Question

The de Broglie wavelength of a proton and $\alpha$ -particle are equal. The ratio of their velocities is :

• A. $4:3$
• B. $4:1$
• C. $4:2$
• D. $1:4$

Answer 1

Answer: (B)

$\lambda =\frac{h}{mv}$
${\lambda }_P={\lambda }_{\alpha }$
$m_P{v}_P=m_{\alpha }{v}_{\alpha }$
$m_P{v}_P=4m_p{v}_{\alpha }\left(m_{\alpha }=4m_P\right)$
$\frac{v_P}{v_{\alpha }}=4$