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  4. What will be the ratio of de-Broglie wavelengths of proton and a-particle of the same energy?

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Q. What will be the ratio of de-Broglie wavelengths of proton and a-particle of the same energy?

AMUAMU 2017

Solution:

de-Broglie wavelength, $\lambda = \frac{h}{p} $
$= \frac{h}{\sqrt{2mKE}}$
For particles of same energy, $\lambda \propto \frac{1}{\sqrt{m}} $
$\therefore \frac{\lambda_p}{\lambda_\alpha} = \sqrt{\frac{m_\alpha}{m_p}} $
$= \sqrt{\frac{4m_p}{m_p}} = \frac{2}{1}$