Modern Physics

The de-Broglie wavelength is given by the relation: where is Planck's constant and is the momentum of the particle.
If two particles — in this case, a photon and an alpha particle — have the same de-Broglie wavelength, then their momenta must be equal because: Hence, both must have the same momentum.
However, since their masses and natures are different, their energy and frequency will not be the same.