The ratio of velocities of a proton and an $\alpha$ particle is 4 : 1. The ratio of their de Broglie wave lengths will be

                            q    m   v
Proton   →           1     1   4
  α  –particle →    2     4   1

$$\begin{gathered} \lambda =\frac{h}{mv} \\ \Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{m_2}{m_1}\frac{v_2}{v_1}=\frac{4}{1}\times \frac{1}{4}=\frac{1}{1} \end{gathered}$$