Question

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 $n^{th}$ orbit of the atom and List-II contains options showing how they depend on n.

List-I	List-II
(I) Radius of the $n^{th}$ orbit	(p) $\propto n^{-2}$
(II) Angular momentum of the electron in the $n^{th}$ orbit	(Q) $\propto n^{-1}$
(III) Kinetic energy of the electron in the $n^{th}$ orbit	(R) $\propto n^0$
(IV) Potential energy of the electron in the $n^{th}$ orbit	(S) $\propto n^1$
	(T) $\propto n^2$
	(U) $\propto n^{1/2}$

Question: Which of the following options has the correct combination considering List-I and List-II?

• A. (I),(P)
• B. (I), (T)
• C. (II), (Q)
• D. (II), (R)

Answer 1

Answer: (B)

$r=0.59\times \frac{n^2}{z}\Rightarrow r\propto n^2\Rightarrow \left(I\right)\left(T\right)$
$mvr=\frac{nh}{2\pi }\Rightarrow \left(mvr\right)\propto n\Rightarrow \left(II\right)\left(S\right)$
$KE=13.6\times \frac{z^2}{n^2}\Rightarrow KE\propto n^{-2}\Rightarrow \left(III\right)\left(P\right)$
$PE=-2\times 13.6\times \frac{z^2}{n^2}\Rightarrow PE\propto n^{-2}\Rightarrow \left(IV\right)\left(P\right)$