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Q.

The ratio of the de-Broglie wavelength proton and $α -$ particle of same energy is $x / y .$ Then $x + y =$ _____ (with minimum values of $x, y$ )

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answer is 3.

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Detailed Solution

$λ = \frac{h}{m v} = \frac{h}{\sqrt{2 m E}} \Rightarrow \frac{λ_{p}}{λ_{a}} = \sqrt{\frac{m_{a}}{m_{p}}} = \sqrt{\frac{4}{1}} = 2 : 1$

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