Out of an electron and a proton,which one will have a higher velocity to produce matter waves of the same wavelength? Explain.

(A) According to the de Broglie relation,the wavelength $\lambda$ is given by $\lambda = \frac{h}{mv}$,where $h$ is Planck's constant,$m$ is the mass of the particle,and $v$ is its velocity.
Since the wavelength $\lambda$ is the same for both particles,the product $mv$ must be constant $(mv = \frac{h}{\lambda} = \text{constant})$.
This implies that $v \propto \frac{1}{m}$.
Since the mass of an electron $(m_e \approx 9.11 \times 10^{-31} \ kg)$ is much smaller than the mass of a proton $(m_p \approx 1.67 \times 10^{-27} \ kg)$,the electron must have a higher velocity to maintain the same wavelength.