If in 4F the number of radial nodes and angular nodes are X and Y respectively. Find the sum of `X+Y`?

Answer

To solve the problem of finding the sum of the number of radial nodes (X) and angular nodes (Y) for the 4f orbital, we can follow these steps:

### Step 1: Identify the principal quantum number (n) and azimuthal quantum number (l)
For the 4f orbital:
- The principal quantum number (n) is 4.
- The azimuthal quantum number (l) for f orbitals is 3.

### Step 2: Calculate the number of angular nodes (Y)
The number of angular nodes is given by the azimuthal quantum number (l):
- Y = l = 3

### Step 3: Calculate the number of radial nodes (X)
The number of radial nodes is calculated using the formula:
\[ \text{Number of radial nodes} = n - l - 1 \]
Substituting the values:
\[ X = 4 - 3 - 1 = 0 \]

### Step 4: Find the sum of X and Y
Now that we have both X and Y:
- X = 0 (number of radial nodes)
- Y = 3 (number of angular nodes)

The sum \( X + Y \) is:
\[ X + Y = 0 + 3 = 3 \]

### Final Answer
The sum of the number of radial nodes and angular nodes for the 4f orbital is 3.

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