The de-Broglie wavelengths of two fast moving particles $X, Y$ are $1 \mathrm{~nm}, 3 \mathrm{~nm}$ respectively. Mass of $X$ is nine times the mass of $Y$. The ratio of kinetic energies of $X, Y$ is

The difference between the radii of 3rd and 2nd orbit of H -atom is $x \mathrm{pm}$. The difference between the radii of 4th and 3rd orbit of $\mathrm{Li}^{2+}$ ion is $y$ pm. $y: x$ is equal to

The de-Broglie wavelength of an electron in the third Bohr orbit of H -atom is

The wavenumber of the first line $\left(n_2=3\right)$ in the Balmer series of hydrogen is overline $\bar{v}_1 \mathrm{~cm}^{-1}$. What is the wavenumber (in $\mathrm{cm}^{-1}$ ) of the second line ( $n_2=4$ ) in the Balmer series of $\mathrm{He}^{+}$?