Term symbol

Key takeaways

Term symbol belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Term symbol to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Term symbol from memory before moving on to harder problems.

Reference excerpt

In atomic physics, a term symbol is an abbreviated description of the spin, orbital and total angular momentum quantum numbers of the electrons in a multi-electron atom. So while the word symbol suggests otherwise, it represents an actual value of a physical quantity. For a given electron configuration of an atom, its state depends also on its total angular momentum, including spin and orbital components, which are specified by the term symbol. The usual atomic term symbols assume LS coupling (also known as Russell–Saunders coupling) in which the all-electron total quantum numbers for orbital (L), spin (S) and total (J) angular momenta are good quantum numbers. In the terminology of atomic spectroscopy, L and S together specify a term; L, S, and J specify a level; and L, S, J and the magnetic quantum number MJ specify a state. The conventional term symbol has the form 2S+1LJ, where J is written optionally in order to specify a level. L is written using spectroscopic notation: for example, it is written "S", "P", "D", or "F" to represent L = 0, 1, 2, or 3 respectively. For coupling schemes other that LS coupling, such as the jj coupling that applies to some heavy elements, other notations are used to specify the term. Term symbols apply to both neutral and charged atoms, and to their ground and excited states. Term symbols usually specify the total for all electrons in an atom, but are sometimes used to describe electrons in a given subshell or set of subshells, for example to describe each open subshell in an atom having more than one. The ground state term symbol for neutral atoms is described, in most cases, by Hund's rules. Neutral atoms of the chemical elements have the same term symbol for each column in the s-block and p-block elements, but differ in d-block and f-block elements where the ground-state electron configuration changes within a column, where exceptions to Hund's rules occur. Ground state term symbols for the chemical elements are given below. Term symbols are also used to describe angular momentum quantum numbers for atomic nuclei and for molecules. For molecular term symbols, Greek letters are used to designate the component of orbital angular momenta along the molecular axis. The use of the word term for an atom's electronic state is based on the Rydberg–Ritz combination principle, an empirical observation that the wavenumbers of spectral lines can be expressed as the difference of two terms. This was later summarized by the Bohr model, which identified the terms with quantized energy levels, and the spectral wavenumbers of these levels with photon energies. Tables of atomic energy levels identified by their term symbols are available for atoms and ions in ground and excited states from the National Institute of Standards and Technology (NIST).

Term symbols with LS coupling The usual atomic term symbols assume LS coupling (also known as Russell–Saunders coupling), in which the atom's total spin quantum number S and the total orbital angular momentum quantum number L are "good quantum numbers". (Russell–Saunders coupling is named after Henry Norris Russell and Frederick Albert Saunders, who described it in 1925). The spin-orbit interaction then couples the total spin and orbital moments to give the total electronic angular momentum quantum number J. Atomic states are then well described by term symbols of the form:

where

S is the total spin quantum number for the atom's electrons. The value 2S + 1 written in the term symbol is the spin multiplicity, which is the number of possible values of the spin magnetic quantum number MS for a given spin S. J is the total angular momentum quantum number for the atom's electrons. J has a value in the range from |L − S| to L + S. L is the total orbital quantum number in spectroscopic notation, in which the symbols for L are:

The orbital symbols S, P, D and F are derived from the characteristics of the spectroscopic lines corresponding to s, p, d, and f orbitals: sharp, principal, diffuse, and fundamental; the rest are named in alphabetical order from G onwards (omitting J, S and P). When used to describe electronic states of an atom, the term symbol is often written following the electron configuration. For example, 1s22s22p2 3P0 represents the ground state of a neutral carbon atom. The superscript 3 indicates that the spin multiplicity 2S + 1 is 3 (it is a triplet state), so S = 1; the letter "P" is spectroscopic notation for L = 1; and the subscript 0 is the value of J (in this case J = L − S). Small letters refer to individual orbitals or one-electron quantum numbers, whereas capital letters refer to many-electron states or their quantum numbers.

Terminology: terms, levels, and states For a given electron configuration,

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Term symbol

Start with the simplest possible case. Write down what Term symbol claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Term symbol before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Term symbol ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Term symbol

In research: Term symbol appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Term symbol in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Term symbol is common in secondary-school and first-year university syllabi. It links to neighbouring topics Atomic physics, Quantum chemistry, Theoretical chemistry, so understanding it makes those chapters shorter.
In everyday life: Look for Term symbol outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Term symbol in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Term symbol means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Term symbol out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Term symbol in simple terms?

In atomic physics, a term symbol is an abbreviated description of the spin, orbital and total angular momentum quantum numbers of the electrons in a multi-electron atom. So while the word symbol suggests otherwise, it represents an actual value of a physical quantity.

Why does Term symbol matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Term symbol?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Term symbol.