Question

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

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

Answer 1

Answer: (C)

$4:1$

Given de Broglie Wavelength ${\lambda }_p={\lambda }_{\alpha }$

So, $\frac{h}{m_p\times v_p}$ = $\frac{h}{m_{\alpha }\times v_{\alpha }}$

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

Because Mass of $\alpha$ particle is 4 times mass of proton.

So 4:1.

Option C is correct answer