Question

Number of spin allowed transition(s) possible for \( d^2 \) octahedral configuration is .............

Hint:

In octahedral fields, spin-allowed transitions occur when electrons move between the \( t_{2g} \) and \( e_g \) orbitals. For \( d^2 \), this results in two possible transitions.

Answer 1

For the \( d^2 \) configuration in an octahedral field, the two electrons occupy the lower-energy \( t_{2g} \) orbitals. The spin-allowed transitions refer to the electron movement between the \( t_{2g} \) and \( e_g \) orbitals.
Step 1: Consider the possible transitions.
- The two electrons are in the \( t_{2g} \) orbitals, and they can transition to the \( e_g \) orbitals.
- For \( d^2 \), both electrons are in \( t_{2g} \), and they can each move to \( e_g \), leading to two spin-allowed transitions.
Step 2: Determine the number of transitions.
- Since the electrons are initially in the \( t_{2g} \) orbitals and can move to the \( e_g \) orbitals, the number of spin-allowed transitions is 2.
Final Answer: \[ \boxed{2} \]