Question

The de-Broglie wavelength associated with a proton and a neutron are found to be equal. Which of the two has a higher value of kinetic energy?

Answer 1

another name for the de-broglie wavelength is  the matter wave

 its relations show that the wavelenght is inversely prportional to the momentum of a particle...  also the frequency of the matter waves is directly prortional to the total energy
 of a particle
λ =h/p
 λ=h/mv
v=h/mλ
 Kinetic energy = 1/2*mv2
 Substituting, K.E = 1/2*h2/mλ2
 as we can see, K.E ∝ 1/m
 mass of proton = 1.6726 x 10-27 kg
mass of neutron = 1.6749 x 10-27 kg
Therefore, since a proton has a lighter mass, it will have a higher value of kinetic energy.