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In a modified atomic model the electron-nucleus interaction potential energy is U = -k*e² / (3*r³) (Bohr quantization still holds). In the nth orbit, match each quantity in List-I with its dependence on n from List-II. List-I: (P) Electric current due to orbiting electron; (Q) Magnetic field at the nucleus due to orbiting electron; (R) Angular momentum of nth orbit; (S) Magnetic moment due to orbiting electron. List-II: (1) n^(-2); (2) n⁷; (3) n⁰; (4) n⁵; (5) n¹.

1. P -> 4; Q -> 2; R -> 5; S -> 5
2. P -> 1; Q -> 2; R -> 5; S -> 5
3. P -> 4; Q -> 2; R -> 5; S -> 1
4. P -> 4; Q -> 2; R -> 1; S -> 5

Correct answer: P -> 4; Q -> 2; R -> 5; S -> 5

Solution

With r proportional to n^(-2) and v proportional to n³: orbital frequency f proportional to n⁵, so current I = ef proportional to n⁵ (P->4); B = mu0*I/(2r) proportional to n⁵/n^(-2) = n⁷ (Q->2); R = n*h-bar proportional to n (R->5); magnetic moment = I*pi*r² proportional to n⁵*n^(-4) = n (S->5).

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