The energy $E$ of a hydrogen atom with principal quantum number $n$ is given by $E = \frac{-13.6}{n^2} \; eV$. The energy of a photon emitted when the electron jumps from the $n = 3$ state to the $n = 2$ state of hydrogen is approximately......$eV$.

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:

How much energy is needed to release the electron from the second excited state in the hydrogen atom (in $eV$)?

For a certain hypothetical one-electron atom,the wavelength (in $\mathring{A}$) for the spectral lines for transition from $n = p$ to $n = 1$ is given by $\lambda = \frac{1500p^2}{p^2 - 1}$ (where $p > 1$). The ionization potential of this element must be ......$V$ (Take $hc = 12420 \text{ eV-} \mathring{A}$).

In the Bohr model of the hydrogen atom,what is the energy required to remove an electron from the ground state $(n = 1)$ (in $eV$)?

The diagram below shows the lowest four energy levels for an electron in a hypothetical atom. The electron is excited to the $-1\,eV$ level and transitions to the lowest energy state $(-12\,eV)$ by emitting exactly two photons. Which of the following energies could not belong to either of the photons (in $eV$)?