devarshi-dt-logo

Question:

A proton and an electron have the same kinetic energy. Which one has a smaller de Broglie wavelength and why?

Solution:

de Broglie wavelength λ = h/p where p = √(2mE) ∴ λ = h/√(2mE) ⇒ λ ∝ 1/√m (Since E = constant) As mₑ < mₚ ⇒ λₚ < λₑ Thus proton has smaller wavelength.