What is the corresponding letter and orbital for L=2?

In quantum mechanics, the orbital angular momentum quantum number ( L ) describes the shape of an electron's orbital and the types of orbitals associated with different values of ( L ). For ( L = 2 ), the corresponding type of orbital is the d-orbital.

The notation for d-orbitals includes various symmetries that correspond to the specific electronic arrangements in crystal field theory. Commonly, these are represented as ( T_{2g} ) and ( E_g ). The ( T_{2g} ) designation is often utilized in octahedral coordination complexes, indicating a set of orbitals that are lower in energy due to the crystal field splitting, while ( E_g ) represents a higher-energy set of orbitals in the same coordination.

Therefore, the correct response associates ( L = 2 ) with d-orbitals and gives the appropriate symmetry labels ( T_{2g} ) and ( E_g ) that identify how these orbitals interact within a given crystal field environment.

Understanding this classification is crucial for predicting the electronic structure and chemical behavior of transition metal complexes, which heavily rely on their d-orbitals.