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 - I | List - 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 |
- A \(\mathrm{P} \rightarrow 4, \mathrm{Q} \rightarrow 3, \mathrm{R} \rightarrow 1, \mathrm{~S} \rightarrow 2\)
- B \(\mathrm{P} \rightarrow 5, \mathrm{Q} \rightarrow 2, \mathrm{R} \rightarrow 1, \mathrm{~S} \rightarrow 4\)
- C \(\mathrm{P} \rightarrow 5, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 4\)
- D \(\mathrm{P} \rightarrow 3, \mathrm{Q} \rightarrow 2, \mathrm{R} \rightarrow 1, \mathrm{~S} \rightarrow 5\)
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
\(\begin{aligned} & \mathrm{E}=-13.6 \frac{\mathrm{Z}^2}{\mathrm{n}^2} \text { So } \\ & \mathrm{E} \propto \mathrm{Z}^2 \\ & \mathrm{P} \rightarrow(5)\end{aligned}\)
(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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