The ratio of kinetic energies of photoelectrons emitted from a metal by light of frequencies $v_1$ and $v_2$ is $1 : 2$. The threshold frequency of the metal will be:

The ground and first excited state energies are $E_1$ and $E_2$ respectively. Which pair of species has the same energy? [Note that energy is indicated in the bracket].

For a $H$ atom,the wavelength for the highest energy transition is $91.2 \ nm$. Calculate the corresponding wavelength for $He^{+}$ in $nm$.

From the following energy levels of a hydrogen atom, the values of $E_{\infty}$ and $E_3$ in $J$ are, respectively: $E_{\infty} = \ldots \ldots \ldots$ $E_3 = \ldots \ldots \ldots$ Given: $E_2 = -0.545 \times 10^{-18} \ J$, $E_1 = -2.18 \times 10^{-18} \ J$.

Assume that the radius of the first Bohr orbit of hydrogen atom is $0.6 \mathring{A}$. The radius of the third Bohr orbit of $He^{+}$ is $..................$ picometer. (Nearest Integer)

Number of spectral lines obtained in $He^{+}$ spectra,when an electron makes transition from fifth excited state to first excited state will be