Question

Identify pair of orbitals having similar \((n+l)\) values from the following.

• A. 3s and 3p
• B. 2p and 4s
• C. 3d and 4p
• D. 2p and 3p

Hint:

Add n and l for each orbital in the pair and look for equal sums.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The (n + l) rule says that the energy of an orbital rises with the sum of its principal quantum number \(n\) and azimuthal quantum number \(l\). Orbitals with the same sum have similar energy.

Step 2: Key Formula or Approach
For s, p, d, f orbitals the value of \(l\) is 0, 1, 2, 3 in that order. Compute \(n+l\) for every orbital in each pair and compare.

Step 3: Check option (A): 3s and 3p
3s: \(3+0=3\). 3p: \(3+1=4\). The values differ, so (A) is not the pair.

Step 4: Check option (B): 2p and 4s
2p: \(2+1=3\). 4s: \(4+0=4\). Different again.

Step 5: Check option (C): 3d and 4p
3d: \(3+2=5\). 4p: \(4+1=5\). Both equal 5, so this pair has similar (n + l) values.

Step 6: Check option (D): 2p and 3p
2p: \(2+1=3\). 3p: \(3+1=4\). Different.

Final Answer:
3d and 4p both have \(n+l=5\), so the answer is option (C). \[ \boxed{\text{3d and 4p}} \]