Let $r, v, E$ be the radius of orbit, speed of electron, and total energy of electron respectively in a $H$-atom. Which of the following quantities, according to Bohr theory, is proportional to the quantum number $n$?

If the first excitation potential of a hydrogen-like atom is $V \, \text{volt}$, then the ionization energy of this atom will be

In the Bohr's hydrogen atom model,the radius of the stationary orbit is directly proportional to ($n =$ principle quantum number)

For a certain hypothetical one-electron atom,the wavelength (in $\mathring{A}$) for the spectral lines for transition from $n = p$ to $n = 1$ is given by $\lambda = \frac{1500p^2}{p^2 - 1}$ (where $p > 1$). The ionization potential of this element must be .....$V$ (Take $hc = 12420\ eV\cdot\mathring{A}$).

Obtain the first Bohr's radius and the ground state energy of a muonic hydrogen atom [i.e.,an atom in which a negatively charged muon $(\mu^-)$ of mass about $207 m_{e}$ orbits around a proton].

The radius of the innermost electron orbit of a hydrogen atom is $5.3 \times 10^{-11} \text{ m}$. What is the radius of the $n = 3$ orbit?