What is the excited state of an atom?

The ionisation energy of a hydrogen atom is $13.6 \, eV$. Following Bohr's theory,the energy corresponding to a transition between the $3^{rd}$ and the $4^{th}$ orbit is.....$eV$.

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:

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 $eV$)?

Assertion : Between any two given energy levels,the number of absorption transitions is always less than the number of emission transitions.
Reason : Absorption transitions start from the lowest energy level only and may end at any higher energy level. But emission transitions may start from any higher energy level and end at any energy level below it.

If the binding energy of a ground state electron in a hydrogen atom is $13.6\,eV$,then the energy required to remove the electron from the second excited state of $Li^{2+}$ will be $x \times 10^{-1}\,eV$. The value of $x$ is $...........$