The following diagram indicates the energy levels of a certain atom. When the system moves from the $2E$ level to the $E$ level, it emits a photon of wavelength $\lambda$. What is the wavelength of the photon produced during its transition from the $\frac{4E}{3}$ level to the $E$ level?

During the transition of an electron from state $A$ to state $C$ of a Bohr atom,the wavelength of the emitted radiation is $2000 \ \mathring A$ and it becomes $6000 \ \mathring A$ when the electron jumps from state $B$ to state $C.$ Then the wavelength of the radiation emitted during the transition of electrons from state $A$ to state $B$ is

The wavelength of the radiation emitted is $\lambda_0$ when an electron jumps from the second excited state to the first excited state of a hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom,the wavelength of the radiation emitted will be $\frac{20}{x} \lambda_0$. The value of $x$ is $........$

The potential energy of the orbital electron in the ground state of a hydrogen atom is $-E$. What is its kinetic energy?

An electron collides elastically with an $H$-like atom and excites it from the ground state to $n = 3$. Find the energy transferred to the $H$-like atom in $eV$.

Find the ratio of energies of photons produced due to the transition of an electron in a hydrogen atom from its $(i)$ second permitted energy level to the first level,and $(ii)$ the highest permitted energy level to the first permitted level.