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, we need to determine the number of radial nodes (X) and angular nodes (Y) for the 4f orbital and then find their sum (X + Y).

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- For the 4f orbital, the principal quantum number \( n \) is 4.

2. **Identify the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number \( l \) corresponds to the type of orbital:
- \( l = 0 \) for s
- \( l = 1 \) for p
- \( l = 2 \) for d
- \( l = 3 \) for f
- Therefore, for the f orbital, \( l = 3 \).

3. **Calculate the Number of Radial Nodes (X)**:
- The formula for calculating the number of radial nodes is:
\[ X = n - l - 1 \]
- Substituting the values of \( n \) and \( l \):
\[ X = 4 - 3 - 1 = 0 \]

4. **Calculate the Number of Angular Nodes (Y)**:
- The number of angular nodes is equal to the value of \( l \):
\[ Y = l \]
- Therefore:
\[ Y = 3 \]

5. **Find the Sum of Radial and Angular Nodes (X + Y)**:
- Now we can find the sum:
\[ X + Y = 0 + 3 = 3 \]

### Final Answer:
The sum of the number of radial nodes (X) and angular nodes (Y) for the 4f orbital is **3**.