Question

If the de-Broglie wavelengths associated with a proton and $\alpha$ -particle are equal, then the ratio of velocities of the proton and the a-particle will be:

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

Answer 1

The correct option is A $4:1$

$\begin{array}{c}{\lambda }_p=\frac{h}{m{V}_1}\\ {\lambda }_{\alpha }=\frac{h}{4m{v}_2}\\ \Rightarrow \frac{h}{m{v}_1}=\frac{h}{4m{v}_2}\\ \Rightarrow v_1=4v_2\\ \Rightarrow \frac{v_1}{v_2}=4:1\\ Hence,\\ optionAiscorrectanswer.\end{array}$