On the basis of dual nature of light, de-Broglie suggested that the dual nature is not only of light, but each moving material particle has the dual nature. He assumed a wave to be associated with each moving material particle which is called the matter-wave. The wavelength of this wave is determined by the momentum of the particle. If $\mathrm{p}$ is the momentum of the particle, the wavelength of the wave associated with it is

$\mathrm{\lambda }=\frac{\mathrm{h}}{\mathrm{p}}$, where $\mathrm{h}$ is Planck's constant.

Since, it is given that, alpha, beta and gamma rays carry the same momentum, so they will have the same wavelength.