Question

If a proton and an electron happen to possesthe same de Broglie wavelength, which among them will have highest velocity

Answer 1

They would both have the same momentum, since the de Broglie wavelength λ is given by the formula; λ = h/p, where p is the momentum. Momentum is given by the formula; p = mv, where m is the mass, and v is the velocity. So if M and V, and m and v, are the mass and velocity of the proton and the electron respectively, then; MV = mv, so v/V = M/m. The ratio of the masses of the 2 particles is about 1,836 to 1, so the electron would be traveling 1,836 times more quickly.