The energy required to excite an electron in a hydrogen atom from the ground state $(n=1)$ to the first excited state $(n=2)$ is $..........$ $eV$.

Answer the following by appropriately matching the lists based on the information given in the paragraph. Consider Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following,$List-I$ contains some quantities for the $n^{\text{th}}$ orbit of the atom and $List-II$ contains options showing how they depend on $n$.

$List-I$	$List-II$
$(I)$ Radius of the $n^{\text{th}}$ orbit	$(P) \propto n^{-2}$
$(II)$ Angular momentum of the electron in the $n^{\text{th}}$ orbit	$(Q) \propto n^{-1}$
$(III)$ Kinetic energy of the electron in the $n^{\text{th}}$ orbit	$(R) \propto n^0$
$(IV)$ Potential energy of the electron in the $n^{\text{th}}$ orbit	$(S) \propto n^1$
-	$(T) \propto n^2$
-	$(U) \propto n^{1/2}$

$(1)$ Which of the following options has the correct combination considering $List-I$ and $List-II$?
$(1) (II), (R)$ $(2) (I), (P)$ $(3) (I), (T)$ $(4) (II), (Q)$
$(2)$ Which of the following options has the correct combination considering $List-I$ and $List-II$?
$(1) (III), (S)$ $(2) (IV), (Q)$ $(3) (IV), (U)$ $(4) (III), (P)$
Give the answer for questions $(1)$ and $(2)$.

The energy required by electrons,present in the first Bohr orbit of hydrogen atom to be excited to the second Bohr orbit is . . . . . . $J \ mol^{-1}$.
Given: $R_{H} = 2.18 \times 10^{-11} \ ergs$

The ratio of the velocity of an electron in the second orbit of $He^{+}$ to the third orbit of $B^{4+}$ is:

The wavelength of the spectral line obtained in the spectrum of $Li^{2+}$ ion,when the transition takes place between two levels whose sum is $4$ and difference is $2$,is

If the wavelength of the first line of the Balmer series is $656.1 \ nm$,then the wavelength of the second line of this series will be ............. $nm$.