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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 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) ^-1
(iii) Kinetic energy of the electron in the nth orbit (R) ∝ n^0
(IV) Potential energy of the electron in the nth (S) ∝ n^1
(T) ∝ n^2
(U) ∝ n^1/2
Which of the following has the correct combination considering List-I and List-II?

(III),(S)

(IV),(U)

(IV),(Q)

(III),(P)

Solution:

Correct option is C (IV),(Q)
The kinetic energy of the electron in the nth orbit is given as:
K.E.=me48ε02n2h2
∴ K.E.∝n−2
Similarly, radius of nth orbit ∝n2/Z
Angular momentum |L|∝n
and Potential energy P.E.∝−Z2/n2
Hence, the correct option is C