As the quantum number $n$ increases,the difference in energy between consecutive energy levels

The ionisation potential of hydrogen atom is $13.6 \ V$. The energy required to remove an electron from the second orbit of hydrogen is......$eV$.

Energy of a stationary electron in the hydrogen atom is $E = -\frac{13.6}{n^2} \text{ eV}$. Calculate the energies required to excite the electron in a hydrogen atom to $(a)$ its second excited state and $(b)$ its ionized state,respectively.

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.

In an inelastic collision,an electron excites a hydrogen atom from its ground state to an $M$-shell state. $A$ second electron collides instantaneously with the excited hydrogen atom in the $M$-state and ionizes it. At least how much energy must the second electron transfer to the atom in the $M$-state?

In the third orbit of a hydrogen atom,the energy of an electron is $E$. In the fifth orbit of a helium ion $(Z=2)$,the energy of an electron will be: