A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ . An alpha particle having certain kinetic energy has the same de-Brogle wavelength λ . The ratio of kinetic energy of proton and that of alpha particle is :

Step-by-step solution

As we know, de Broglie wavelength is given by, λ = h p Now kinetic energy can be written as, K = 1 2 m v 2 = p 2 2 m = h 2 2 m λ 2 Therefore, K ∝ 1 m Hence, required ratio K p K α = m α m p = 4 ⇒ m α : m p = 4 : 1