=\frac{m_{\alpha }}{m_p}=\frac{4m_p}{m_p}\end{array}$$ $(\because$ mass of $\alpha$-particle is 4 times of mass of proton) So, $\frac{v_p}{v_{\alpha }}=\frac{4}{1}$; i.e., $4:1$