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 can follow these steps:

### Step 1: Understand Nodal Planes
A nodal plane is a plane where the probability of finding an electron is zero. The number of nodal planes in an orbital is determined by the azimuthal quantum number (l).

### Step 2: Identify the Principal Quantum Number
For the third shell, the principal quantum number (n) is equal to 3.

### Step 3: Determine Possible Values of l
The azimuthal quantum number (l) can take values from 0 to n - 1. Therefore, for n = 3:
- l can be 0, 1, or 2.

### Step 4: Identify the Subshells
The corresponding subshells for these values of l are:
- l = 0 corresponds to the 3s subshell
- l = 1 corresponds to the 3p subshell
- l = 2 corresponds to the 3d subshell

### Step 5: Count Nodal Planes for Each Subshell
- For the 3s subshell (l = 0): There are **0 nodal planes**.
- For the 3p subshell (l = 1): There is **1 nodal plane** (since there are 3 orbitals, each has 1 nodal plane).
- For the 3d subshell (l = 2): There are **2 nodal planes** for each of the 5 orbitals, but the 3d z² orbital has 0 nodal planes. Thus, the total for 3d is **5 nodal planes**.

### Step 6: Calculate Total Nodal Planes
Now, we can sum the nodal planes from all subshells:
- 3s: 0 nodal planes
- 3p: 1 nodal plane
- 3d: 5 nodal planes

Total nodal planes = 0 + 3 + 5 = **8 nodal planes**.

### Final Answer
The total number of nodal planes present in the third shell is **8**.

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