If the radius of the first orbit of hydrogen atom is $a_0$, then de Broglie's wavelength of electron in $3^{rd}$ orbit is (in $\pi a_0$)

The De Broglie wavelength $\lambda$ of an electron in the $2^{nd}$ Bohr orbit is:

If the velocity of the electron in Bohr's first orbit is $2.19 \times 10^{6} \, m s^{-1}$, calculate the de Broglie wavelength associated with it.

$A$ proton and a $Li^{3+}$ nucleus are accelerated by the same potential. If $\lambda_{Li}$ and $\lambda_{P}$ denote the de Broglie wavelengths of $Li^{3+}$ and proton respectively,then the value of $\frac{\lambda_{Li}}{\lambda_{P}}$ is $x \times 10^{-1}$. The value of $x$ is ............
(Rounded off to the nearest integer)
(Mass of $Li^{3+} = 8.3 \times \text{mass of proton}$)

The two particles $A$ and $B$ have de Broglie wavelengths $1 \ nm$ and $5 \ nm$ respectively. If the mass of $A$ is four times the mass of $B$,the ratio of kinetic energies of $A$ and $B$ would be

The kinetic energy of a proton wave is $500 \ eV$. Calculate its de Broglie wavelength. (Mass of proton $= 1.67 \times 10^{-27} \ kg$)