JEE Advanced 2025 — Paper 1 — PHY-IV solution

JEE Advanced2025Paper 1PHY-IV

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 $\to$ 4; Q $\to$ 3; R $\to$ 1; S $\to$ 2
B
P $\to$ 5; Q $\to$ 2; R $\to$ 1; S $\to$ 4
C
P $\to$ 5; Q $\to$ 1; R $\to$ 2; S $\to$ 4
D
P $\to$ 3; Q $\to$ 2; R $\to$ 1; S $\to$ 5

Solution

(P) Energy of a hydrogen-like atom: $E_{n} = - 13.6 \frac{Z ^{2}}{n ^{2}}$ eV, so $E \propto Z^{2}$ . This is the energy of radiation from electronic transitions in hydrogen-like atoms. Matches (5).

(Q) Moseley's law for characteristic X-rays gives $E = 13.6 (Z - 1)^{2} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}})$ , so $E \propto (Z - 1)^{2}$ . Matches (1).

(R) The Coulomb (electrostatic) contribution to nuclear binding energy scales as $\frac{Z ( Z - 1 )}{A ^{1/3}}$ , proportional to $Z (Z - 1)$ . Matches (2).

(S) In the mass-number range 30 to 170, the binding energy per nucleon is approximately constant (around 8.5 MeV), so it is practically independent of $Z$ . Matches (4).

$∴$ P $\to$ 5, Q $\to$ 1, R $\to$ 2, S $\to$ 4. Option (C).

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