If the first excitation potential of a hypothetical hydrogen-like atom is $15 \ V$,then the third excitation potential of the atom is

$A$ difference of $5.4 \ eV$ separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level? (Take $1 \ eV = 1.6 \times 10^{-19} \ J$,$h = 6.625 \times 10^{-34} \ Js$)

The figure shows the energy levels of a certain atom. When the electron de-excites from $3E$ to $E$,an electromagnetic wave of wavelength $\lambda$ is emitted. What is the wavelength of the electromagnetic wave emitted when the electron de-excites from $\frac{5E}{3}$ to $E$?

An electron makes a transition from an excited state to the ground state of a hydrogen-like atom. Out of the following statements, which one is correct?

$A$ hydrogen sample is prepared in a particular excited state $A$ of quantum number $n_A=3$. The ground state energy of the hydrogen atom is $-|E|$. Photons of energy $\frac{|E|}{12}$ are absorbed by the sample,which results in the excitation of some electrons to an excited state $B$ of quantum number $n_B$. The value of $n_B$ is:

If $\lambda_1$ and $\lambda_2$ are the wavelengths of the photons emitted when electrons in the $n^{\text{th}}$ orbit of a hydrogen atom fall to the first excited state and ground state respectively,then the value of $n$ is: