The total number of nodal planes present in the third shell will be

Options

A. 7
B. 11
C. 13
D. 14

Answer

To determine the total number of nodal planes present in the third shell (n=3), we first need to understand the relationship between the principal quantum number (n) and the azimuthal quantum number (l), which defines the shape of the orbitals.

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- For the third shell, the principal quantum number \( n \) is 3.

2. **Determine the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number \( l \) can take values from 0 to \( n-1 \). Therefore, for \( n = 3 \):
\[ l = 0, 1, 2 \]
- This corresponds to the following orbitals:
- \( l = 0 \) corresponds to the s orbital (3s)
- \( l = 1 \) corresponds to the p orbital (3p)
- \( l = 2 \) corresponds to the d orbital (3d)

3. **Count the Nodal Planes for Each Orbital**:
- The number of nodal planes in an orbital is equal to the azimuthal quantum number \( l \):
- For 3s (\( l = 0 \)):
- Nodal planes = 0
- For 3p (\( l = 1 \)):
- Nodal planes = 1
- For 3d (\( l = 2 \)):
- Nodal planes = 2

4. **Calculate the Total Number of Nodal Planes**:
- Now, we sum the nodal planes from each type of orbital:
\[ \text{Total nodal planes} = \text{Nodal planes from 3s} + \text{Nodal planes from 3p} + \text{Nodal planes from 3d} \]
\[ = 0 + 1 + 2 = 3 \]

### Final Answer:
The total number of nodal planes present in the third shell is **3**.

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