Term Symbol  

The term symbol is a shorthand notation used in atomic spectroscopy to represent the electronic state of an atom or ion, accounting for the total spin, orbital angular momentum, and total angular momentum of electrons.

 General Form of a Term Symbol:

2S+1LJ

Where:

• S = total spin quantum number

• L = total orbital angular momentum (represented by letters: S, P, D, F, G, ...)

• J = total angular momentum quantum number
  
  

Steps to Determine Term Symbol: Let’s take it step by step using Hund's rules and electronic configurations.

Step 1: Determine the Electron Configuration

Especially the valence electrons (those in unfilled subshells).

Step 2: Determine All Possible Microstates & Term Symbols

🧩 What are Microstates?

 A microstate is a unique arrangement of electrons in orbitals, defined by their:

• magnetic quantum number (ml) – related to orbital angular momentum

• spin quantum number (ms​) – related to electron spin

For a given configuration (like p2, d3, etc.), each electron can occupy different combinations of ml and ms. The total number of such combinations gives the total microstates.

 Example: p² configuration (e.g., carbon)

• A p orbital has three sub-orbitals:

ml = −1, 0, +1

• Each can hold one or two electrons with spins:

ms = +1/2, −1/2

 Step 2: Count Possible Microstates

• Use Russell-Saunders (LS) coupling to determine all combinations of LL and SS.
  
  

• Apply Hund’s Rules to identify the ground state:
  
  

  1. Maximum multiplicity (2S+1) → largest spin SS
     
     

  2. For same SS, maximum LL
     
     

  3. For < half-filled shell: lowest JJ; > half-filled: highest JJ
     
     

🔷 Orbital Symbols for LL:

L

Letter

0

S

1

P

2

D

3

F

4

G

🔷 Examples:

1. Carbon (C) – 1s² 2s² 2p²

• Only 2p² electrons are considered (2 electrons in p-orbitals → l = 1)
  
  

• Max S=1S = 1, L=1L = 1 (triplet P: 3P^3P), possible J=2,1,0J = 2,1,0
  
  

• Apply Hund’s Rule: Less than half-filled → lowest JJ
  
  

• Term symbol: 3P0^3P_0
  
  

2. d⁵ Configuration (e.g., Mn²⁺)

• Max spin: all unpaired → S=52S = \frac{5}{2}
  
  

• L=0L = 0 (since d orbitals' ml values cancel)
  
  

• Term symbol: 6S5/2^6S_{5/2}
  
  

3. d⁷ Configuration (e.g., Co²⁺)

• Consider pairing and microstates
  
  

• Ground state term symbol is 4F9/2^4F_{9/2}
  
  

🔶 Shortcuts for Common Configurations (Ground States Only):

Configuration

Term Symbol

p¹

2P1/2^2P_{1/2}

p²

3P0^3P_0

p⁵

2P3/2^2P_{3/2}

d¹

2D3/2^2D_{3/2}

d²

3F2^3F_2

d³

4F3/2^4F_{3/2}

d⁵

6S5/2^6S_{5/2}

d⁶

5D0^5D_0

d⁷

4F9/2^4F_{9/2}

d⁸

3F4^3F_4

f¹

2F5/2^2F_{5/2}

f³

4I9/2^4I_{9/2}

f⁷

8S7/2^8S_{7/2}

Let me know if you’d like a specific element or ion’s term symbol explained in detail.