The energy required to ionise a hydrogen-like ion in its ground state is $9$ Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state? ........$nm$

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).

The de-Broglie wavelength of the electron in the ground state of a hydrogen atom is ........ $\mathring{A}$.

In the Bohr model of a hydrogen atom,the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If ${a_0}$ is the radius of the ground state orbit,$m$ is the mass,$e$ is the charge on the electron,and ${\varepsilon _0}$ is the vacuum permittivity,the speed of the electron is:

$A$ particle of mass $m$ moves in a circular orbit in a central potential field $U(r) = \frac{1}{2}kr^2$. If Bohr's quantization conditions are applied,radii of possible orbits and energy levels vary with quantum number $n$ as

Mention the value of the Rydberg constant with its unit.