An electron, an $\mathrm{\alpha }$ - particle and a proton have the same kinetic energy. Shortest de - Broglie wavelength is associated with

All the particles have same kinetic energy but their masses are different.

The de-Broglie wavelength associated with each of them in terms of mass m and kinetic energy E is given as:

$\lambda = \frac{h}{\sqrt{2mE}}$

From the relation, if kinetic energy E is constant, de Broglie wavelength decreases with increase in mass of particle.

since the mass of $\mathrm{\alpha }-$ particle is highest, therefore it will have shortest wavelength.