The ionization potential of a hydrogen atom is $13.6 \text{ eV}$. How much energy needs to be supplied to ionize a hydrogen atom in the first excited state (in $\text{ eV}$)?

The total energy of an electron in the first excited state of the hydrogen atom is about $-3.4 \; eV.$
$(a)$ What is the kinetic energy of the electron in this state?
$(b)$ What is the potential energy of the electron in this state?
$(c)$ Which of the answers above would change if the choice of the zero of potential energy is changed?

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 ionisation energy for the hydrogen atom is $13.6 \ eV$,then the energy required to excite it from the ground state to the next higher state is nearly: (in $eV$)

Which of the following transitions in hydrogen atoms emit photons of highest frequency?

$A$ photon of wavelength $\lambda$ is absorbed by an electron confined to a box of length $L = \sqrt{(35 h \lambda / 8 m c)}$. As a result,the electron makes a transition from state $k=1$ to the state $n$. Subsequently,the electron transitions from the state $n$ to the state $m$ by emitting a photon of wavelength $\lambda^{\prime} = 1.75 \lambda$. Then,