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 ($2$)

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

Answer

Correct option: A.
$3,4$
a
($1$) $\begin{array}{l} r =0.529 \times \frac{ n ^2}{ z } \quad \Rightarrow r \propto n ^2 \quad \Rightarrow( I )( T ) \\ mVr =\frac{ nh }{2 \pi} \quad \Rightarrow( mVr ) \propto n \quad \Rightarrow \text { (II) (S) } \\ KE =+13.6 \times \frac{ z ^2}{ n ^2} \quad \Rightarrow KE \propto n ^{-2} \quad \Rightarrow \text { (III) (P) } \\ PE =-2 \times 13.6 \times \frac{ z ^2}{ n ^2} \Rightarrow PE \propto n ^{-2} \quad \Rightarrow \text { (IV) (P) } \\\end{array}$

($2$) Same as $1$ $(Section-3)$

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