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An electron and an alpha particle have s...

An electron and an alpha particle have same kinetic energy. How are the de Broglie wavelengths associated with them related ?

Text Solution

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Kinetic energy of the particle `K = (1)/(2) mv^(2) = (p^(2))/(2m) = (h^(2))/(2m lambda^(2))" "[lambda = (h)/(p)]`
i.e. `lambda = (h)/(sqrt(2mK)), lambda prop (1)/(sqrt(m))`
`(lambda_(e))/(lambda_(a)) = sqrt((m_(a))/(m_(e)))`
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