The radii of the first four Bohr orbits of the hydrogen atom are related as:

How is the linear velocity $v$ of an electron in a $Bohr$ orbit related to its principal quantum number $n$?

If the radius of the first orbit of a hydrogen atom is $5.29 \times 10^{-11} \, m$,the radius of the fourth orbit will be ......... $\mathring{A}$.

$A$ light of energy $12.75 \; eV$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $\frac{x}{\pi} \times 10^{-17} \; eVs$. The value of $x$ is $........$ (use $h=4.14 \times 10^{-15} \; eVs$)

The energy of $He^{+}$ ion in its first excited state is $......eV$ (The ground state energy for the Hydrogen atom is $-13.6\,eV$).

The radius of the first (lowest) orbit of the hydrogen atom is $a_0$. The radius of the second (next higher) orbit will be (in $a_0$)