List-I shows various functional dependencies of energy (E) on the atomic number (Z). Energies associated with certain phenomena are given in List-II. Choose the option that describes the correct match between the entries in List-I to those in List-II.

Question

List-I shows various functional dependencies of energy (E) on the atomic number (Z). Energies associated with certain phenomena are given in List-II. Choose the option that describes the correct match between the entries in List-I to those in List-II. [2025]

	List-I		List-II
(P)	$E \propto Z^{2}$	(1)	Energy of characteristic X-rays
(Q)	$E \propto {(Z - 1)}^{2}$	(2)	Electrostatic part of the nuclear binding energy for stable nuclei with mass numbers in the range 30 to 170
(R)	$E \propto (Z - 1)$	(3)	Energy of continuous X-rays
(S)	E is practically independent of Z	(4)	Average nuclear binding energy per nucleon for stable nuclei with mass number in the range 30 to 170
		(5)	Energy of radiation due to electronic transitions from hydrogen-like atoms

Smart Achievers · Accepted Answer

(3)

$(P) Energy of H-like atom$ $E = - 13.6 \frac{Z^{2}}{n^{2}}$

$∴$ $E \propto Z^{2}$ $E \propto {(Z - 1)}^{2}$

$(Q) Energy of characteristic X-ray by Moseley's correction$

$E = - 13.6 {(Z - 1)}^{2} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]$

$or, E \propto {(Z - 1)}^{2}$ $(Q) \to (1)$

$(R) Electrostatic binding energy \propto Z (Z - 1)$

$(R) \to (2)$

$(S) For stable nuclei with mass number in the range 30 to 170,$ $binding energy per nucleon is constant and the graph is a straight line.$

$∴$ $(S) \to (4)$

Solution

1 (P) → (4), (Q) → (3), (R) → (1), (S) → (2)

2 (P) → (5), (Q) → (2), (R) → (1), (S) → (4)

3 (P) → (5), (Q) → (1), (R) → (2), (S) → (4)

4 (P) → (3), (Q) → (2), (R) → (1), (S) → (5)

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