In a hydrogen atom,if $9 \, eV$ of energy is supplied,how many spectral lines will be emitted?

The energy of the third orbit of $Li^{2+}$ ion (in $J$) is

In the atomic spectrum of hydrogen, the wavelengths of the spectral lines corresponding to electronic transitions $(i)$ $n=4$ to $n=2$ and $(ii)$ $n=3$ to $n=1$ are $\lambda_1$ and $\lambda_2$ $\mathring{A}$ respectively. The value of $(\lambda_1-\lambda_2)$ (in cm) is ($R_H$ = Rydberg constant)

Given below are two statements:
Statement $I$: Bohr's theory accounts for the stability and line spectrum of $Li^{+}$ ion.
Statement $II$: Bohr's theory was unable to explain the splitting of spectral lines in the presence of a magnetic field.
In the light of the above statements,choose the most appropriate answer from the options given below:

For a $H$-atom,what is the wavelength in $nm$ associated with the transition of an electron from an infinite energy level to the first energy level? (Rydberg constant = $1.097 \times 10^{7} \ m^{-1}$)

Calculate the energy associated with the first orbit of $He^{+}$. What is the radius of this orbit?