An electron moves in an electric field with a kinetic energy of $2.5 \, eV$. The de Broglie wavelength associated with it is .....

Calculate the wavelength in nanometers associated with a particle moving with a velocity of $1.0 \times 10^3 \, m s^{-1}$. (Given: mass $m = 1.67 \times 10^{-27} \, kg$ and Planck's constant $h = 6.63 \times 10^{-34} \, J s$)

If the de Broglie wavelength of the electron in the $n^{th}$ Bohr orbit in a hydrogenic atom is equal to $1.5 \, \pi \, a_0$ ($a_0$ is Bohr radius),then the value of $n/Z$ is:

$A$ stream of electrons from a heated filament was passed between two charged plates kept at a potential difference $V$ esu. If $e$ and $m$ are the charge and mass of an electron, respectively, then the value of $h/\lambda$ (where $\lambda$ is the wavelength associated with the electron wave) is given by:

Given the ratio of kinetic energy of an electron in two orbitals is $16:9$. Calculate the ratio of the wavelength of the electron waves.

Calculate the $\lambda$ associated with an electron moving with the velocity of light.