The number of spherical nodes and planar nodes present in `4d_(x^(2) - y^(2))` and ......and ........respectively.

Answer

To find the number of spherical nodes and planar nodes present in the orbital \(4d_{(x^2 - y^2)}\), we will follow these steps:

### Step 1: Identify the Principal Quantum Number (n)
The principal quantum number \(n\) for the \(4d\) orbital is 4.

### Step 2: Identify the Azimuthal Quantum Number (l)
The azimuthal quantum number \(l\) for a \(d\) orbital is 2.

### Step 3: Calculate the Number of Spherical Nodes
The formula for calculating the number of spherical nodes is given by:
\[ \text{Number of spherical nodes} = n - l - 1 \]
Substituting the values we have:
\[ \text{Number of spherical nodes} = 4 - 2 - 1 = 1 \]

### Step 4: Calculate the Number of Planar Nodes
The number of planar nodes (or angular nodes) is equal to the azimuthal quantum number \(l\). Therefore:
\[ \text{Number of planar nodes} = l = 2 \]

### Final Answer
Thus, for the orbital \(4d_{(x^2 - y^2)}\):
- Number of spherical nodes = 1
- Number of planar nodes = 2