Discussion
Assertion (S): The total angular momentum for light atoms (low atomic number) is obtained by Russell-Saunders coupling, whereas jj-coupling is used for heavy atoms (high atomic number).
Reasoning (R): The spin-orbit interactions are weak in light atoms (low atomic number) and strong in heavy atoms (high atomic number).
The correct option is
Answer: A
The correct option is S and R are true; and R is the correct reason for S.
In light atoms the electrostatic interactions between electrons are much stronger than spin-orbit coupling, so the individual orbital momenta first combine to a total L and the spins to a total S, which then couple weakly to give J: Russell-Saunders (LS) coupling. Spin-orbit coupling grows steeply with nuclear charge (roughly as Z4 for a given orbital), so in heavy atoms each electron's own l and s couple first to a j, and the j values then combine: jj-coupling.
The strength of the spin-orbit interaction is precisely what decides which scheme applies, so R both is true and explains S, ruling out the other three options.
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