JEE Advanced 2025 · Paper 1 · Physics Q16

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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

P
$E \propto Z^2$
Q
$E \propto (Z-1)^2$
R
$E \propto Z(Z-1)$
S
$E$ is practically independent of $Z$

List-II

1
energy of characteristic x-rays
2
electrostatic part of the nuclear binding energy for stable nuclei with mass numbers in the range 30 to 170
3
energy of continuous x-rays
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

P → 4; Q → 3; R → 1; S → 2

P → 5; Q → 2; R → 1; S → 4

P → 5; Q → 1; R → 2; S → 4

P → 3; Q → 2; R → 1; S → 5

Answer and worked solution

Official answer: C

(P) $E\propto Z^2$ : photon energies from hydrogen-like atoms, $E_n\propto\frac{Z^2}{n^2}$ → (5).
(Q) $E\propto(Z-1)^2$ : characteristic x-rays (Moseley's law, screened nucleus) → (1).
(R) $E\propto Z(Z-1)$ : the Coulomb (electrostatic) term of nuclear binding energy, which counts proton pairs → (2).
(S) Independent of $Z$ : binding energy per nucleon, roughly constant at about 8 MeV for $A$ = 30-170 → (4).

The match is P→5, Q→1, R→2, S→4, which is option (C).

Topics:Moseley's law Mass defect and binding energy Bohr model and hydrogen spectrum

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