The $21\, cm$ radio wave emitted by hydrogen in interstellar space is due to the interaction called the hyperfine interaction in atomic hydrogen. The energy of the emitted wave is nearly

The ionization energy of hydrogen is $13.6 \, eV$. If $h = 6.6 \times 10^{-34} \, J \cdot s$,the order of magnitude of the Rydberg constant $R$ will be:

The radius of the first permitted Bohr orbit for the electron in a hydrogen atom equals $0.53 \mathring{A}$ and its ground state energy equals $-13.6 \; eV$. If the electron in the hydrogen atom is replaced by a muon $(\mu^{-})$ [charge same as electron and mass $207 m_{e}$], the first Bohr radius and ground state energy will be:

The Hitomi satellite recently observed the Lyman alpha emission line ($n=2$ to $n=1$) of hydrogen-like iron ion (atomic number of iron is $26$) from the Perseus galaxy cluster. The wavelength of the line is closest to ............... $\mathring{A}$.

In Bohr's model of the hydrogen atom,the ratio between the period of revolution of an electron in the orbit of $n=1$ to the period of revolution of the electron in the orbit $n=2$ is

The ionisation energy of $10$ times ionised sodium atom is: