Which hydrogen-like species will have the same radius as that of the $1^{st}$ Bohr orbit of a hydrogen atom?

In the spectrum of $Li^{2+}$,the difference between two energy levels is $2$ and their sum is $4$. Find the wavelength of the photon emitted during the transition between these two energy states.

The energy of the electron in the first orbit of $He^{+}$ is $-871.6 \times 10^{-20} \ J$. The energy of the electron in the first orbit of hydrogen would be

The wavelength of a spectral line emitted by a hydrogen atom in the Lyman series is $\frac{16}{15 R} \ cm$. What is the value of $n_2$? $(R = \text{Rydberg constant})$

$(i)$ What is the energy of an electron for hydrogen in $J \ atom^{-1}$ and $J \ mol^{-1}$?
$(ii)$ Calculate the energy of this electron per mole for the first transition ($n=1$ to $n=2$).
$(iii)$ Calculate the ionization energy of hydrogen.

In a hydrogen atom,electrons are excited to the $5^{th}$ quantum level. How many different spectral lines may appear in the emission spectrum?