Term Symbol Calculator

In atomic spectroscopy, term symbols provide a concise notation for an atom's electronic state. They are generally expressed in the form ^2S+1L_J, where:

• \(S\) is the total spin quantum number (and the multiplicity is \(2S+1\)),
• \(L\) is the total orbital angular momentum quantum number, represented by a letter (0 = S, 1 = P, 2 = D, 3 = F, etc.),
• \(J\) is the total angular momentum, which can range from \(|L-S|\) to \(L+S\) in steps of 1.

For example, if \(S = 2\) (multiplicity \(2(2)+1=5\)), \(L = 1\) (P), and \(J = 2\), the term symbol is ⁵P₂. (For more details, see the Wikipedia Term Symbol page.)

Scientific Explanation

Term symbols encapsulate an atom’s electronic configuration by specifying the total spin and orbital angular momentum. The term symbol is written as ^2S+1L_J, where:

• \(2S+1\) (the multiplicity) indicates the number of possible spin states,
• \(L\) is expressed as a letter corresponding to the orbital angular momentum quantum number (0 = S, 1 = P, 2 = D, 3 = F, etc.),
• \(J\) is the total angular momentum, which is determined by the vector coupling of \(L\) and \(S\). In LS coupling, the allowed values of \(J\) range from \(|L-S|\) to \(L+S\) in integer steps.

This calculator updates the term symbol dynamically as you adjust the total spin \(S\), orbital angular momentum \(L\), and total angular momentum \(J\).