If the potential energy of an electron in the second orbit of $He^+$ is $-27.2 \, eV$,then calculate the double value of the energy of the first excited state of a hydrogen atom in $eV$.

Energy levels $A, B, C$ of a certain atom correspond to increasing values of energy,$i.e.,$ $E_A < E_B < E_C$. If $\lambda_1, \lambda_2$ and $\lambda_3$ are the wavelengths of radiations corresponding to the transitions $C$ to $B$,$B$ to $A$ and $C$ to $A$ respectively,which of the following statements is correct?

When an electron transitions from the $n^{th}$ orbit to the $2^{nd}$ orbit in a $Li^{2+}$ ion,$15$ spectral lines are obtained. What is the value of $n$?

The correct representation of the wavelength-intensity relationship of an ideal black body radiation at two different temperatures $T_{1}$ and $T_{2}$ (where $T_{2} > T_{1}$) is:

The energy of an electron in the ground state $(n=1)$ for $He^{+}$ ion is $-x \ J$. What is the energy for an electron in the $n=2$ state for $Be^{3+}$ ion in $J$?

The frequency of one of the lines in the Paschen series of a hydrogen atom is $2.340 \times 10^{11} \ Hz$. The quantum number $n_2$ which produces this transition is