Question

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

• A. S and R are true; and R is the correct reason for S
• B. S and R are true; but R is NOT the correct reason for S
• C. S is true but R is false
• D. S is false but R is true

Hint:

For light atoms (\(Z\) small): Russell–Saunders coupling applies (\(LS\)-coupling).
For heavy atoms (\(Z\) large): \(jj\)-coupling dominates due to strong spin–orbit interactions.
Remember: strength of spin–orbit interaction \(\propto Z^4\).

Answer 1

The Correct Option is A

Step 1: Understand coupling schemes. - In light atoms: Spin–orbit interaction is weak compared to electrostatic interactions, so orbital angular momenta first couple (\(L\)), spins couple (\(S\)), then total \(J = L+S\) is formed. This is Russell–Saunders (\(LS\)) coupling.
- In heavy atoms: Spin–orbit interaction is strong, so each electron’s \(l_i\) couples with \(s_i\) to form \(j_i\). Then, total \(J\) is the vector sum of individual \(j_i\). This is \(jj\)-coupling.
Step 2: Evaluate assertion and reason. - Assertion (S): Correct. - Reason (R): Correct, because the weak spin–orbit coupling in light atoms vs strong in heavy atoms explains the choice of coupling scheme.
Step 3: Logical connection. Since R correctly explains why S is true, option (A) is correct.