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JEE Advanced · Physics · 27. Atomic 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 - IList - II
(P) \(E\text { propto } Z^2\)(1) energy of characteristic x-rays
(Q) \(E\text { propto } (Z-1)^2\)(2) electrostatic part of the nuclear binding energy for stable nuclei with mass numbers in the range 30 to 170
(R) \(E \text { propto } Z(Z-1)\)(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

  1. A \(\mathrm{P} \rightarrow 4, \mathrm{Q} \rightarrow 3, \mathrm{R} \rightarrow 1, \mathrm{~S} \rightarrow 2\)
  2. B \(\mathrm{P} \rightarrow 5, \mathrm{Q} \rightarrow 2, \mathrm{R} \rightarrow 1, \mathrm{~S} \rightarrow 4\)
  3. C \(\mathrm{P} \rightarrow 5, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 4\)
  4. D \(\mathrm{P} \rightarrow 3, \mathrm{Q} \rightarrow 2, \mathrm{R} \rightarrow 1, \mathrm{~S} \rightarrow 5\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\mathrm{P} \rightarrow 5, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 4\)

Step-by-step Solution

Detailed explanation

(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
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