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# The de Broglie wavelength

Question:

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

1. $4: 3$

2. $4: 1$

3. $4: 2$

4. $1: 4$

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