If proton and electron have same de-Broglie wavelength then….

Options

A. both will have same kinetic energy
B. kinetic energy of proton will be more than kinetic energy of electron
C. kinetic energy of electron will be more than kinetic energy of proton
D. Both will have same velocity

Answer

C

Explanation

de-Broglie wavelength `lambda=(h)/(mv)`
Here `lambda` is same (given)
`therefore (h)/(m_(p)v_(p))=(h)/(m_(e)v_(e))`
`therefore m_(p)v_(p)=m_(e)v_(e)`
`(v_(p))/(v_(e))=(m_(e))/(m_(p))`
`therefore (E_(p))/(E_(e))=((1)/(2)m_(p)vp^(2))/((1)/(2)m_(2)v_(e)^(2))`
`=(m_(p))/(m_(e))xx((m_(e))/(m_(p)))^(2)=(m_(e))/(m_(p))`
but `m_(e)ltm_(p)` thus `(m_(e))/(m_(p))lt1`
`therefore (E_(P))/(E_(e))lt1 therefore E_(P)ltE_(e)`