Question

If alpha particle and deutron move with velocity $v$ and $2v$ respectively, the ratio of their de-Broglie wavelength will be ______

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

Answer 1

The correct option is C $1:1$

de-Broglie wavelength $\lambda =\frac{h}{mv}$
$⟹\frac{{\lambda }_{\alpha }}{{\lambda }_d}=\frac{m_d{v}_d}{m_{\alpha }{v}_{\alpha }}$
We know, $m_{\alpha }=2m_d$
Given : $v_{\alpha }=v$ and $m_d=2v$
$⟹\frac{{\lambda }_{\alpha }}{{\lambda }_d}=\frac{m_d\left(2v\right)}{2m_{d}v}=1$
So, option C is correct.