The ratio of the radius of the $2^{nd}$ orbit of $H$ to the radius of the $3^{rd}$ orbit of $He^{+}$ is ......

Which of the following orders is $NOT$ correct for the $1^{st}$,$2^{nd}$,and $3^{rd}$ orbits of a hydrogen-like atom?

How many emission spectral lines are possible when a hydrogen atom is excited to the $n$th energy level?

Supposing the energy (in arbitrary units) of the energy levels in the hydrogen atom is given as under:

Energy level	$K$ $(n=1)$	$L$ $(n=2)$	$M$ $(n=3)$	$N$ $(n=4...n=\infty)$
Energy	$-864 \ a.u.$	$-216 \ a.u.$	$-96 \ a.u.$	$0 \ a.u.$

The excitation energy needed to raise the electron from $M$ level to $n = \infty$ would be:

As an electron moves away from the nucleus,its energy:

Emission transitions in the Paschen series end at orbit $n=3$ and start from orbit $n$ and can be represented as $\nu = 3.29 \times 10^{15} \, Hz \left(\frac{1}{3^2} - \frac{1}{n^2}\right)$. Calculate the value of $n$ if the transition is observed at $1285 \, nm$. Find the region of the spectrum.