Frequently Asked Question

The ground state free ion term symbol for a d³ electron configuration is indeed ⁴F. To determine the microstates associated with this term symbol, follow these steps:
1. Identify the possible values of L and S:
- For d³ configuration, the maximum value of L is 3 (when all three electrons are in different orbitals with parallel spins, giving L = 2 + 1 + 0 = 3, corresponding to F).
- The maximum value of S is 3/2 (when all three electrons have parallel spins, giving S = 1/2 + 1/2 + 1/2 = 3/2).
2. Calculate the possible values of J:
- J ranges from |L - S| to L + S. Therefore, for ⁴F, J can be 1/2, 3/2, 5/2, 7/2, 9/2.
3. Determine the microstates for each J value:
- You'll need to use Hund's rules and the appropriate quantum numbers (n, l, m_l, m_s) for each electron to determine the specific microstates for each J value. This process involves constructing microstate tables and applying the selection rules.
Example: For the ⁴F term symbol, the microstates corresponding to J = 9/2 would have the following spin configurations (using the m_l and m_s quantum numbers):
- (2, 1/2), (1, 1/2), (0, 1/2) (m_l = 3, S = 3/2)
- (2, 1/2), (1, 1/2), (0, -1/2) (m_l = 2, S = 1/2)
- (2, 1/2), (1, -1/2), (0, 1/2) (m_l = 1, S = 1/2)
- (2, -1/2), (1, 1/2), (0, 1/2) (m_l = 0, S = 1/2)
Note: This is a simplified explanation. Determining all microstates for a given term symbol can be complex and requires detailed knowledge of atomic spectroscopy and Hund's rules.