The ratio of the difference between the $1^{st}$ and $2^{nd}$ Bohr orbits energy to the difference between the $2^{nd}$ and $3^{rd}$ Bohr orbits energy is:

The longest wavelength of light that can be used for the ionisation of lithium atom $(Li)$ in its ground state is $x \times 10^{-8} \, m$. The value of $x$ is $.....$ (Nearest Integer)
(Given : Energy of the electron in the first shell of the hydrogen atom is $-2.2 \times 10^{-18} \, J$; $h = 6.63 \times 10^{-34} \, Js$ and $c = 3 \times 10^{8} \, ms^{-1}$ )

What is the shortest wavelength for the Paschen series of the $Li^{2+}$ ion?

Calculate the longest wavelength in the hydrogen emission spectrum of the Lyman series $\left(R_H = 109677 \ cm^{-1}\right)$.

Wave number of a spectral line for a given transition is $y \ cm^{-1}$ for $He^{+}$,then its value for $Li^{2+}$ for the same transition is

Find the value of wave number $(\bar{v})$ in terms of Rydberg's constant,when the transition of an electron takes place between two levels of $He^{+}$ ion whose sum is $4$ and difference is $2$.