The energy required for the ionisation of a hydrogen atom is $13.6 \ eV$. What is the energy required for the ionisation of $He^+$ ion (in $eV$)?

For a $Bohr$ atom,the angular momentum of an electron is given by $M(n = 1, 2, 3, .....)$ :

For the hydrogen emission spectrum,the energy change $E$ (in Joules) is given by $\Delta E = 2.18 \times 10^{-18} \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \ J$,where $n_1 = 1, 2, 3, \dots$ and $n_2 = 2, 3, 4, \dots$. Which of the following corresponds to the Paschen series?

The approximate ratio of the speed of light in vacuum to that of an electron in the first Bohr orbit of hydrogen atom is (in $: 1$)

The shortest wavelength of $He^{+}$ ion in Balmer series is $x$. Then,the longest wavelength in the Paschen series of $Li^{2+}$ is:

Explain the importance and the main postulates of Planck's quantum theory.