The ionization energy of a hydrogen atom is $13.6 \ eV$. The energy required to excite the electron in a hydrogen atom from the ground state $(n=1)$ to the first excited state $(n=2)$ is (Note: The question asks for energy per atom in Joules. Given $1 \ eV = 1.602 \times 10^{-19} \ J$)

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.

What is the number of photons of light with a wavelength of $4000 \ pm$ that provide $1 \ J$ of energy?

According to Bohr's atomic theory :-
$A$. Kinetic energy of electron is $\propto \frac{Z^{2}}{n^{2}}$.
$B$. The product of velocity $(v)$ of electron and principal quantum number $(n)$,'$vn$' $\propto Z^{2}$.
$C$. Frequency of revolution of electron in an orbit is $\propto \frac{Z^{3}}{n^{3}}$.
$D$. Coulombic force of attraction on the electron is $\propto \frac{Z^{3}}{n^{4}}$.
Choose the most appropriate answer from the options given below :

Select the incorrect graph for the velocity of an electron $(e^-)$ in an orbit vs. $Z$,$\frac{1}{n}$,and $n$.

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