The nuclear theory of the atom was put forward by:

Which of the following electronic transitions in a hydrogen atom will require the largest amount of energy?

Two electrons are revolving around a nucleus at distances $r$ and $4r$. The ratio of their time periods is

The energy of an electron in a hydrogen atom in its ground state is $-13.6 \ eV$. The energy of the level corresponding to the quantum number equal to $5$ is ............. $eV$.

If the maximum kinetic energy of photoelectrons ejected from a metal surface when it is irradiated with a radiation of frequency $4 \times 10^{14} \ s^{-1}$ is $6.63 \times 10^{-20} \ J$,then the threshold frequency of the metal is

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 $(2)$.