The angular momentum of an electron in a stationary state of $Li^{2+} (Z=3)$ is $\frac{3h}{\pi}$. The radius and energy of that stationary state are respectively:

When electromagnetic radiation of wavelength $310 \ nm$ falls on the surface of a metal having work function $3.55 \ eV$,the velocity of photoelectrons emitted is $x \times 10^5 \ ms^{-1}$. The value of $x$ is (Nearest integer). Given: $m_{e} = 9 \times 10^{-31} \ kg$,$h = 6.63 \times 10^{-34} \ J \cdot s$,$c = 3 \times 10^8 \ m/s$,$1 \ eV = 1.6 \times 10^{-19} \ J$.

If $\lambda_0$ and $\lambda$ are respectively the threshold wavelength and wavelength of incident light,the velocity of photoelectrons ejected from the metal surface is

The radii of the first Bohr orbit of $H$ $(r_{H})$,$He^{+}$ $(r_{He^{+}})$ and $Li^{2+}$ $(r_{Li^{2+}})$ are in the order

The radius of the second excited state of $Li^{2+}$ is ................ $\mathring{A}$.

The observation of the line spectrum of the hydrogen atom indicates that