If an electron falls from $n = 3$ to $n = 2$,then the emitted energy 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 $(2)$.

If '$X$' is the ionization energy of hydrogen,then the energy required for the excitation of a $Li^{2+}$ electron from the $2^{nd}$ excited state to the $5^{th}$ excited state is:

If the shortest wavelength in the Lyman series of a hydrogen atom is $A$,then the longest wavelength in the Paschen series of $He^{+}$ 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 $eV$)

The velocity of an electron in the $3^{rd}$ excited state of $Be^{3+}$ is .......