As The de-Broglie wavelength is given as
where p=momentum
As given The de-Broglie wavelength associated with a proton and a neutron are found to be equal.
that means they both will have same p (momentum)
Now kinetic energy is given as
Since for both p is same
So we can say that
and
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.