Question

The de-Broglie wavelength of a proton and alpha particle is same, the ratio of their velocities is :

• A. 1:2
• B. 2:1
• C. 1:4
• D. 4:1

Answer 1

The correct option is D 4:1

de-Broglie wavelength, $\lambda =\frac{h}{mv}$

$⟹v=\frac{h}{m\lambda }$

We get $\frac{v_p}{v_{\alpha }}=\frac{m_{\alpha }}{m_p}$

Given : $m_{\alpha }=4m_p$

$\therefore$ $\frac{v_p}{v_{\alpha }}=\frac{4m_p}{m_p}=4$