Final answer:
In physics, as a proton and an electron are accelerated to the same kinetic energy, they exhibit different de Broglie wavelengths because of their mass and velocity differences, with the electron having a shorter wavelength.
Step-by-step explanation:
The subject in question involves the concept of the de Broglie wavelength in physics, which relates the momentum of a particle to its wavelength as a wave. The given scenario is of a proton and an electron being accelerated to the same final kinetic energy, which implies they will have different wavelengths due to their mass difference. According to the de Broglie hypothesis, the wavelength λ is inversely proportional to the momentum p of the particle, given by λ = h/p, where h is Planck's constant and p is the momentum of the particle.
Since kinetic energy K is given by K = p^2/(2m), and both particles are accelerated to the same kinetic energy K, we can understand that a lighter particle like the electron must have a greater velocity to achieve the same kinetic energy as the heavier proton. Consequently, the electron will have a greater momentum and thus a shorter de Broglie wavelength (λe) compared to the proton's de Broglie wavelength (λp), assuming non-relativistic speeds where the momentum p can be defined as p = mv (mass times velocity).