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)

$r=0.59\times\frac{n^{2}}{z} \Rightarrow r \propto n^{2} \Rightarrow \left(I\right) \left(T\right)$
$mvr=\frac{nh}{2\pi} \Rightarrow \left(mvr\right)\propto n \Rightarrow \left(II\right) \left(S\right)$
$KE=13.6\times\frac{z^{2}}{n^{2}} \Rightarrow KE \propto n^{-2} \Rightarrow \left(III\right) \left(P\right)$
$PE=-2\times13.6\times\frac{z^{2}}{n^{2}} \Rightarrow PE \propto n^{-2} \Rightarrow \left(IV\right) \left(P\right)$