Q48 / 48 · JEE Advanced 2025 (Paper 1) · 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.\nChoose 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
| 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$\mathrm{P} \rightarrow 4, \mathrm{Q} \rightarrow 3, \mathrm{R} \rightarrow 1, \mathrm{~S} \rightarrow 2$
- B$\mathrm{P} \rightarrow 5, \mathrm{Q} \rightarrow 2, \mathrm{R} \rightarrow 1, \mathrm{~S} \rightarrow 4$
- Correct answerC$\mathrm{P} \rightarrow 5, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 4$
- D$\mathrm{P} \rightarrow 3, \mathrm{Q} \rightarrow 2, \mathrm{R} \rightarrow 1, \mathrm{~S} \rightarrow 5$
Solution
(P) Energy of H -like atom is
$\begin{aligned} & \mathrm{E}=-13.6 \frac{\mathrm{Z}^2}{\mathrm{n}^2} \text { So } \\ & \mathrm{E} \propto \mathrm{Z}^2 \\ & \mathrm{P} \rightarrow(5)\end{aligned}$
(Q) Energy of characteristic X-ray by moseley's correction
$\begin{aligned} & E=-13.6(Z-1)^2\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right] \text { So } \\ & E \propto(Z-1)^2 \\ & Q \rightarrow(1)\end{aligned}$
(R) Electrostatics binding energy is proportional to $Z(Z-1)$
$R \rightarrow(2)$
(S) For stable nuclei with mass no. in range 30 to 170 . Binding energy per nucleon is constant \& graph is straight line
$S \rightarrow(4)$
Ans. (C) is correct
Hence, the correct answer is option: 'C'.