On the basis of dual nature of light, Lious 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 $p$ is the momentum of the particle, the wavelength of the wave associated with it is
$\lambda=\frac{h}{p}$
where $h$ is Planck's constant.
Since, it is given that, alpha, beta and gamma rays carry same momentum, so they will have same wavelength.