Find the wavelength of the third line in the Brackett series of the hydrogen spectrum.

The electron energy in a hydrogen atom is given by $E_n = (-2.18 \times 10^{-18})/n^2 \ J$. Calculate the energy required to remove an electron completely from the $n = 2$ orbit. What is the longest wavelength of light in $cm$ that can be used to cause this transition?

According to Bohr's model,the energy of an electron is given by $E = -\frac{2.176 \times 10^{-18}}{n^2} \, J \, atom^{-1}$. Calculate the minimum energy required to remove an electron from the $3^{rd}$ orbit of a $He^{+}$ ion,and also calculate the corresponding wavelength of the photon.

What is the separation energy (in $eV$) for $Be^{3+}$ in the first excited state?

The ratio of the lowest energy in terms of wave numbers of the Balmer and Lyman series of lines of the atomic spectrum of hydrogen is

The radius of a hydrogen atom in its ground state is $0.53 \ \mathring{A}$. The radius of the $Li^{2+}$ ion in the same state (atomic number = $3$) is ............. $\mathring{A}$.