## Step-by-Step Solution ### 1. **Understanding "Ungerade" Orbitals** - **Ungerade (u)**: An orbital is called **ungerade** if, upon inversion through the center of symmetry, its wavefunction changes sign (i.e., it is antisymmetric with respect to inversion). - **Gerade (g)**: An orbital is called **gerade** if, upon inversion, its wavefunction does **not** change sign (i.e., it is symmetric). ### 2. **How to Identify** - **Inversion**: Imagine a point at the center (origin). Every part of the orbital is mapped to the opposite side through the origin. - If colors (representing phase/sign) are swapped after inversion, it is **ungerade**. - If colors remain the same, it is **gerade**. ### 3. **Analyzing Each Orbital** #### **i)** - The lobes switch colors (green ↔ magenta) when inverted. - **Ungerade** #### **ii)** - The lobes switch colors (green ↔ magenta) upon inversion. - **Ungerade** #### **iii)** - The lobes do **not** switch colors—the pattern remains the same on inversion. - **Gerade** #### **iv)** - The two lobes are different colors, and these swap places upon inversion. - **Ungerade** #### **v)** - The top and bottom lobes are different colors and switch upon inversion. - **Ungerade** #### **vi)** - The orbital is symmetric (the colors don't change), so it is **gerade**. ### 4. **Final Answer** **The ungerade orbitals are: i, ii, iv, and v.** ### 5. **Mark the Correct Option** - The answer is: **i, ii, iv, and v** --- ## **Final Answer** **Option: i, ii, iv, and v** --- ### **Summary Table** | Orbital | Symmetry | Ungerade/Gerade | |---------|---------------|-----------------| | i | Changes sign | Ungerade | | ii | Changes sign | Ungerade | | iii | Symmetric | Gerade | | iv | Changes sign | Ungerade | | v | Changes sign | Ungerade | | vi | Symmetric | Gerade | --- **Let me know if you need an explanation of why a specific orbital is ungerade!**