In the hydrogen spectrum,a line corresponds to a transition from the $3^{rd}$ to the $5^{th}$ orbit. Identify the series to which this transition belongs.

The hydrogen spectrum consists of several spectral lines in the Lyman series ($L_1, L_2, L_3 \ldots$; $L_1$ has the lowest energy among the Lyman series). Similarly,it consists of several spectral lines in the Balmer series ($B_1, B_2, B_3 \ldots$; $B_1$ has the lowest energy among the Balmer lines). The energy of $L_1$ is $x$ times the energy of $B_1$. The value of $x$ is . . . . . . $\times 10^{-1}$ (Nearest integer).

The ratio of the velocity of an electron in the ground state of a hydrogen atom to its velocity in the second excited state of a $He^{+}$ ion is:

In a hydrogen atom,the minimum energy required to excite an electron from the $2^{nd}$ orbit to the $3^{rd}$ orbit is: (in $eV$)

Calculate the energy required for the process $He_{(g)}^{+} \rightarrow He_{(g)}^{2+} + e^{-}$. The ionization energy for the $H$ atom in the ground state is $2.18 \times 10^{-18} \, J \, atom^{-1}$.

An electron initially present in an excited state of $H$ atom is further excited to another energy level by an incident photon. It releases $10$ photons while coming back to the ground state,out of which $7$ have higher energy than the incident photon. The electron was initially present in: