Question:
The de Broglie wavelength of a proton and $\alpha$-particle are equal. The ratio of their velocities is :
Correct Option: , 2
Solution:
$\lambda=\frac{\mathrm{h}}{\mathrm{mv}}$
$\lambda_{\mathrm{P}}=\lambda_{\alpha}$
$m_{P} v_{P}=m_{\alpha} v_{\alpha}$
$m_{P} v_{P}=4 m_{p} v_{\alpha} \quad\left(m_{\alpha}=4 m_{P}\right)$
$\frac{\mathrm{v}_{\mathrm{P}}}{\mathrm{v}_{\alpha}}=4 \quad($ Option 2) is correct