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 the quantum number $ l $. The angular nodes are regions in an atom where the probability of finding an electron is zero. For d-orbitals, the azimuthal quantum number $ l $ is 2. Therefore, the number of angular nodes is equal to $ l $, which is 2.

1. **Explanation for Option 3 (Correct Answer):**
   - The d-orbitals have an azimuthal quantum number $ l = 2 $. According to the formula for angular nodes, the number of angular nodes is equal to the azimuthal quantum number $ l $. Therefore, d-orbitals have 2 angular nodes. This is why Option 3 is correct.

2. **Explanation for why other options are incorrect:**
   - **Option 1 (0 angular nodes):** This is incorrect because having 0 angular nodes would imply that the orbital has an azimuthal quantum number $ l = 0 $, which corresponds to s-orbitals, not d-orbitals.
   - **Option 2 (1 angular node):** This is incorrect because having 1 angular node would imply that the orbital has an azimuthal quantum number $ l = 1 $, which corresponds to p-orbitals, not d-orbitals.
   - **Option 4 (3 angular nodes):** This is incorrect because having 3 angular nodes would imply that the orbital has an azimuthal quantum number $ l = 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.