The angular momentum of an electron in an $H$ atom in a particular $n$ state is $\frac{h}{\pi}$. What is the energy in $J$ required to excite the electron from this particular $n$ state to $(n+1)$ state? $(x = 2.18 \times 10^{-18} \ J)$

What is the maximum number of different spectral lines obtained when a sample of a large number of $H$-atoms in the $5^{th}$ excited state makes transitions to the ground state,given that no lines are emitted in the Balmer series?

The relation between the stopping potential $(V_0)$ and frequency $(v)$ is correctly represented in $[\phi = \text{Work function}]$

Heat treatment of muscular pain involves radiation of wavelength of about $900 \ nm$. Which spectral line of $H$ atom is suitable for this? Given: Rydberg constant $R_{H}=10^5 \ cm^{-1}, h=6.6 \times 10^{-34} \ J \ s, c=3 \times 10^8 \ m / s$.

When an electric discharge is passed through hydrogen gas,the hydrogen molecules dissociate to produce excited hydrogen atoms. These excited atoms emit electromagnetic radiation of discrete frequencies which can be given by the general formula
$\bar{v} = 109677 \left[ \frac{1}{n_{i}^{2}} - \frac{1}{n_{f}^{2}} \right] \ cm^{-1}$
What points of Bohr's model of an atom can be used to arrive at this formula? Based on these points,derive the above formula,giving a description of each step and each term.

In the spectrum of $Li^{2+}$,the difference between two energy levels is $2$ and their sum is $4$. Find the wavelength of the photon emitted during the transition between these two energy states.