Question

Match the Column-I and Column-II.

Column I		Column II
A	Radius of $n^{\text {th }}$ orbit	1	$\frac{2 \pi k Z e^2}{n h}$
B	Velocity of electron in $n ^{\text {th }}$ orbit	2	$\frac{-k Z e^2}{r_n}$
C	Potential energy in $n ^{\text {th }}$ orbit	3	$\frac{k Z e^2}{2 r_n}$
D	Kinetic energy in $n ^{\text {th }}$ orbit	4	$\frac{n^2 h^2}{4 \pi^2 k Z m e^2}$

• A. $(A) \rightarrow (4); (B) \rightarrow (1); (C) \rightarrow (2); (D) \rightarrow (3)$
• B. $(A) \rightarrow (4); (B) \rightarrow (3); (C) \rightarrow (1); (D) \rightarrow (2)$
• C. $(A) \rightarrow (2); (B) \rightarrow (1); (C) \rightarrow (4); (D) \rightarrow (3)$
• D. $(A) \rightarrow (4); (B) \rightarrow (2); (C) \rightarrow (1); (D) \rightarrow (3)$

Answer 1

Answer: (A)

$( A ) \rightarrow(4) ;( B ) \rightarrow(1) ;( C ) \rightarrow(2) ;( D ) \rightarrow(3)$
Radius of $n$th orbit, $r_n$
$r_n=\frac{n^2 h^2}{4 \pi^2 k Z m e^2}$
Velocity of election in $n$th orbit, $v_n$
$v _{ n }=\frac{2 \pi k Z e ^2}{ nh }$
Potential energy in nth orbit, U
$U =-\frac{ kZe^{2 } }{ r _{ n }}$
kinetic energy in nth orbit, $K$
$K=\frac{k Z e^2}{2 r_n}$