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. | 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) | $E \propto Z(Z-1)$ | (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 |

JEE Advanced · 2025 · 18 May 2025 · Paper 1 · Modern Physics

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.

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)	$E \propto Z (Z - 1)$	(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

(A)P→5, Q→1, R→3, S→4
(B)P→5, Q→2, R→1, S→4
(C)P→5, Q→1, R→2, S→4✓ Correct
(D)P→3, Q→2, R→1, S→5

Answer: (C)

Solution

(P) Energy of hydrogen-like atoms:

E = - 13.6 \frac{Z ^{2}}{n ^{2}}

, so

E \propto Z^{2}

→ (5)

(Q) Energy of characteristic X-rays (Moseley's law with screening):

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

, so

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

→ (1)

(R) Electrostatic binding energy in nucleus is proportional to the number of proton pairs:

E \propto Z (Z - 1)

→ (2)

(S) For stable nuclei with mass numbers 30-170, the binding energy per nucleon is approximately constant (flat region of binding energy curve) → (4)

Therefore: P→5, Q→1, R→2, S→4

JEE Advanced · 2025 · 18 May 2025 · Paper 1 · Single correct option

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JEE Advanced · 2025 · 18 May 2025 · Paper 1 · Modern Physics

Solution

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