JEE Advanced 2025 Paper 1 · Q16 · X-rays

Question

List-I shows functional dependences of energy $E$ on atomic number $Z$. List-II names energies of various phenomena. List-I: (P) $E \propto Z^2$; (Q) $E \propto (Z - 1)^2$; (R) $E \propto Z(Z - 1)$; (S) $E$ is practically independent of $Z$ (for stable nuclei with mass number 30–170). List-II: (1) energy of characteristic X-rays; (2) electrostatic part of nuclear binding energy for stable nuclei (mass numbers 30–170); (3) energy of continuous X-rays; (4) average nuclear binding energy per nucleon for stable nuclei (mass numbers 30–170); (5) energy of radiation due to electronic transitions in hydrogen-like atoms. Choose: (A) P->4,Q->3,R->1,S->2; (B) P->5,Q->2,R->1,S->4; (C) P->5,Q->1,R->2,S->4; (D) P->3,Q->2,R->1,S->5.

SolveKar AI · Accepted Answer

(P) $E \propto Z^2$: hydrogenic energy levels go as $Z^2$ (Bohr model). Match (5). (Q) $E \propto (Z-1)^2$: Moseley's law for characteristic X-rays uses screening, giving $E_K \propto (Z-1)^2$. Match (1). (R) $E \propto Z(Z-1)$: the electrostatic (Coulomb) part of nuclear binding energy in the semi-empirical mass formula is $-a_C Z(Z-1)/A^{1/3}$; for nuclei in the stated range it scales like $Z(Z-1)$. Match (2). (S) $E$ independent of $Z$: average binding energy per nucleon is roughly $8$ MeV across the stable region ($A \approx 30$–$170$). Match (4). So P→5, Q→1, R→2, S→4. Answer: (C).

JEE Advanced 2025 Paper 1 · Q16 · X-rays

Solution