The number of angular nodes for d-orbitals are:

Question

Accepted Answer

The number of angular nodes for d-orbitals is determined by the azimuthal quantum number, denoted as $ l $. For d-orbitals, the azimuthal quantum number $ l $ is equal to 2. The formula to calculate the number of angular nodes is given by the azimuthal quantum number itself, which means the number of angular nodes is equal to $ l $.

1. **Explanation for Option 3 (Correct Answer):**
   - Since the azimuthal quantum number $ l $ for d-orbitals is 2, the number of angular nodes is also 2. Angular nodes are regions in an atom where the probability of finding an electron is zero, and they are determined by the shape of the orbital. For d-orbitals, which have complex shapes, there are exactly 2 angular nodes. Therefore, 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 no angular dependence, which is not the case for d-orbitals. D-orbitals have a specific shape that results in 2 angular nodes.
   - **Option 2 (1 angular node):** This is incorrect because 1 angular node corresponds to p-orbitals, where the azimuthal quantum number $ l $ is 1. D-orbitals, with $ l = 2 $, have 2 angular nodes.
   - **Option 4 (3 angular nodes):** This is incorrect because 3 angular nodes would correspond to f-orbitals, where the azimuthal quantum number $ l $ is 3. D-orbitals have only 2 angular nodes, as determined by their azimuthal quantum number.

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