Question

A certain orbital having 2 angular nodes and no radial nodes is:

• A. 3d
• B. 3s
• C. 3p
• D. 2p

Hint:

Remember: Angular nodes = \( l \), Radial nodes = \( n - l - 1 \). Use both formulas together to identify the correct orbital.

Answer 1

The Correct Option is A

Step 1: Understanding angular nodes.
Angular nodes are given by the azimuthal quantum number \( l \).
\[ \text{Number of angular nodes} = l \] Given in the question:
\[ l = 2 \]

Step 2: Identifying the type of orbital.
The value of \( l \) determines the type of orbital:
\[ l = 0 \Rightarrow s\text{-orbital} \] \[ l = 1 \Rightarrow p\text{-orbital} \] \[ l = 2 \Rightarrow d\text{-orbital} \] So, the required orbital must be a \( d \)-orbital.

Step 3: Understanding radial nodes.
Radial nodes are given by the formula:
\[ \text{Number of radial nodes} = n - l - 1 \] Given that there are no radial nodes:
\[ n - l - 1 = 0 \]

Step 4: Substituting the value of \( l \).
\[ n - 2 - 1 = 0 \] \[ n - 3 = 0 \] \[ n = 3 \]

Step 5: Determining the orbital.
From the values:
\[ n = 3, \quad l = 2 \] This corresponds to the orbital:
\[ 3d \]

Step 6: Verifying other options.
- 3s: \( l = 0 \), angular nodes = 0
- 3p: \( l = 1 \), angular nodes = 1
- 2p: \( l = 1 \), angular nodes = 1
Only 3d satisfies both conditions.

Step 7: Final Answer.
Thus, the orbital having 2 angular nodes and no radial nodes is:
\[ \boxed{3d} \] Hence, the correct answer is option (A).