Question

If an alpha particle and a deuteron move with velocities of $v$ and $2v$ respectively, the ratio of their de-Broglie wavelengths will be

• A. $1:\sqrt{2}$
• B. $2:1$
• C. $1:1$
• D. $\sqrt{2}:1$

Answer 1

The correct option is C $1:1$

Let mass of deuteron be, $m_d=m$
$\Rightarrow m_{\alpha }=2m$
Also, momentum of deuteron will be
$p_d=m\left(2v\right)$
and, $p_{\alpha }=2m\left(v\right)$

Now, $\lambda =\frac{h}{p}$
$\Rightarrow \frac{{\lambda }_{\alpha }}{{\lambda }_d}=\frac{\left(\frac{h}{p_{\alpha }}\right)}{\left(\frac{h}{p_d}\right)}=\frac{p_d}{p_{\alpha }}=\frac{m\left(2v\right)}{2m\left(v\right)}=1$

Hence, $\left(C\right)$ is the correct answer.