Question

Match the Column-I and Column-II.

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

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

Answer 1

Answer: (A)

$(A)\to (4);(B)\to (1);(C)\to (2);(D)\to (3)$
Radius of $n$th orbit, $r_n$
$r_n=\frac{n^2{h}^2}{4{\pi }^{2}kZm{e}^2}$
Velocity of election in $n$th orbit, $v_n$
$v_n=\frac{2\pi kZ{e}^2}{nh}$
Potential energy in nth orbit, U
$U=-\frac{kZ{e}^2}{r_n}$
kinetic energy in nth orbit, $K$
$K=\frac{kZ{e}^2}{2r_n}$