If '$X$' is the ionization energy of hydrogen,then the energy required for the excitation of a $Li^{2+}$ electron from the $2^{nd}$ excited state to the $5^{th}$ excited state is:

The potential energy of an electron present in $He^{+}$ is:

$A$ single-electron species has a nuclear charge of $+Ze$,where $Z$ is a constant. The energy required to excite an electron from the $2^{nd}$ Bohr orbit to the $3^{rd}$ Bohr orbit is $47.2 \ eV$. Calculate the value of $Z$.

The radius of the electron in the first excited state of a hydrogen atom is:

Light of frequency $1.6 \times 10^{16} \ Hz$ falling on a metal plate emits electrons that have double the kinetic energy compared to the kinetic energy of electrons emitted when light of frequency $1.0 \times 10^{16} \ Hz$ falls on the same plate. The threshold frequency $(v_0)$ of the metal in $Hz$ is:

What is the maximum number of emission lines when the excited electron of an $H$ atom in $n=6$ drops to the ground state?