If the ratio of the area of two orbits of an $H$ atom is $4 : 1$,then the ratio of the frequency of the $e^-$ in these two orbits is:

The energy of an electron in the first Bohr orbit of $H$ atom is $-13.6 \ eV$. The possible energy value$(s)$ of the excited state$(s)$ for electrons in Bohr orbits of the hydrogen atom is(are) $............ \ eV$.

As an electron is brought from an infinite distance close to the nucleus of the atom,the energy of the electron-nucleus system :

The energy (in $J$) released when an excited electron of the $5^{th}$ orbit of a hydrogen atom returns to its ground state is

Calculate the wavelength of the emitted radiation when an electron transitions from $n = 3$ to $n = 2$ in a hydrogen atom. To which region does this radiation belong?

Identify the pair of species having the same energy from the following (The number given in the bracket corresponds to the principal quantum number $(n)$ in which the electron is present).