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

The wavelength of a particular electron transition for $He^{+}$ is $100 \ nm$. The wavelength (in $\mathring{A}$) of $H$ atom for the same transition is

With increasing Principal Quantum number,the energy difference between adjacent energy levels in $H$ atom:

Neon gas is generally used in sign boards. If it emits strongly at $616 \, nm$,calculate $(a)$ the frequency of emission,$(b)$ distance traveled by this radiation in $30 \, s$,$(c)$ energy of a quantum,and $(d)$ number of quanta present if it produces $2 \, J$ of energy.

In the hydrogen spectrum,if an electron transitions from the $6^{th}$ orbit to the $3^{rd}$ orbit,what is the total number of spectral lines produced?

In an electron transition from an infinite state to the ground state in an $H$ atom,find the emitted wavelength. (in $nm$)