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 nth orbit of the atom and List-II contains options showing how they depend on n. List - I List - II (I) Radius of the nth orbit (P) ∝n–2 (II) Angular momentum of the electron in the nth orbit (Q) ∝n–1 (III) Kinetic energy of the electron in the nth orbit (R) ∝n0 (IV) Potential energy of the electron in the nth orbit (S) ∝n1 (T) ∝n2 (U) ∝n1/2 Which of the following options has the correct combination considering List-I and List-II ?

Engineering

Chemistry

Bohrs Model for Hydrogen Atom

Question

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^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) ∝n^–2
(II) Angular momentum of the electron in the n^th orbit	(Q) ∝n^–1
(III) Kinetic energy of the electron in the n^th orbit	(R) ∝n⁰
(IV) Potential energy of the electron in the n^th orbit	(S) ∝n¹
	(T) ∝n²
	(U) ∝n^1/2

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

(IV), (U)

(III), (P)

(III), (S)

(IV), (Q)

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$KE = \frac{13 .6 Z^{2}}{n^{2}} eV / atom$

$PE = \frac{- 2 \times 13 .6 Z^{2}}{n^{2}} eV / atom$

$Radius = 0 .529 \frac{n^{2}}{Z} Å$

Angular momentum of electron $(mvr) = \frac{nh}{2 π}$