For an emission line of atomic hydrogen from $n_i = 8$ to $n_f = n$,the plot of wave number $(\bar{\nu})$ against $(\frac{1}{n^2})$ will be (The Rydberg constant,$R_H$ is in wave number unit).

In the hydrogen atomic spectrum,a series limit is found at $12186.3 \ cm^{-1}$. To which series does it belong?

The radius of a hydrogen atom in its ground state is $0.53 \ \mathring{A}$. The radius of the $Li^{2+}$ ion in the same state (atomic number = $3$) is ............. $\mathring{A}$.

The work function for a metal is $4 \, eV$. To emit a photo electron of zero velocity from the surface of the metal,the wavelength of incident light should be : ................ $\mathring{A}$

The total energy of the electron in the hydrogen atom in the ground state is $-13.6 \, eV$. What is the stopping potential in volts required to remove this electron from the ground state?

An electromagnetic radiation of wavelength $331.5 \ nm$ is made to strike the surface of a metal. Electrons are emitted with a kinetic energy of $1.2 \times 10^5 \ J \ mol^{-1}$. The work function (in $eV$) of the metal is (given: $h=6.63 \times 10^{-34} \ Js$, $N_{A}=6 \times 10^{23} \ mol^{-1}$, $1 \ eV = 1.6 \times 10^{-19} \ J$)?