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 $(2)$.

  • A
    $3, 4$
  • B
    $3, 2$
  • C
    $3, 1$
  • D
    $1, 2$

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