Final answer:
The de Broglie wavelengths of particles are determined by their momentum, which is related to their mass and kinetic energy. In this case, the proton, neutron, electron, and alpha particle have the same energy, so their de Broglie wavelengths compare according to their masses. The correct answer is Option A: λproton=λneutron<λelectron<λalpha.
Step-by-step explanation:
The de Broglie wavelength, given by λ = h/p, is a fundamental concept in quantum mechanics that relates the wavelength of a particle to its momentum. In this case, since the proton, neutron, electron, and alpha particle all have the same energy, their kinetic energies are equal. As a result, their momenta, and therefore their de Broglie wavelengths, are determined by their masses.
Since the proton and neutron have similar masses, their de Broglie wavelengths will be similar. The electron, being much lighter, will have a shorter de Broglie wavelength, and the alpha particle, being much heavier, will have a longer de Broglie wavelength. Therefore, the correct option is Option A. λproton=λneutron<λelectron<λalpha.