The radius of the innermost orbit of a hydrogen atom is $5.3 \times 10^{-11} \ m$. The radius of the third allowed orbit of the hydrogen atom is $... \ \mathring{A}$.

The figure below is the plot of potential energy versus internuclear distance $(d)$ of $H_2$ molecule in the electronic ground state. What is the value of the net potential energy $E_0$ (as indicated in the figure) in $kJ \ mol^{-1}$, for $d=d_0$ at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As reference, the potential energy of $H$ atom is taken as zero when its electron and the nucleus are infinitely far apart.
Use Avogadro constant as $6.023 \times 10^{23} \ mol^{-1}$.

Which of the following is quantized according to Bohr's theory of the hydrogen atom?

The period of revolution of an electron revolving in $n^{th}$ orbit of $H$-atom is proportional to

The radius of the third stationary orbit of an electron for a Bohr atom is $R$. The radius of the fourth stationary orbit will be

In the $n^{\text{th}}$ Bohr orbit,the ratio of the kinetic energy of an electron to the total energy of it is: