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 Subshell  has three orbitals[px,py,pz]:

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 L and S.
  
  

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

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

  2. For the same S, maximum L
     
     

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

Orbital Symbols for L:

 L  =  0    S 

        =  1     P 

         =  2    D 

          = 3    F 

         = 4    G

Examples. Carbon (C) – 1s² 2s² 2p²

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

• L= ∣l1​−l2​∣,∣l1​−l2​∣+1,...,l1​+l2​

• Here:

• L = ∣1−1∣,   ∣1−1∣+1,    ...,   1+1  =  0,  1,  2

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

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

• Term symbol: 3P0^3P_0