The $log-log$ graph between the energy $E$ of an electron and its de-Broglie wavelength $\lambda$ will be

An electron microscope uses electrons of $40 \ keV$. The de Broglie wavelength associated with these electrons is approximately:

The ratio of momenta of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of $100 \ V$ is

The de Broglie wavelength of a proton and $\alpha$-particle are equal. The ratio of their velocities is ...... .

$A$ particle having electric charge $3 \times 10^{-19} \text{ C}$ and mass $6 \times 10^{-27} \text{ kg}$ is accelerated by applying an electric potential of $1.21 \text{ V}$. The wavelength of the matter wave associated with the particle is $\alpha \times 10^{-12} \text{ m}$. The value of $\alpha$ is . . . . . . . (Take Planck's constant $h = 6.6 \times 10^{-34} \text{ J} \cdot \text{s}$)

The wavelength of light from the spectral emission line of sodium is $589 \; nm$. Find the kinetic energy at which
$(a)$ an electron,and
$(b)$ a neutron,would have the same de Broglie wavelength.