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Derive the ground state free ion term symbol for the Ni2+ ion. How many microstates does the ground state contain
Accepted Answer
The ground state free ion term symbol for Ni2+ is 3F. Here's how to derive it:
1. Electronic Configuration: Ni2+ has an electronic configuration of [Ar] 3d8.
2. Hund's Rules: Apply Hund's rules to determine the ground state term symbol:
Rule 1: Maximize the total spin multiplicity (S). There are 4 unpaired electrons in the 3d orbitals, so S = 2.
Rule 2: Maximize the total orbital angular momentum (L). The 3d orbitals have l = 2. To maximize L, we fill the orbitals with the maximum possible ml values (2, 1, 0, -1, -2). This gives us L = 2 + 1 + 0 + (-1) + (-2) = 0. L = 0 corresponds to an S term.
Rule 3: For a subshell that is less than half-filled, the lowest energy state is the one with the lowest value of J (the total angular momentum). Since we have 4 unpaired electrons, J = |L - S| = |0 - 2| = 2.
3. Term Symbol: The term symbol is written as (2S+1)LJ. So, the ground state term symbol for Ni2+ is 3F2.
The ground state has a 21 microstates. To calculate the number of microstates, we use the formula (2S+1)(2L+1), which gives (2(2)+1)(2(3)+1) = 21.
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