Find the energy of the third stationary orbit of Bohr's model of the hydrogen atom if the energy of the ground state is $-E \text{ J}$.

Angular momentum of an electron in a hydrogen atom is $\frac{3h}{\pi}$, then the energy of the electron is . . . . . . eV.

Suppose in a hypothetical world, the angular momentum is quantized to be even integral multiples of $\frac{h}{2 \pi}$. According to Bohr's model, what will be the largest possible wavelength emitted by hydrogen atoms in the visible range in this world (in $\text{ nm}$)? (Consider $hc = 1242 \text{ eV-nm}$)

To accommodate the view that matter is made up of $5$ elements only,a scientist proposed the following hypothesis: atoms can have a maximum principal quantum number $n_{\max}$ and no higher. Then,which of the following statements must be true?

In a hydrogen atom,the radius of the $n^{th}$ Bohr orbit is $r_n$. The graph between $\log \left( \frac{r_n}{r_1} \right)$ and $\log n$ will be:

In a hydrogen atom and a $Li^{2+}$ ion,the electron is in the second excited state. If $l_{H}$ and $l_{Li}$ are the angular momenta of the electrons and $E_H$ and $E_{Li}$ are their respective energies,then: