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

Based on the equation $E = -2.178 \times 10^{-18} \ J \left( \frac{Z^2}{n^2} \right)$,certain conclusions are written. Which of them is not correct?

In the hydrogen spectrum,a line corresponds to a transition from the $3^{rd}$ to the $5^{th}$ orbit. Identify the series to which this transition belongs.

What is the wave number of the lowest energy transition associated with the Lyman series?

If the radius of the first orbit of a hydrogen-like ion is $1.763 \times 10^{-2} \ nm$, the energy associated with that orbit (in $J$) is

The ionization energy of a hydrogen atom is $13.6 \ eV$. The energy required to excite the electron in a hydrogen atom from the ground state $(n=1)$ to the first excited state $(n=2)$ is (Note: The question asks for energy per atom in Joules. Given $1 \ eV = 1.602 \times 10^{-19} \ J$)