To find term symbols in chemistry (especially for atoms and ions), you follow a systematic procedure based on the quantum numbers of the electrons in the given electron configuration. Term symbols give information about the total spin, total orbital angular momentum, and total angular momentum of the electrons. Here's the step-by-step procedure:

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Procedure to Find Term Symbols:

Step 1: Write the Electron Configuration

Start with the electron configuration of the atom/ion, especially focusing on the partially filled subshell (s, p, d, or f) since closed subshells do not contribute to the term symbol.

Step 2: Determine All Possible Microstates

Calculate all possible combinations of the electrons' quantum numbers:

ml (magnetic quantum number): ranges from −l to +l

ms (spin quantum number): ±½

Generate all possible microstates (combinations of ml and ms) for the given number of electrons in the subshell.

Step 3: Determine the Maximum Values of L and S

From all microstates:

S = total spin angular momentum = ½ × (number of unpaired electrons)

L = total orbital angular momentum = sum of individual ml values

Convert L into spectroscopic notation:

L = 0 → S

L = 1 → P

L = 2 → D

L = 3 → F

L = 4 → G

etc.

Step 4: Calculate the Term Symbol

Use the notation:

(2S + 1)L

(2S + 1) is the multiplicity, indicating the number of spin states.

L is the spectroscopic term symbol (S, P, D, F, etc.)

This gives the basic term symbol without J.

Step 5: Determine the Possible J Values

Use:

J = L + S, L + S − 1, ..., |L − S|

For less than half-filled subshells, the lowest J is the ground state.

For more than half-filled subshells, the highest J is the ground state.

Step 6: Select the Ground State Term Symbol (Hund’s Rules)

Apply Hund's rules:

1. Maximum multiplicity (i.e., highest S) = lower energy

2. For same multiplicity, higher L = lower energy

3. For subshell less than half-filled → lowest J is most stable;

for more than half-filled → highest J is most stable.

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Example: Find Term Symbol for Carbon (1s² 2s² 2p²)

Focus on 2p² (2 electrons in p orbitals, l = 1)

Possible values of ml = −1, 0, +1; ms = ±½

After evaluating all microstates:

Highest S = 1 → multiplicity = 3

Highest L = 1 → P

So the terms are: ³P, ¹D, ¹S

Apply Hund's rules:

Highest multiplicity → ³P

Then for ³P → S = 1, L = 1 → J = 2, 1, 0

Ground state term symbol = ³P₀