The wavelength of the energy emitted when an electron transitions from the fourth orbit to the second orbit in a hydrogen atom is $20.397 \, cm$. The wavelength of the energy for the same transition in $He^+$ is .......... $cm$.

The ground state energy of a hydrogen atom is $-13.6 \text{ eV}$. The potential energy of the electron in this state is: (in $\text{ eV}$)

In a hydrogen atom,the electron and proton are bound at a distance of about $0.53 \; \mathring{A}$.
$(a)$ Estimate the potential energy of the system in $eV$,taking the zero of the potential energy at infinite separation of the electron from the proton.
$(b)$ What is the minimum work required to free the electron,given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in $(a)$?
$(c)$ What are the answers to $(a)$ and $(b)$ above if the zero of potential energy is taken at $1.06 \; \mathring{A}$ separation?

What is the moment of inertia of the electron moving in the second Bohr orbit of a hydrogen atom? ($h=$ Planck's constant,$m=$ mass of electron,$\varepsilon_0=$ permittivity of free space,$e=$ charge on electron)

The time period of revolution of an electron in the $n^{\text{th}}$ orbit in a hydrogen-like atom is given by $T = \frac{T_0 n^a}{Z^b}$,where $Z$ is the atomic number. Identify the correct values for $T_0$,$a$,and $b$.

In Bohr's model of the hydrogen atom,let $PE$ represent potential energy and $TE$ represent total energy. When an electron transitions to a higher energy level,