First slide

Wave nature of matter

Question

What will be the ratio of de-Broglie wavelengths of proton and $α$ -particle of same energy?

Moderate

Solution

$λ = \frac{h}{\sqrt{2 m E}} \Rightarrow λ \propto \frac{1}{\sqrt{m}} \Rightarrow \frac{λ_{p}}{λ_{α}} = \sqrt{\frac{m_{α}}{m_{p}}} = \frac{2}{1}$

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