Calculate the wavelength of an electron moving with a velocity of $2.05 \times 10^{7} \,m s^{-1}$.

Calculate the de-Broglie wavelength of an electron travelling at $1\%$ of the speed of light.

The de-Broglie's wavelength of an electron present in the first Bohr orbit of an $H$ atom is:

The de Broglie wavelength of an electron in the $4^{th}$ Bohr orbit is (in $\pi a_{0}$)

The wavelength of electrons accelerated from rest through a potential difference of $40 \, kV$ is $X \times 10^{-12} \, m$. The value of $X$ is $......$. (Nearest integer)
Given:
Mass of electron $= 9.1 \times 10^{-31} \, kg$
Charge on an electron $= 1.6 \times 10^{-19} \, C$
Planck's constant $= 6.63 \times 10^{-34} \, J \cdot s$

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