MCQ
Answer the following by appropriately matching the lists based on the information given in the paragraph Consider the 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 $n^{t /}$ orbit of the atom and List$-II$ contains options showing how they depend on $n$. Which of the following options has the correct combination considering List$-I$ and List$-II$?
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 or quetion $(1)$ and $(2)$
  • A
    $3,4$
  • B
    $3,2$
  • C
    $3,1$
  • D
    $1,2$

Answer

$(1)  r =0.529 \times \frac{ n ^2}{ z } \Rightarrow r \propto n ^2 \Rightarrow( I )( T )$
$mVr =\frac{ nh }{2 \pi} \Rightarrow( mVr ) \propto n \Rightarrow \text { (II) (S) }$
$KE =+13.6 \times \frac{ z ^2}{ n ^2} \Rightarrow KE \propto n ^{-2} \Rightarrow \text { (III) (P) }$
$PE =-2 \times 13.6 \times \frac{ z ^2}{ n ^2} \Rightarrow PE \propto n ^{-2} \Rightarrow \text { (IV) (P) }$
$(2)$ Same as $1\ ($Section$-3)$

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