Let $$\lambda$$_p, $$\lambda$$_$$\alpha$$, m_p, m_$$\alpha$$, v_p, v_$$\alpha$$, p_p and p_$$\alpha$$ be the wavelength, mass, velocity and momentum of proton and $$\alpha$$-particle, respectively.

Given, $$\lambda$$_p = $$\lambda$$_$$\alpha$$

As we know that,

$$\lambda$$ = h/p

$$\therefore$$ $${h \over {{p_p}}} = {h \over {{p_\alpha }}}$$

$$\Rightarrow$$ p_p = p_$$\alpha$$

$$\Rightarrow$$ m_pv_p = m_$$\alpha$$v_$$\alpha$$

$$\Rightarrow$$ m_pv_p = 4m_pv_$$\alpha$$ ($$\because$$ m_$$\alpha$$ = 4m_p)

$$\Rightarrow$$ $${{{v_p}} \over {{v_\alpha }}} = {4 \over 1}$$ or 4 : 1