The number of angular nodes for d-orbitals are:

Question

Accepted Answer

The number of angular nodes for d-orbitals is determined by the formula for angular nodes, which is given by $ l $, where $ l $ is the azimuthal quantum number (also known as the angular momentum quantum number). For d-orbitals, the value of $ l $ is 2. Therefore, the number of angular nodes for d-orbitals is 2.

### Explanation Supporting Option 3:

1. **Understanding Angular Nodes:**
   - Angular nodes are regions in an atom where the probability of finding an electron is zero. These nodes are determined by the angular part of the wave function and are dependent on the azimuthal quantum number $ l $.

2. **Azimuthal Quantum Number for d-Orbitals:**
   - For d-orbitals, the azimuthal quantum number $ l $ is 2. This directly indicates that there are 2 angular nodes in d-orbitals.

3. **Calculation of Angular Nodes:**
   - The formula for calculating angular nodes is simply the value of $ l $. Since $ l = 2 $ for d-orbitals, the number of angular nodes is 2.

### Explanation for Why Other Options are Incorrect:

1. **Option 1 (0 Angular Nodes):**
   - This is incorrect because a value of 0 angular nodes would imply an $ l $ value of 0, which corresponds to s-orbitals, not d-orbitals.

2. **Option 2 (1 Angular Node):**
   - This is incorrect because 1 angular node corresponds to an $ l $ value of 1, which is characteristic of p-orbitals, not d-orbitals.

3. **Option 4 (3 Angular Nodes):**
   - This is incorrect because 3 angular nodes would imply an $ l $ value of 3, which corresponds to f-orbitals, not d-orbitals.

In conclusion, the correct number of angular nodes for d-orbitals is 2, which is why Option 3 is the correct answer.