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

Supposing the energy of the fourth shell for a hydrogen atom is $-25 \, a.u.$ (arbitrary unit). What would be its potential energy in the ground state?

Which of the following equations gives the angular momentum of an electron in a stationary orbit?

What is the kinetic energy of an electron in the second excited state of $He^{+}$? (Energy of an electron in the first shell of $H = -13.6 \ eV$)

If the electron of a hydrogen atom is present in the first orbit, the total energy of the electron is

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.