The total number of nodes are given by

Options

A. (n+1)
B. (n-l-1)
C. (n-1)
D. (n-l-1)

Answer

To find the total number of nodes in an atomic orbital, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Nodes**:
- Nodes are points in an atomic orbital where the probability of finding an electron is zero. There are two types of nodes: radial nodes and angular nodes.

2. **Identify the Types of Nodes**:
- **Radial Nodes**: These are spherical surfaces where the probability density of finding an electron is zero. The formula to calculate the number of radial nodes is:
\[ \text{Radial Nodes} = N - L - 1 \]
where \( N \) is the principal quantum number and \( L \) is the azimuthal quantum number.

- **Angular Nodes**: These are planes where the probability density of finding an electron is zero. The formula to calculate the number of angular nodes is:
\[ \text{Angular Nodes} = L \]

3. **Calculate Total Nodes**:
- The total number of nodes in an orbital is the sum of radial nodes and angular nodes:
\[ \text{Total Nodes} = \text{Radial Nodes} + \text{Angular Nodes} \]
- Substituting the formulas:
\[ \text{Total Nodes} = (N - L - 1) + L \]
- Simplifying this expression:
\[ \text{Total Nodes} = N - 1 \]

4. **Conclusion**:
- Therefore, the total number of nodes in an atomic orbital is given by:
\[ \text{Total Nodes} = N - 1 \]