The de Broglie wavelength of a particle is given by the equation:
λ = h / p
where λ is the wavelength, h is the Planck constant, and p is the momentum of the particle. Since momentum is defined as the product of mass and velocity (p = mv), we can rewrite the equation as:
λ = h / (mv)
From this equation, we can see that the wavelength is inversely proportional to the product of mass and velocity.
If an electron and a proton have the same wavelength, and we assume their masses are constant, then the velocity of the particles must be inversely proportional to their masses. Since the mass of an electron (me) is significantly smaller than the mass of a proton (mp), the electron would have a higher velocity compared to the proton in order to maintain the same wavelength.
In other words, the electron would have a higher speed than the proton if they have the same wavelength.