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A proton and an alpha particle, both ini...

A proton and an alpha particle, both initially at rest, are accelerated so as to have the same kinetic energy. What is the ratio of their de-Broglie wavelength ?

Text Solution

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de-Broglie wavelength,
`lambda = (h)/(p) = (h)/(sqrt(2 mK))`
i.e. `lambda prop (1)/(sqrt(m)) " "[m_(alpha) = 4 m_(p)]`
`(lambda_(p))/(lambda_(alpha)) = sqrt((m_(alpha))/(m_(p))) = sqrt((4 m_(p))/(m_(p))) = sqrt((4)/(1)) = (2)/(1)`
`lambda_(p) : lambda_(alpha) = 2 : 1`
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