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 energy of an electron in the ground state of a hydrogen atom is $E$. What is the energy of an electron in the $2^{nd}$ excited state of $Li^{++}$?

Suppose an electron is attracted towards the origin by a force $F = \frac{k}{r}$,where $k$ is a constant and $r$ is the distance of the electron from the origin. By applying the Bohr model to this system,the radius of the $n^{th}$ orbital of the electron is found to be $r_n$ and the kinetic energy of the electron is $K_n$. Then which of the following is true?

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 ......... $\mathring{A}$.

$A$ sample of hydrogen-like atoms produces an emission spectrum consisting of $10$ wavelengths arising from all possible transitions. During this process,the maximum angular momentum change for an electron transitioning from a higher energy level to a lower energy level is:

The potential energy of an electron in an orbit of a hydrogen atom is $-6.8 \text{ eV}$. The de Broglie wavelength of the electron in this orbit is (where $r_0$ is the Bohr radius).