Question

Total number of angular nodes of orbitals associated with third shell $ (n=3) $ of an atom is:

• A. 3
• B. 4
• C. 2
• D. 1

Hint:

The number of angular nodes for an orbital is equal to \(l\), and for a given shell \(n\), the total number of angular nodes is the sum of the angular nodes for each orbital.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
The question asks for the total number of angular nodes of orbitals associated with the third shell \( (n = 3) \).
The angular nodes are associated with the azimuthal quantum number \( l \). Step 2: Finding the value of \(l\).
For \(n = 3\), the possible values of \(l\) are:
\(l = 0\) for the \(s\)-orbital
\(l = 1\) for the \(p\)-orbital
\(l = 2\) for the \(d\)-orbital
Step 3: Counting the angular nodes.
The number of angular nodes for an orbital is equal to \(l\). So:
\(s\)-orbitals (\(l = 0\)) have 0 angular nodes.
\(p\)-orbitals (\(l = 1\)) have 1 angular node.
\(d\)-orbitals (\(l = 2\)) have 2 angular nodes.
\ Step 4: Total number of angular nodes.
The total number of angular nodes is the sum of the angular nodes for each orbital type:
0 for the \(s\)-orbitals, 1 for the \(p\)-orbitals, and 2 for the \(d\)-orbitals.
Total angular nodes = \(0 + 1 + 2 = 3\).
Step 5: Conclusion.
Thus, the correct answer is option (1).