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An electron and alpha particle have the ...

An electron and alpha particle have the same de-Broglie wavelength associated with them. How are their kinetic energies related to each other?

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The wavelength associated with electron is greater. Wavelength of an electron is `lamda_(e)= (h)/(sqrt(2m_(e )E_(e )))` …(i)
and the wavelength of an `alpha`-particle is:
`lamda_(a)= (h)/(sqrt(2m_(alpha) E_(alpha)))` ..(ii)
`because lamda_(e) = lamda_(alpha) rArr (h)/(sqrt(2m_(e )E_(e )))= (h)/(sqrt(2m_(alpha) E_(alpha)))`
`rArr (E_(e ))/(E_(alpha))= (m_(alpha))/(m_(e ))`
As `m_(alpha) gt m_(e)`
`rArr (m_(alpha))/(m_(e )) gt 1`
`rArr (E_(e))/(E_(alpha))gt 1`
`rArr E_(e) gt E_(alpha)`
So K.E. of electron is more than that of `alpha`-particle
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